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This is to certify that the

dissertation entitled

Two-photon Spectroscopy of Quadruply Bonded Metal Dimers:

An Investigation of Zwitterionic Excited States

presented by

Daniel Scott Engebretson

has been accepted towards fulfillment
of the requirements for

MS Chemistry

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6/01 c:/CIRC/DateDue.p65cp.15

TWO-PHOTON SPECTROSCOPY OF QUADRUPLY BONDED METAL DIMERS:
AN INVESTIGATION OF ZWITTERIONIC EXCITED STATES

By

Daniel Scott Engebretson

A Thesis

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Chemistry

1998

ABSTRACT

TWO-PHOTON SPECTROSCOPY OF QUADRUPLY BONDED METAL DIMERS:
AN INVESTIGATION OF ZWITTERIONIC EXCITED STATES

By

Daniel Scott Engebretson

Two electrons in two weakly coupled orbitals give rise to two states (diradical)
with electrons residing in separate orbitals and two states (zwitterionic) with both
electrons paired in one orbital or the other. This two-center, two-electron state manifold
has eluded experimental confirmation because the zwitterionic states have been difficult
to locate. Two-photon excitation of fluorescence of quadruply bonded metal dimers has
been utilized to reveal the zwitterionic nature of the Singlet excited states of the
5-manifold. The assignment of the band observed in the two-photon fluorescence
excitation spectra to the hidden zwitterionic state (2'A1g) has been aided by measuring
the quadratic dependence of the fluorescence on the incident laser intensity and
measuring the relative intensity when two circularly polarized photons are used as

compared to two linearly polarized photons.

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. iv
LIST OF FIGURES ............................................................................................................. v
Chapter I .............................................................................................................................. 1
Introduction ..................................................................................................................... 1
LA. Electronic Structure of Quadruply Bonded Metal-Metal Complexes ...................... 2
LB. Electronic Spectroscopy of Quadruply Bonded Metal-Metal Complexes ............. 12
LB]. M02X4(PR3)4 Complexes .................................................................................... 14
I.B.2. cis-M02C12(mhp)2(PMe2Ph)2 Complexes ........................................................... 17
LC. Two Photon Spectroscopy ...................................................................................... 20
LC. 1. Selection Rules .................................................................................................... 26
I.C.2. Power Dependence .............................................................................................. 29
I.C.3. Polarization Dependence ..................................................................................... 30
ID. Motivation .............................................................................................................. 33
Chapter II ........................................................................................................................... 38
Experimental ................................................................................................................. 38
ILA. Two-Photon Techniques ...................................................................................... 38
DB. Materials and Instrumentation ............................................................................. 40
DC. Two-Photon Excitation Measurement ................................................................. 42
DD. Power Dependence Measurements ...................................................................... 45
DE. Polarization Control and Polarization Ratio Measurement ................................... 47
Chapter III ......................................................................................................................... 50
Results and Discussion .................................................................................................. 50
Appendix I ......................................................................................................................... 68
References ......................................................................................................................... 71

iii

LIST OF TABLES

Table 1.1. Comparison of the 1(5 -> 5*) excitation energy and 2(8 —-> 5*) excitation
energy and bond length changes for some selected quadruply bonded dimers and
their one-electron oxidized counterparts. Values were obtained from reference 10,

except for the M02[OZP(OC6H5)2]4+/° pair which was obtained from Chang, I. 1.;
Nocera, D. G., Inorg. Chem, 1989, 28, 4309. ............................................................ 5

Table 1.2. Values for the polarization functions F,G, and H, depending on the eight
polarization cases. From References 37 and 39. ...................................................... 32

Table 1.3. Two-photon tensor patterns and the polarization ratio (0) expected for each
transition in the D2d and D4,1 point groups. From References 37, 39, and 41. ........ 34

Table 111.1. Selected singlet state energies for the RezClgz' anion. From Reference 5.. 60

Table 111.2. There are twelve metal-based transitions which satisfy the criteria of an A1
excited state and an A1 ground state. The four transitions listed are expected to

occur in the near UV or visible region of the spectrum. The remaining eight
transitions involve either the 0' or 0* orbitals and should not occur in the near UV or
visible region of the spectrum. .................................................................................. 62

Table 111.3. Four possible two-photon transitions, their symmetry and the expected
polarization ratio, 0. ................................................................................................. 64

Table 111.4. Comparison of the 21A]g - 1A2u energy gap as determined by two-photon

spectroscopy with the 3A2u — 1A1 g energy gap as measured by Cotton in Reference
50. .............................................................................................................................. 65

iv

LIST OF FIGURES

Figure 1.1. The Molecular Orbital Diagram for the formation of M2L8 from two ML4
fragments. .................................................................................................................... 3

Figure 1.2. Qualitative comparison of the energies obtained from the molecular orbital
(MO) model, the valence bond (VB) model, and a realistic Morse type potential.
These energies are representative of those obtained for the hydrogen molecule in
Reference 20 ................................................................................................................ 9

Figure 1.3. Behavior of the electronic states of the 8-manifold as a function of orbital
overlap (S) or internuclear separation (R). ................................................................ 13

Figure 1.4. Molecular orbital correlation diagram between D4,, and Du symmetries. 15

 

Figure 1.5. Solution phase (3-methylpentane) electronic absorption ( ) and emission
( ------ ) spectra of M02C14(PMe3)4 ............................................................................. 16

Figure 1.6. Fluorescence excitation spectrum of MozCl4(PMe3)4 in 3-methylpentane... l8

 

Figure 1.7. Fluorescence excitation ( ) and emission ( ------ ) spectra of cis-
M02C12(mhp)2(PM62Ph)2 .......................................................................................... 1 9

Figure 1.8. The effect of refractive index on an oscillating electric field propagating in
the z direction. b is the sample thickness. ................................................................ 22

Figure 1.9. Second Harmonic Generation. Two electric fields are mixed through the
second order susceptibility tensor, x9), to produce a third electric field. ................. 25

Figure 1.10. Sum Frequency Generation (SFG). Three electric fields are mixed through
the third order susceptibility tensor, x“), to produce a fourth electric field .............. 27

Figure 1.11. Two examples of nonlinear spectroscopy. (a) Two-photon absorption
(TPA) spectroscopy and (b) coherent anti-Stokes Raman spectroscopy (CARS). 28

Figure 1.12. (a) Transient absorption spectra of W2Cl4(dppm)2 recorded 100 ns (solid
squares) and 4 us (open circles) after 532 nm, 10 ns excitation. (b) Absorption
spectra of W2Cl6(PEt3)4 ( ----- ) and W2C16(dppm)2 (—) in toluene and CHZCIZ
repectively. Data from Reference 43. ....................................................................... 36

Figure 11.1. Multiphoton ionization techniques. Left, two photons simultaneously
absorbed through a nonresonant virtual state to the ionization continuum (2 PI).
Right, two photon simultaneously absorbed to create a "final" state, which then
absorbs a third photon to the ionization continuum (2+1 PI). ................................... 39

Figure 11.2. Two-photon excitation spectroscopy. Two-photons are simultaneously
absorbed to create an excited state, which then decays to an emissive state of lower
energy. ....................................................................................................................... 41

Figure 11.3. Block diagram of the instrument used to collect two-photon excitation
spectra. SHG second harmonic generator, PDL pulsed dye laser. GL Glan-Laser
polarizer DFR double Fresnel Rhomb, SFR single Fresnel Rhomb. L1 and L2
collection lenses. PMT photomultiplier tube. Amp. Lecroy amplifier, Disc.
Phillips Scientific Window discriminator, PC personal computer. ........................... 43

Figure 11.4. Tuning curves for the laser dyes and dye combinations used: LDS 750
(solid circles), LDS 765 (open squares), LDS 765/LDS 821 (solid diamonds), LDS
821 ("x"), LDS 821/LDS 867 ("+"), LDS 867 (open triangles), LDS 867/LDS 925
(open diamonds), and LDS 925 (solid squares) ........................................................ 44

Figure 11.5. Wavelength response function for the silicon photodiode used to measure
the relative laser power .............................................................................................. 46

Figure 11.6. Experimental determination of the polarization state. GL Glan-Laser
polarizer, DFR double (Fresnel Rhomb, SFR single Fresnel rhomb. H horizontal
polarization, V vertical polarization, C circular polarization, C’ circular polarization
in the opposite sense to C .......................................................................................... 48

Figure 111.1. Energies of 3A2u (solid squares), 1A2u (solid triangles) and the difference of
the two energies (solid circles). Data from Reference 50 ........................................ 53

Figure 111.2. One- (—) (Ame= 546 nm) and Two-photon (solid circles) (Aexfi 860 nm)
excited emission spectra of M02C14(PMe3)4 ............................................................. 54

Figure 111.3. One- ( ) (Aexfi 546 nm) and Two-photon (solid circles) (ken: 860 nm)
excited emission spectra of cis-M02C12(mhp)2(PMe2Ph)2 ....................................... 55

 

Figure 111.4. Power Dependence plot for M02C14(PMe3)4. The instrument was
configured for vertically polarized light and Aexc = 860 nm. Power depencences

were taken at 10 nm intervals using both polarizations, across the spectral range
scanned and similar results were obtained for each. ................................................. 56

Figure 111.5. Power Dependence plot for cis-M02C12(mhp)2(PMe2Ph)2. The instrument
was configured for vertically polarized light and Acxc = 840 nm. Power depencences

were taken at 10 nm intervals using both polarizations, across the spectral range
scanned and similar results were obtained for each. ................................................. 57

 

Figure 111.6. One- ( ----- ) and Two-photon ( ) fluorescence excitation spectrum of
MozCl4(PMe3)4 in 3-methylpentane. ........................................................................ 58

Figure 111.7. Polarization ratio , Q, for M02C14(PMe3)4. ................................................ 61

vi

 

Figure 111.8. One- ( ----- ) and two-photon( ) fluorescence excitation spectrum of cis-
MozClz(mhp)2(PMe2Ph)2 in benzene. ....................................................................... 66

Figure 111.9. Polarization ratio, (2, for cis-M02C12(mhp)2(PMe2Ph)4 ............................. 67

vii

Chapter I

Introduction

The 5 bond has been an enigma since its discovery in 1964 with the preparation
and characterization of the octachlorodirhenate ion, R32C182—.l The electronic
configuration was proposed by Cotton to be 021:452, implying a sigma bond, two pi bonds
and a delta bond between the two rhenium atoms. This configuration explained the
observed diarnagnetism and the short metal-metal bond distance, as well as the eclipsed
geometry of the Cl" ligands that was determined in the crystal structure of
KzRezCls-HZO. Although the existence of the 8 bond was questioned years thereafter,
the spectroscopy and calculations of the 705 and 803 confirmed its existence.

The spectroscopic work was pioneered by Cowman and Gray’s polarized electronic
absorption spectroscopy of single crystal R62C182—.2 This study revealed the lowest
energy transition to be polarized along the Re—Re internuclear axis (z-polarized), and a
progression with a spacing of 248 cm‘1 was consistent with the ground state metal-metal
stretching frequency of 274 cm“1 reported in early Raman work.3 These observations led

to an assignment of the absorption as the 52-9188“ (1(6 -—) 8*)) transition. Early

calculations performed on quadruply bonded dimers were tenuous at best. Calculations
carried out by Benard indicated that the R32C182_ anion should possess a staggered D4,,
geometry and that this conformation would be 60 kcal/mole more stable than the
experimentally observed eclipsed D4}1 structure.4 Furthermore, these calculations
indicated that the ground state of the molecule would be a paramagnetic triplet state, in
contrast to the observed diamagnetism. As computers became more powerful, it became
possible to expand the basis set for the calculations to include multiconfigurational
interactions. Taking advantage of this, Hay was able to perform calculations on Re2C182‘
that qualitatively agreed with experimental observations.5 While these calculations
differed from experiment in some respects, such as the 1(5 —-) 8*) excitation energy
(calculated = 23,000 - 30,500 cm‘l; observed = 14,500 cm'l), they did result in the proper

geometry (D4,) and electronic configuration 621:482.

1.A. Electronic Structure of Quadruply Bonded Metal-Metal Complexes

The 8 bond, a feature unique to quadruply bonded metal-metal (M—4— M) dimers,
is formed by the overlap of two atomic dxy orbitals on adjacent metals as shown in the
molecular orbital diagram (Figure 1.1). Even though the metal centers are very close to
one another (~2.2 A),6 there is very little overlap of the parent dxy orbitals owing to their
parallel disposition.7 This leads to a very weak bond, as was encountered early in the
study of these systems.

The weakness of the 8 bond was first recognized in the spectroscopy of RezClsz'.7
While the 1A2u (— lAlg l(8 ——) 5*) transition is dipole and spin allowed, it is quite weak
(5:max = 1530 M‘lcm'l). Generally, one electron charge transfer transitions such as this
give rise to very intense absorptions (emax a 15000 M'lcm").8 It has been shown by
Mulliken, however, that charge transfer transitions become less intense as the coupling

between the parent atomic orbitals becomes weak.8 The parameter that governs the

 

 

 

 

\
\
I
M-L 6* -4”- 0* D2”) is“ M-L 6*
-=<::_4_‘_ _L__::>=—
d ny 2 I; 19 “\ d ny 2
I, \\
I, * \
x 7‘ aeae— ~ .
’ I (69) \\ \t
I ’l \ \
I \\ \
I \

 

,dZZ \:::: fl l,’ I’dxy,d22
’ dYZ ‘\\\\:\\\ :(b29)x 2 :51, dXZ'de

Figure 1.1. The Molecular Orbital Diagram for the formation of M2L8 from two ML4
fi‘agments.

intensity of a transition is the oscillator strength, f, which is related to the orbital overlap
(and hence the bond strength):
f=1.096x10ll vsz r2 (1.1)

where V is the transition energy (cm‘I), S is the overlap of the parent atomic orbitals, and
r is the internuclear separation. For the 1(5 —-) 5*) transition for RezClsz’, f = 0.023.
When the internuclear separation, determined by X-ray crystallography, is substituted
into Equation 1.1, S is determined to be ~ 0.1.7

The weakness of the 5 bond is further supported by the spectroscopy of the one
electron oxidized or reduced congeners of quadruply bonded molecules. In these
molecules, the ground state electronic configuration is 0'21t45l or 621:4525", which leads
to a formal bond order of 3.5. Despite the difference in ground state electronic
configuration, however, the structural parameters, including the internuclear separation
and hence the orbital overlap, remain quite constant, with typical bond length changes on
the order of 0.05A for each 5 electron removed or added.9 In the oxidized species, where
there is only a single electron in the 5 orbital, there are no two-electron energies such as
electron correlation energy. Because of this, the one electron 2(5 -> 5*) transition
between the 5 and 5* molecular orbitals provides a direct measure of the 5 bond
strength.10 The situation is similar for the reduced species.10 The 2(5 —> 5*) transition
for a number of these oxidized and reduced molecules have been measured; they are
collected, along with the 1(5 -) 5*) transitions of their quadruply bonded counterparts
and bond length change, in Table 1.1. It can be seen that most of the 2(5 -—) 5*)
transitions occur between 1400 nm and 1600 nm (7,000 cm'1 and 6,000 cm"). This
indicates that the 5 bond is very weak when compared to typical sigma and pi bonds
(15,000 cm'1 to 30,000 cm").11 A few of the tabulated molecules have a 2(5 -9 5*)
transition somewhat higher in energy, but the 1(5 -—> 5*) transition energy of their

quadruply bonded counterparts is also higher in energy.

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Electrons that reside in weakly coupled orbitals have been a point of theoretical
interest for several decades. The two classic examples are the stretched hydrogen
molecule and the twisted ethylene molecule. The case of stretched hydrogen was first
investigated by Mulliken in his explanation of the electronic spectra of homonuclear
diatomic molecules.12 Later, the stretched hydrogen molecule gained considerable
attention when it was investigated by Coulson and F ischer.l3 At dihydrogen's
equilibrium geometry there is very good overlap of the hydrogen atomic orbitals.
However, as the bond is stretched from its equilibrium position the overlap of the atomic
orbitals decreases. As the atomic orbitals become more weakly coupled, they can no
longer be properly interpreted as a molecular orbital. For twisted ethylene, also proposed
by Mulliken,l4 and popularized by Salem and Two,” the situation is very similar. As
one side of the molecule is twisted with respect to the other, the overlap of the atomic p
orbitals that form the 1: bond decreases (the bond is firlly ruptured at a twist angle of 90°). .
For both of these cases, the four electronic states that arise (three singlet states and a
triplet state) from two electrons in two orbitals can be represented as a pair of diradical
states and a pair of zwitterionic states. The diradical like states are the fully occupied
bonding orbital and the triplet state with one electron in the bonding orbital and one in the
antibonding orbital with their spins parallel. The zwitterionic states consist of the singlet
state with one electron in the bonding orbital and one in the antibonding orbital with their
spins antiparallel and the doubly occupied antibonding orbital. While no direct evidence
for this manifold has been provided for hydrogen, this manifold has been observed in the
photoreactions of substituted ethylenes and other alkenes that undergo cis-trans
isomerization.16 The first spectroscopic evidence for the existence of twisted ethylene
was provided by Ziegler and Hudson in their resonance Raman study of ethylene.17
Recently, as pulsed lasers have become faster, there has been a resurgence in the effort to

quantitate the excited states of twisted ethylene and some indirect spectroscopic evidence

for the existence of ionic excited states has been obtained from time-resolved
spectroscopy. '8

Due to the poor coupling of the atomic orbitals that form the 5 bond, it too can be
represented with the same collection of electronic states. It is quite ironic that a similar
situation exists in inorganic chemistry, and even more that it exists in quadruply bonded
metal dimers that possess the shortest bonds in inorganic chemistry.

In order to better understand the electronic states of the 5 manifold (and, for that
matter, the n: manifold for twisted ethylene and the 0' manifold for stretched hydrogen), it
is useful to investigate the two limits of bond formation. At one extreme, where the
atomic orbitals are strongly overlapped, the molecular orbital model is valid. At the other
extreme, the weak coupling limit, the valence bond model is preferred. The inadequacy
of the molecular orbital model is revealed when the 5 bonds are derived. In the
molecular orbital model, the orbitals are written as a linear combination of atomic orbitals
(LCAO-MO). The simple linear combinations of atomic dxy orbitals on metals A and B

are:19

59k... (A)+dxy (3)155 am
5241., (AHxy (B)J56* (1.21»

The doubly occupied ground state (52) and excited state (5*2) are then given by:
2 covalent terms
a. = [as (An... (BM... (3»... on]
ionic terms 2
'1'[dxy(Aflxy(‘6‘)i'dxy(B)ixy(B)]E 8MO (133)

62=[d.,(A)d..iiiiiiI§(B)d.,(B)]
[a(an.§°iii'la?‘:'iA)a.,<B)]ss;§o (Lab)

It can readily be seen that the molecular orbital model predicts an equal probability for
the electrons to be associated with separate atoms as it does for the electrons to be near
the same atom.20 A direct consequence of this is that upon dissociation the fragments are
as likely to be neutral as ionic.

The valence bond (VB) model represents the opposite extreme in bond formation.
In this model, the electrons are assumed to remain associated with their "correct" nucleus,

the result of this is a purely covalent description of the bond:
612:dxy (Aflxy (B)+dxy (thy (A #8318 (1-4)

When the energies of the two extremes (LCAO-MO and VB) are plotted as a function of
internuclear separation, R (or orbital overlap, S), and compared with a realistic Morse
type potential (Figure 1.3), the difference between the two models becomes obvious. The
LCAO-MO method is a sound approximation when the parent orbitals are strongly
coupled at short R or large S. However, as the bond is broken, the orbitals become
weakly coupled and the LCAO method fails to predict the proper dissociation energy
because the molecule has an equal probability of forming ions as compared to neutrals.
The VB model, on the other hand, properly predicts the dissociation of the molecule to
neutrals in the weak coupling limit since it assumes the electrons remain associated with
a particular nucleus, but fails to properly predict the energy when the orbitals are strongly
coupled because it ignores the favorable attraction between ions.

These two methods do converge. In the valence bond model this is done by

allowing a certain amount of ionic character to be built into the wavefunction:19

6i=dxy (Md.y (B)+«i,.y(B)dxy (A)
Mid.y (Add.y (AM.y (1nd,.y (8)12 52 (1.5)

where A is referred to as the ionicity. The LCAO-MO model requires a more subtle

approach.19 To do this, the states that arise from placing two electrons into two orbitals

MO

 

L--- _ ------------------- - --

Energy

 

 

Internuclear Separation

Figure 1.2. Qualitative comparison of the energies obtained from the molecular orbital
(MO) model, the valence bond (VB) model, and a realistic Morse type potential. These
energies are representative of those obtained for the hydrogen molecule in Reference 20

must be considered. There are four possible states to be considered, along with their
symmetries (in the D411 point group). The first is the doubly occupied ground state 52
(Alg). Two states can be formed by the promotion of one electron to the antibonding
orbital, 355* and 155* (“A2“). The fourth state is the doubly occupied antibonding state
5'”2 (2'A1g). The wavefimctions for each of these states, including their spin functions
(ignoring normalization) are:21

52 =51 (1)51 (”11152-51012 i”- lAlg (115a)

355‘ ={81(1»2(2)'82(1»l(2)}E1152+B1a2}13A2u (I-Gb)

155. ={51(1)52(2)+52(1)51 (2)]{0‘1132—1310‘2VA2‘1 (L66)

8“2:52 (152(2)i0‘1132‘i310‘2}21Aig (1-6d)

where l and 2 are electron labels, or and B are spin functions for the electrons and 5, and
52 represent the bonding molecular orbital and antibonding molecular orbital described
by the LCAO model above (Equations 1.2a and 1.2b).

To adjust the LCAO model to more correctly describe the actual system, the
interaction between states of the same symmetry must be considered (so-called
configuration interaction (C1)). The effect of configuration interaction can be seen by
allowing the Hamiltonian, which is a totally symmetric function (A,g in the D4,, point
group), to act on the states of like symmetry (the two ‘Alg states). The matrix elements
for this interaction are given by (‘Alg i H i 21A]g = 1A] g. This interaction between the
states is repulsive and forms the basis for the non-crossing rule of states of like
symmetry.19 As a result, the doubly occupied ground state wavefunction (52) and excited
state wave function (5”) are better represented by:

'.«x,g=c,5"-+c',5’2 (1.7a)
2'.4>.,g=c252+c'225"2 (1.7b)

where Ci and Ci’ are coefficients which represent the weighting of each wavefunction (C,2

+ Ci'z = 1). As Ci approaches Ci' (= lNZ) the wavefunctions become those given in the

10

LCAO model. This representation can be easily interpreted in the VB picture also; then
C, represents the covalent character of the ground state and Cl' represents the ionic
character. With these wave functions, it is possible to determine the relative energy of
each state in the 5 manifold.

The Hamiltonian for the total energy of the system (HT) consists of a Hamiltonian
for each of the electrons (11(1) and 11(2)) and a l/rlz operator that describes the

interactions (electron correlation effects) between the two electrons:22

HT=H(‘)+H(2)+—l— (1.8)
l' 12

where H“) takes the form of a typical one electron Hamiltonian:19

2
HG)=- [Livzw (1.9)

2m
‘1

and V is the potential energy for the interaction between the electron and the nucleus.
HT can be employed to calculate the energies of each of the states (including
configuration interaction). The energies of the states (for a complete derivation, see

Appendix I) are given by:‘0

E82£12{2w1+111}‘-C1C1K12 (1.103)
E388O=W1+W2+J12—K12 (1.101))
E1580 =W1+W2+J12+K12 (LIOC)

135.2 =c§ {2W2+122 }+c,c',r<l, (1. 10d)

where W, represents the energy of an electron in orbital i (the one-electron energy of the
orbital). 16 is the Coulomb repulsion of two electrons in the same orbital (i = j) or two
electrons in different orbitals (i at j). K12 is the exchange energy, and is a measure of the
energy required to move an electron from one metal center to another.

If there is no overlap of atomic orbitals (complete neglect of differential overlap

(CNDO) approximation), then I H = .122 = J12. This allows the J terms to be neglected as a

ll

constant offset in energy. Taking the average energy of the molecular orbitals (5 and 5*)
as a reference point (l/2{Wl + W2} = O), and setting AW = W2 - W, simplifies the
energy expressions a great deal:

155, =- #1922.»sz (1.1 la)

E355.=— K,2 (I.l]b)
E1680=+K12 (1.110)

138.2 =+,/1<,22+Aw2 (1.1 1d)

These energies are plotted as a fimction of internuclear separation (or orbital overlap) in
Figure 1.3.10 The left side of the figure represents a typical bonding situation where there
is a great deal of overlap of the atomic orbitals, leading to AW >> K. The exchange
energy can be ignored in this situation and the total energy is approximated by sum of the
one-electron energies. In other words, the energy is given by the LCAO model. It should
be mentioned, however, that at this limit, the CNDO approximation is less valid so the
electronic states are not necessarily symmetrically disposed. The right side represents the
opposite extreme. There is very little overlap of the atomic orbitals that results in AW ~
0, and K, the two-electron exchange energy, dominates the energy. At this extreme, the
ground state is described by a purely covalent wavefunction, and the doubly excited state

by a purely ionic wavefunction.

1.B. Electronic Spectroscopy of Quadruply Bonded Metal-Metal Complexes

The most studied transition of quadruply bonded metal (M—i— M) dimers is the
l52 —) 155* ('(5 ——) 5*)) transition. This transition has provided the basis for using the
VB approach to interpret the electronic states of the 5 manifold. The paradigm system, as
mentioned in the Introduction (LA), is Re2C132'. There are, however, many compounds
that contain quadruple bonds. One particular class of compounds, those with the
empirical formula M2X4L4 (M = M0 or W; X = Cl, Br, or I, and L = monodentate P or As

12

18*2

 

 

 

 

 

 

 

 

 

 

 

Zwitterionic
“ /‘
155* A
>.
8’
g 2(K2‘1" Aw2)l/2 2K
LL}
3 *
as f ,
l \
Covalent
182
R(M2) >
< S

 

Figure 1.3. Behavior of the electronic states of the 5-manifold as a function of orbital
overlap (S) or internuclear separation (R).

13

ligand), has also been studied a great deal. Although these molecules are not as highly
symmetric as RezClgz‘ (D4h), the reduction in symmetry to DZd, while it has some effect
on the MO diagram (Figure 1.4), has no effect on the resultant energies of the electronic

states of the 5 manifold.

1.13.1. M02X4(PR3)4 Complexes

Of particular interest, in the context of this thesis, is the molecule in which X = Cl
and R = Me. There are three prominent bands in the absorption spectrum of
MozCl4(PMe3)4 (Figure 1.5). Each of the bands has been assigned in the literature”,24
using polarized, single crystal spectroscopy. The highest energy band (Amax = 325 nm,
sum = 3720), is very strongly polarized perpendicular to the Mo—4— Mo (2) axis.24
When the crystal is irradiated parallel to the axis at low temperatures the intensity of this
band is very weak, which indicates the parallel component is possibly due to vibronic
coupling. The strong perpendicular component is consistent with the band being
assigned as the ligand-to-metal charge transfer (LMCT), 0(MP) —) 5‘”.24 Here MP
indicates association with the phosphine ligand. The next band is quite weak (27m = 435
nm, em = 210).24 The absorption appears in both parallel and perpendicular
polarizations; however, the temperature dependence of the band is significantly different
in each polarization. Under perpendicular polarization, the band sharpens and its
intensity increases as the sample is cooled, which indicates the transition is dipole
allowed. In parallel polarization, however, the intensity decreases with decreasing
temperature suggesting the parallel component is vibronically induced. Since the
perpendicular component is dipole allowed, the likely assignment of this absorption is
metal-to-metal charge transfer (MMCT) l(11: —) 5*);24 the low intensity is attributable to
the fact that this transition correlates with a dipole forbidden transition in D4,1
symmetry.24 The lowest energy band (1mm, = 585 nm, em = 3110) is almost exclusively

parallel polarized.24 The ratio of the intensity of the parallel component to the

14

 

 

Cg — 15* 71* — C
b)“ _ 5* 8* — 32
b28 — 5 8 _ bl
— —
en — 1t 1t _ e
alg 0' 0 al
D4}, DZd

Figure 1.4. Molecular orbital correlation diagram between D4,1 and D2d symmetries.

l5

 

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perpendicular component is nearly 100. At low temperature, the perpendicular

2" consistent with the excited state

component progresses with a spacing of ~340 cm‘l,
v1(Moz) stretch (ground state v1(Moz) = 355 cm“),23 leading to the assignment of this
band as the MMCT 1(5 —> 5*).24

As shown in Figure 1.5, MozCl4(PMe3)4 is emissive (Xmfim = 673 um; I = 140
ns in 2-methylpentane, ¢em = 0.26)?5 Since the emission spectrum overlaps with the
1(5 —-> 5*) absorption band, it is apparent that the fluorescence originates from the ‘55*
state.25 This is further supported by low temperature emission studies of the molecule
dissolved in a 2-methylpentane glass. The band progresses with a spacing of 335 cm",
consistent with the ground state v1(M02). Fluorescence excitation spectroscopy has also
been performed on this molecule26 and the excitation spectrum is shown in Figure 1.6.
The bands in the excitation spectrum mirror those in the absorption spectrum (since all of

the bands in the absorption spectrum populate the 5* orbital), and are assigned to the

same states.

1.B.2. cis-MozClz(mhp)2(PMe2Ph)2 Complexes

Replacement of two Cl's and two PMe3s in MozCl4(PMe3)4 with two bidentate
mhp ligands (mhp = deprotonated 6-methyl-2-hydroxypyridine) also produces very
emissive complexes (Amamm = 602 nm; 1: = 45 us in n-hexane;27 (Dem = 0.228). The
excitation and emission spectra of cis-M02C12(mhp)2(PMe2Ph)2 [PMezPh =
dimethylphenylphosphine] are shown in Figure 1.7. This molecule is not as symmetric as
M02C14(PMe3)4 (C2 vs. DZd), which makes spectroscopic assignment more difficult since
transitions are more readily vibronically induced. The spectroscopy of this compound
has not been rigorously investigated. However, by comparison with the absorption and
emission spectra of the closely related molecules M02C12(mhp)2(PEt2Ph)2,29
M02(mhp)430 and M02C14(PMe3)4,23’24 which have been reported in the literature,

reasonable assignments can be made. The maximum in the excitation spectrum at 550

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nm is assigned as 1(5 —> 5*), the maximum at 440 nm is 1(it —> 5*), but may contain
some ligand based components through vibronic coupling; the maximum at 370 nm is
assigned as a purely ligand-based transition. Since the emission band overlaps the 1(5 —>

5*) transition, the emission band originates from the 55* excited state.

I.C. Two Photon Spectroscopy

Perhaps one of the most often referred to equations in chemistry is Beer's Law

(Beer-Lambert Law):3'
A=£ b c (1. l2)

where A is the absorbance of the sample, 8 is the molar absorptivity, b is the path length,
and c is the concentration of the sample. Beer's law can be easily recast into a form
which relates the intensity of radiation after the sample (If) to the intensity incident upon
the sample (10):31

1f=10e:“°‘bc (1.13)

where or is the absorption coefficient and is related to the extinction coefficient by: ‘9

(1

e=—— 1.14
mm ( )

It is e (or a), then, which carries the quantum mechanical information about the molecule

via the oscillator strength ( f ):32

 

 

 

4mece0ln10 81:2 m v 2
= e v dv- e
NAez .i ( ) hez li‘lfil

f (1.15)

where 115 is the transition dipole between the initial and final state (W1 and \Vf):
11114111131111. ;u=er (1.16)

Another fundamental property of a molecule, the refractive index (n) can also be

obtained from Beer's law. The refractive index is a measure of how much light slows

20

down (the phase is changed) as it passes through a material (Figure 1.8). The electric

field of the radiation (E(z,t)) at a point much behind the sample (z>>b) is given by:33

E(z, t)=e{iu)(n-l)b/c}Eoe{-io)(t-z/c)} (1.17)

where z is the direction of propagation of the field, b is the sample thickness (Figure 1.8)
c is the speed of light, E0 is the unperturbed electric field amplitude and 0) is the angular
frequency of the radiation (0) = 21w). The first term is often referred to as the phase

factor and for n-l < 1 can be expanded as:33

E(z, t)=[l+i(o(n -1)b/c+....]EOe{"‘°(“Z’°)} (1. 1 8)

One can assume that the dipole can be approximated by an electron (charge q)
attached to an infinitely heavy mass (nucleus). When an oscillating electric field (Eoe'iw‘)
is applied to the dipole it behaves as a driven, damped (through reradiation of the incident
electromagnetic field) harmonic oscillator. The equation of motion for the dipole in one

dimension (x) is then:34

mx+yx+kx=E0e_m (1.19)

where m is the mass of the electron, y is the damping constant, and k is the restoring force
(k = mewoz, coo is the angular frequency of the oscillator). The trajectory of the electron,

x(t), is then:

 

x(t)= (q/zmfiiOC—m (1.20)

(DO-(1) -i(DC

All of the dipoles following this trajectory reradiate electromagnetic energy at frequency
a) and have a strong resonance (absorption) at o) = coo. The total field at some distance
away from the sample is then the sum of unaffected electric field, plus the field that is

phase shifted:33

 

, 2
E(z,t)=Eoe"“’(t_Z/C’ 1+ b‘qu‘”, 4] (1.21)
280cmicoo—0) —i(nry)

/

21

 

 

 

 

 

 

 

 

 

(b)

 

(2)-.

Figure 1.8. The effect of refractive index on an oscillating electric field propagating in
the z direction. b is the sample thickness.

22

 

where N is the number of dipoles and so is the permitivity of free space. Equating this

expression for the field with Equation 1.18 above allows n to be determined:
=1+A(w0;miw% «02%wa (1.22)

where A(o)0;(o) = Nq2/2150m¢[(0002402)2 + 72032]. This demonstrates that the refractive

index is a complex number that can be written as:
n=Re(n)+i Im(n) (1.23)
where the real and imaginary parts are given by:

Re(n)=1+A(m0;m)(m3-w2) (1.24a)
Im(n)=ymA(a)0;(o) (1.24b)

When this index of refraction is substituted into the phase shift term (Equation 1.18) and
the resultant electric field is squared, the intensity at a point after the sample is given
by:35

E(z,t)‘E(z,t)ceo
2

 

1(2): (1.25)

Similarly, 10 can be determined from E0. A different expression for Beer's law is found,

this time dependent on the imaginary part of the refractive index:

1(z)=10e‘2“"m(“)b’ ° (1.26)

Therefore, the refractive index serves two roles; the real part imparts a phase shifi onto
the incident beam, and the imaginary part (the absorption coefficient) serves to attenuate
the beam.

A second way to look at refraction and absorption is through the relationship
between the average dipole moment density (P) which is induced in the sample by the

driving electromagnetic field (E):36
P=xE (1.27)

23

 

The incident electric field is attenuated and phase shifted by x, the susceptibility of the

material. It has been shown that x is related to the refractive index:36

n2=l+41cx (1.28)

The susceptibility has both imaginary and real components, just as the refractive index

does:
x=Re(x}+i Im(x) (1.29)
where the real part serves to retard the phase of the incident electric field, and the
imaginary part attenuates the electric field. The real and imaginary components of x in

terms of the refractive index are then:33

Re(n)2—Im(n)2-l

 

 

Re(x)= (1.30a)
41:
Im(x)= Rem) 1mm) (1.30b)
21:
Therefore, Beer's law can also be written in terms of the susceptibility:
Ileoe-41t11‘n(X)b/CRC(D) (1.31)

To this point, the dipole has been assumed to behave linearly as a harmonic
oscillator responding to a harmonic driving force. However, as the driving force
becomes more intense, the dipole can no longer respond linearly (either the electron is
ejected, or the oscillator becomes overdriven), this results in a nonlinear response as the
dipole becomes anharmonic. This anharmonicity is treated by expanding the

susceptibility as a power series:33

P=(x(')+x(2>E+x(3)E2+-.)a (1.32)

These higher order susceptibilities give rise to nonlinear responses to the driving force,
which are well known in optics. Second harmonic generation, where two frequencies are
mixed to form a third frequency that is the sum of the original two frequencies, arises

from x0) (Figure 1.9). Sum frequency generation is a common example where three

24

 

hvl

hv2= hv1+hv1

 

hvl

_. r

 

i

Figure 1.9. Second Harmonic Generation. Two electric fields are mixed through the
second order susceptibility tensor, )6”, to produce a third electric field.

25

 

frequencies are mixed through 1(3) to generate a fourth frequency (Figure 1.10). In
addition to these optical effects, nonlinear responses to driving forces are also common in
spectroscopy. Coherent anti-stokes Raman spectroscopy (CARS) and two-photon
absorption spectrosc0py are but two examples of four wave mixing through 1(3) in
spectroscopy (Figure 1.1 1).

Two-photon spectroscopy has several characteristics that separate it from
conventional, linear spectroscopy. The first is the difference in selection rules. Using
two-photon techniques it is possible to observe states that are forbidden to conventional
spectroscopy.37 A second characteristic is the quadratic dependence of the observed
signal on the incident electric field.38 The third, and perhaps the most useful distinction,
is the dependence of the two-photon transition probability on the polarization of the
incident radiation.39 Advantage can be taken of this characteristic to determine symmetry
assignments of two-photon allowed excited states by appropriate choice of the

experimental arrangement.

I.C.l. Selection Rules

The allowedness of a spectroscopic transition is governed by orbital, vibronic, and
spin selection rules. The one most important to distinguish between one- and two-photon
spectroscopy is the orbital or Laporte selection rule. The transition dipole, ufi, for a one-

photon process is given by:40

ufi=<wf|uj|m>m=er (1.33)

where w; and ‘Vi are wavefunctions representing the final and initial states respectively,
and H is the dipole moment in the j direction. From group theory, for a transition to have
nonzero intensity, the product wflrjwi must be an even function (must include the totally
symmetric irreducible representation). Since 11,- is an odd function that transforms as x, y,

or z, the product of may, must also be an odd fimction. For centrosymmetric systems this

26

 

 

I
I
hvl :
I
I
I
I
I
I
I
I
I
I
hvn i hv3=hv.+hv,+hv,
I
I
I
I
I
i .
I
I
I
hvl i
I
I

 

Figure 1.10. Sum Frequency Generation (SF G). Three electric fields are mixed through
the third order susceptibility tensor, )6”, to produce a fourth electric field.

27

 

 

 

T—
I
A i I i
(1). Eu), Iv

 

 

 

(a) (b)

Figure 1.11. Two examples of nonlinear spectroscopy. (a) Two-photon absorption
(TPA) spectroscopy and (b) coherent anti-Stokes Raman spectroscopy (CARS).

28

results in g <—> u transitions being allowed and g <—> g or u <—> u transitions being
forbidden.
In two-photon spectroscopy, on the other hand, the allowedness of the transition is

given by the two-photon transition tensor, S238a

1).)...

where Wu describes an intermediate state (that can be either real or virtual), and H and u,

(.1)
J

 

 

s... (vflu piz’lv.) (1.34)

indicates that the dipole moments involved in the transition need not necessarily be the
same. The effective two-photon operator is then 151% The product of the two dipole
moment operators transforms as x2, yz, 22, xy, xz, or yz, all of which are even functions.
Therefore, g <——> g and u <—-> u transitions are allowed in two-photon spectroscopy and

g <-—) u transitions are forbidden.

I.C.2. Power Dependence

The probability for a two—photon transition can be determined from time-
dependent perturbation theory.38a When both photons involved in the transition are from
the same laser (to, = (02 = (1),), the transition probability, w(2), is given by:

(”(2)0C 1% Z<Wf|FIWn><WnIHIWi>|2

(1.35)
n AEni—hCOr I

 

where I is the intensity of the incident laser beam, urn represents the intermediate state
and W1 and \Vf are the initial and final state wavefunctions, respectively. AEnj is the
energy of the intermediate state and u)r is the frequency of the incident radiation. This
equation shows that the transition probability is proportional to the square of the intensity
of the incident laser beam. In general, for any n-photon transition induced by a single
source and below saturation, the probability it proportional to I". When a two-photon
transition is saturated, the probability can be shown to be proportional to 13/2983 In

general, quadratic dependence can be a powerful tool in determining if an observed

29

transition results from a two-photon absorption. Taking the logarithm of each side of

equation (35) results in the more familiar expression:

logW(2)=210g I+logC (1.36)

where the terms have the same meaning as before and C represents the terms in the
summation along with experimental variables that are independent of the irradiation

power.

I.C.3. Polarization Dependence

In linear spectroscopy the symmetry of an excited state can only be determined by
using a rigidly oriented sample. In two-photon spectroscopy, however, excited state
symmetries can be determined for randomly oriented samples. The role of polarization in
two-photon spectroscopy was first investigated by Monson and McClain39 and later by
Nascimento.“ This attribute has made two-photon spectroscopy a valuable tool to
spectroscopists.

In one-photon spectroscopy the absorption cross-section, o, for randomly oriented
molecules is related to the transition dipole (defined in equation 33):
'2

each-pf, (1.37)

where A is the unit polarization vector of the absorbed photon. Since 7v}: = 1 there is no
polarization information contained in the observed transition.
In two-photon spectroscopy, however, the cross-section, (5) (more correctly, the

absorptivity), is given by:39

(8)=|).-S‘,’—,b ~r< [2 (1.33)

30

 

where K and A are the polarization vectors of the two absorbed photons and Sfib , the
two-photon transition tensor is:39

Stb=2 Ml “WM “"i’ii + (Vil HMXWEI ulw?)
n (Uni—(0K (uni—0)),

 

(1.39)

where (”n1 is the energy of the intermediate state and wj (j = K or A) is the energy of the
photon absorbed. The cross-section is most ofien written in terms of molecular
parameters and polarization (experimental) parameters”

(5)=5FF+5GG+5HH (1.40)

where, F, G, and H are functions of the polarization of the absorbed photons:

 

 

2 . 2
F=4|1.x|-1—|r-x
(I.41a)
2 at 2
G=—|>.-x| +4—lx-x
(I.4lb)
2 at 2
H=—|1-x| —1+4|1-x|
(I.41c)
and 5;, 5G and 5“ are functions of molecular parameters:
5px): )1; silf'sgb’ (1.422.)
a
86 ngsgasga‘ (I.42b)
a
sflxzzsgasgb‘ (I.42c)
a b

where a and b represent the molecular axes and SE“ are the two-photon transition tensors
as before. If two photons of the same energy are used then 56 = 5“ (Sbal = Sab). Since 51:
is then the square of the trace of the tensor (which implies it is totally symmetric), it is
only nonzero if the excited state is of the same symmetry as the ground state.

The values of F, G, and H have been calculated for the eight possible polarization
cases39 (using circularly and linearly polarized light) and are shown in Table 1.2. The

tensor patterns have also been deterrnined39r‘" for most symmetries and the relevant

31

Table 1.2. Values for the polarization functions F ,G, and H, depending on the eight
polarization cases. From References 37 and 39.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Case 1 2 3 4 5 6 7 8
n r-o o» no 12 to oo 00

F 2 -1 -1 -1/4 1/2 1/2 -2 3

c 2 4 4 7/2 3 3 3 3

11 2 -1 -1 -1/4 1/2 1/2 3 -2

 

Polarization Cases:

(1)
(2)
(3)

(4)
(5)
(6)

(7)
(8)

Two linearly polarized photons with parallel polarization.
Two linearly polarized photons with perpendicular polarization.

One linear and one circular with the linear photon polarized such that it is
perpendicular with the plane of the circularly polarized photon.

Both circular with propagation opposite to each other.
Both linear, with 45° between their polarization vectors.

One linear and one circular with the linear photon polarized such that it is
parallel with the plane of the circularly polarized photon.

Two circularly polarized with polarization in the same sense.

Two circularly polarized with polarization in the opposite sense.

32

 

patterns are shown in Table 1.3 along with their polarization ratio, 9, that is defined as:38a

o=—<5°i'> (1.43)

(511.)

here (5“,) and (51111) are the cross sections for using two circularly and two linearly
polarized photons respectively and are given by:

(5,,,)= 1:13F + (G + mag = — 25F+656 (I.44a)
(81in): 1:5F + (G + H )5G = + 26F+415G (I.44b)

where F, G, and H have been taken from Table 1.2 (cases 7 and 1 for two circularly

polarized photons and two linearly polarized photon respectively). The polarization ratio

is bounded by:

0 s o 3% (1.45)

Therefore, by measuring the intensity of a transition when two circularly polarized
photons are used and comparing that to the intensity when two linearly polarized photons

are used, the symmetry of the states involved in the transition can be determined.

I.D. Motivation

The applicability of the VB model would have significant ramifications on the
potential photochemistry of these molecules. If the model provides a fair representation

of the upper excited states of the 5 manifold, then these states should undergo

33

Table 1.3. Two-photon tensor patterns and the polarization ratio (9) expected for each
transition in the D2d and D4}, point groups. From References 37, 39, and 41.

 

 

 

 

 

 

Tensor Pattern Transition Symmetry Polarization Ratio
operator (gs <-—) es)’r Q
A,;x2+y2,22 AIHAI;A2<—>A2; Q<l
S] O O
0 S] 0 BIHBl;B2('—)Bz
O 0 52
B“ x2‘y2 Ale—>8, n=3/2
S3 0 O
O _ s3 0 A2 <-> B2
0 0 0
B :
2 X” A, H 132 Q = 3/2
0 S4 0
_ S4 0 0 A2 (—> B]
0 O 0
szz’yz A HE (FM
0 0 85 l
O O — 1'55 and E H E
S6 - iS6 O
0 o s;
o 0 — is;

t . t
56 -zs6 O

 

 

 

T gs = ground state symmetry; es = excited state symmetry.

34

 

unprecedented multielectron chemistry due to the ionic nature of the excited states (+M—
Mr). Multielectron photochemistry has already been observed from these states in the

oxidative addition of CH3I to W2Cl4(dppm)2:42

 

PIL. CH :Ph PIL. CH\2 Ph
Ph—" ’ 5—Ph Ph—" ’ 54Ph
P P P .C1_.P

.IC .ICl hv Cll . ICH3
a >
C1’ h7ICI’ I CH31111’11I)Cl:II)I
P';Ph P\IIIPh

This reaction has been shown to proceed upon excitation of the l(1t—)5*) transition. It is
presumed that it is necessary to excite this transition to provide a weakened 1: bond
involving the Cl' ligands, which then allows the Cl' ligands to fold over to an edge-
sharing bioctahedral arrangement, thus providing a vacant coordination site on the

reduced metal center:43

 

PIL. CH .Ph Ph. CH _.-Ph
Ph-LP’ 3P:_.Ph PhSP’Cl‘zp'APh
Cln. -
f, "Cl hv >14“ \I/
Cl’ ICl’ I1’|‘Cl|
phth wuph Ph"'P ""Ph
lbI'IIZP\P /bHZP\P

The product species has been observed in nanosecond transient absorption studies (I >
100 us) (Figure 1.12a)43944. The spectrum of the transient species is consistent with the
spectra of the edge-sharing bioctahedral analogs W2Cl6(PEt3)4 and W2Cl6(dppm)2
(Figure 1. 12b). This mechanism is plausible in the context of the VB model where ionic

excited states are presumed to exist.

35

AOD.

0.15

0.10

0.05

0.00

Absorbance

 

 

 

 

 

450 500 550 600 650

Wavelength

Figure 1.12. (a) Transient absorption spectra of W2Cl4(dppm)2 recorded 100 ns (solid

squares) and 4 Its (open circles) after 532 nm, 10 ns excitation. (b) Absorption spectra of
WZC16(PEt3)4 ( ----- ) and W2Cl6(dppm)2 (
from Reference 43.

 

) in toluene and CH2C12 repectively. Data

36

Two-photon spectroscopy should provide access to the 21A,g state of the 5
manifold. By comparing the energy of this state with the other known energies, it will be

possible to evaluate the validity of the VB model.

37

Chapter 11

Experimental

ILA. Two-Photon Techniques

There are many ways two-photon processes can be detected. Perhaps the most
obvious is two-photon absorption. This technique, however, is plagued with difficulties.

45"molecule‘

Since the cross-section for a two-photon process is very small (5 ~ 10'50 cm
I), there is very little difference in the intensity of the emanating beam with respect to the
incident beam. To avoid this problem, two-photon absorption is usually measured in
very concentrated solutions using cells with long pathlengths. Also, fluctuation in laser
intensity causes the signal to noise ratio to be extremely poor.

A popular technique involves the detection of ions produced by the absorption of
two photons. Two common ways to perform this method are illustrated in Figure 11.1.

The first is for the final state to be in the ionization continuum. A second approach is to

produce a final state by two-photon absorption, and before that state decomposes employ

38

 

 

 

 

 

Figure 11.1. Multiphoton ionization techniques. Lefi, two photons simultaneously
absorbed through a nonresonant virtual state to the ionization continuum (2 PI). Right,
two photon simultaneously absorbed to create a "final" state, which then absorbs a third
photon to the ionization continuum (2+1 PI).

39

another laser beam to ionize to the continuum. While ionization techniques are very
powerful, they are not applicable to solution phase samples.

The method most widely used to obtain solution phase spectra is two-photon
excitation. In this technique, the final state decays to a lower energy, emissive state
(Figure 11.2). The emission is then monitored as a function of incident wavelength. Two-
photon excitation is an attractive technique since it provides the low detectivity limits
afforded by detecting against a dark background. Also, the emitted photons are often
much higher energy than the absorbed photon. Scattered light is therefore easily
discriminated against by proper filtration or use of a monochromator. Two-photon
excitation is often coupled with gated integration to increase the signal-to-noise ratio

even further.

[1.8. Materials and Instrumentation

The compounds studied in this work, M02Cl4(PMe3)4 (l) and
cis-MozC12(mhp)2(PMe2Ph)2, (2) were prepared by Tsu-Ling Carolyn Hsu and Ann

Macintosh respectively, by previously described methods“.

MeP Cl
3 c1 I‘PMe3 / I

0
{$3 i.~‘\0 In“
1 Mo- 0
(”ii L d1

(1) (2)

Saturated solutions were prepared in n-hexane (Burdick and Jackson, spectroscopic

 

grade), which was degassed by several freeze-pump-thaw cycles. The cell used has been
described previously.46 Conventional excitation and emission spectra were acquired
using a spectrometer that has been previously described also,47 absorption spectra were

measured on a Cary 2300 UV-visible spectrophotometer. The two-photon excitation

40

 

 

 

____L__

Figure 11.2. Two-photon excitation spectroscopy. Two-photons are simultaneously
absorbed to create an excited state, which then decays to an emissive state of lower
energy.

41

spectra were collected in the MSU LASER Laboratory, using the instrument depicted in
Figure 11.3. The laser source is a Quanta-Ray DCR2-A nanosecond pulsed Nd:YAG
laser whose fundamental frequency is doubled by a Quanta-Ray HGII second harmonic
generator. The 532 nm output (200 mJ/pulse, 8 ns FWHM) is sent to a Quanta-Ray PDL-
2 dye laser, where wavelengths from 710 nm to 970 nm can be produced using various
dyes and dye combinations. The tuning curves for the dyes used are shown in
Figure 11.4. The laser beam is directed to the sample chamber using three prisms and a
telescope. The telescope is used to maintain collimation of the laser beam and to aid in
focusing the beam onto the sample.

Before reaching the sample, the laser beam is passed through three optics to
provide control of the polarization of the incident radiation. The first optic is a Glan-
Laser polarizer. The second and third optics are a double Fresnel rhomb and single
Fresnel rhomb, respectively. These three optics, when used in series, allow for complete
control of the polarization of the incident laser beam without changing the position of the
laser beam. These components are described in greater detail later in this chapter. After
leaving the third polarization optic, the laser beam is passed through the sample. The
sample fluorescence is collected at a 90 degree angle to the incident laser beam by two
f/4.0 quartz collection lenses. The fluorescence is dispersed through a monochromator
and is detected by a photomultiplier tube. After the laser beam passes through the sample
it is scattered through a piece of opal glass onto a photodiode, so that the relative

intensity of each laser pulse can be monitored.

II.C. Two-Photon Excitation Measurement

The output signals from the photomultiplier tube and the photodiode are sent to a
pair of Stanford Research Systems SR250 gated integrator/boxcar averager modules. The

photodiode signal is split into two parts. The first part passes through a Phillips Scientific

42

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44

window discriminator that serves as a trigger source for the averagers. The second part
goes directly to the boxcar as a measure of the laser intensity. The lower limit of the
discriminator is set such that only pulses intense enough to cause the two-photon process
result in a trigger of the averagers. The upper limit of the discriminator is set such that
laser pulse that would saturate the photomultiplier tube do not result in trigger pulses.
These limits are determined by monitoring the photodiode signal and photomultiplier
signal simultaneously on an oscilloscope. Typically, 300 laser shots are averaged by the
boxcars. The averaged output is sent to a personal computer where Stanford Research
Systems SR267 software package is used to collect the raw photomultiplier and
photodiode data for display on the monitor. Afier 300 shots are collected, the boxcars
send an output pulse to the stepping motor of the dye laser. A device designed by Martin
Rabb is used to control the step size and has been described previously.46 For most
experiments, the dye laser advanced in 0.5 nm steps. This averaging and advancing
process is repeated until the desired spectral range is covered.

The raw data are sent to a program called TWOPH, which is a modification, by
Dr. Jeffrey Zaleski, of the program used on the excitation spectrophotometer and has
been described in great detail previously.47 The program reads the raw photodiode and
photomultiplier files and corrects for the wavelength response of the photodiode that is
shown in Figure 11.5. It also normalizes the photomultiplier signal by the square of the
corrected photodiode signal and divides the wavelength by two to reflect the energy of

the transition.

ILD. Power Dependence Measurements

The photomultiplier and photodiode signals are sent to a digital storage scope.
There, the signal intensity is measured as a function of laser power. Typically 500 or

1,000 laser shots are averaged and the averaged values are placed into a spreadsheet

45

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program on the personal computer for manipulation. The log of the signal intensity is

plotted against the log of the laser intensity and a least squares fit is performed.

ILE. Polarization Control and Polarization Ratio Measurement

The polarization of the laser beam is manipulated to be either circularly or
linearly polarized by three optics. These optics are a Glan-Laser polarizer (GL), a double
Fresnel rhomb (DFR) and a single Fresnel rhomb (SF R). The GL is used to maintain a
constant vertical polarization of the laser beam before it reaches the next two optics. The
DFR is mounted in a rotatable mount such that it can be rotated about the optical axis of
the laser beam. When the DFR is rotated, the plane of polarization of the laser beam is
rotated with respect to the incoming laser beam. This results in changing the plane of
polarization of the laser beam with respect to the optical axis of the SFR. The SFR
produces either circularly polarized or linearly polarized light depending on the plane of
polarization of the incident laser beam. This is accomplished by variably retarding either
the magnetic field or electric field of the laser beam. The degree of retardation is
dependent upon the plane of polarization of light incident upon the SF R.

The polarization state of the laser beam is experimentally determined as shown in
Figure 11.6. By placing a mirror in the beam path and rotating the DFR, a minimum is
observed in the reflected laser beam when the light is circularly polarized. Linearly
polarized light is determined by placing a Glan-Thompson (GT) polarizer in the beam
path. By rotating the DF R, a minimum is observed afier the GT when the light is linearly
polarized.

The polarization ratio, 9, is determined by scanning the dye laser with the
polarization optics configured such that circularly polarized light reaches the sample.
The polarization optics are then reconfigured so that linearly polarized light reaches the

sample and the wavelength region is scanned again. The polarization ratio is the ratio of

47

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48

the observed signal intensity when circularly polarized light is used with respect to the
intensity when linearly polarized light is used. Alternatively, the (2 measurement is made
point-by-point at 5 nm increments, using the digital storage scope to measure the

averaged signal intensity.

”'3'!

‘: arm 3L~OFQ .-

 

49

Chapter III

Results and Discussion

The valence bond model developed in the Introduction provides important
qualitative descriptions of the electronic states of the 8 manifold. It shows that the two
low energy states (1A1g and 3A2“) can be described as diradical states, with one electron
on each metal. It also suggests that the two highest energy states (1A2u and 2'Alg) can be
described as zwitterionic states, with two electrons on one metal, and no electrons on the
other center. Also, it predicts that the energy separating the two lowest energy diradical
states (‘Alg and 3A2“) is equal to the energy that separates the highest energy ionic states
(1A2u and 2'Alg).

Several facets of this model have been experimentally confirmed. The ionic
nature of the '55“ state has been reported by Winkler and Sutin and their coworkers.
They determined that the 185* excited state of M02Cl4(PMe3)4 possesses a dipole
moment of 4.0 Debye (the ground state is apolar).48 Also, they have shown that the 185*
state is ionic by studying the time resolved emission spectrum.48 The maximum of the

emission spectrum shifis on the time-scale of microscopic solvent motion. This implies

50

that the solvent configuration around the ground state molecule (which has no dipole)
does not stabilize the polar excited state and the emission spectrum evolves as the solvent
reorients to stabilize the polar excited state.

The energy of the diradical triplet state (3A2u) has been pursued since the early
805. As the 8 bond is broken, the energy that separates the triplet state from the ground
state gets smaller. There are two ways to break the 8-bond. The most obvious is to
stretch the bond until the molecule dissociates. This results in the rupture of the o and
two It bonds also. A more subtle way to break the 8-bond is to twist the two halves of the
molecule with respect to each other. Since the o and two 1: bonds are cylindrically
symmetric, they are essentially unaffected by twisting; therefore only the S-bond is
broken. As the bond is twisted to near extinction (45°), the ground state and triplet state
become nearly degenerate, making it possible to populate the triplet state thermally.
. Gray and coworkers were the first to try to directly measure the energy of this state by
measuring the temperature dependence of the paramagnetism induced by populating the
triplet state of B-MozCl4(dmpe)2 [dmpe = l,2-bis-(dimethylphosphino)ethane], which is a
twisted analog (x = 40°) of M02C14(PMe3)4.49 However, the sample decomposed at
moderate temperatures and a great deal of approximation and extrapolation was required
to estimate the triplet state energy of the nontwisted molecule MozCl4(PMe3)4
(5200 cm“).

Cotton et al have recently used a similar strategy to determine the energy of the
3A2u state.50 Rather than directly observing the paramagnetism, they studied the effect of
the induced paramagnetism on the NMR spectra of a series of M2X4(l;l’)2 complexes
[(1%) is a bridging phosphine ligand]. By varying the (19’) ligand they were able to
obtain a series of compounds with twist angles that spanned the range of 24.7° to 69.4°
(determined from the crystal structures) which "break" the 5 bond to varying extents. By

studying the temperature dependence of the 3'P{'H} NMR spectra of these so-called

5]

"rotamers," it was possible to extrapolate a value for the triplet state energy of the non-
twisted (or twisted 90°, depending on the definition of twist angle) M2X4P4 molecule.
They determined the energy of the 388* state to be 4840 cm", which is much lower than
that of the 188* state (17,000 cm'1 for MozCl4(PMe3)4). Cotton, et al. also compared the
triplet state energy of these molecules with the energy of their 188’“ states (Figure 111.1).
The energy separating these two states is essentially independent of twist angle (orbital
overlap), as predicted by the VB model.50

The energy of the 21A,g state, the last unobserved state in the 8 manifold, has
eluded spectroscopic determination because the transition from ground state is orbitally
forbidden by one-photon selection rules (g <—> g); the transition is also forbidden because
it involves promotion of two-electrons. If this state can be observed, all of the energies of
the 8 manifold will be determined, thus providing a conclusive test for using the VB
model to interpret the electronic states of the 8 manifold.

The one- and two-photon excited emission spectra of MozCl4(PMe3)4, (1), are
shown in Figure 111.2. The similarity of the two spectra indicates that in both cases, the
emission arises from the same state, namely 188'”. This implies that the state prepared by
the two-photon absorption interconverts to the 188'“ state. The corresponding spectra for
cis-MozCl2(mhp)2(PMe2Ph)2, (2), are shown in Figure 111.3. The observed emission is
higher in energy than the photons absorbed in the two-photon excitation. This indicates
that the excitation results from the mixing of the electric fields of two photons. The
dependence of the emission intensity on the power of the incident radiation for each
molecule is shown in Figure 111.4 (1) and Figure 111.5 (2). The log-log plots of signal
intensity versus laser power have slopes of 2, which further indicates that the excitation
represents a non-saturated, two-photon absorption.

The linearly polarized two-photon fluorescence excitation spectrum of

M02Cl4(PMe3)4 is shown in Figure 111.6, along with the one-photon fluorescence

52

 

 

 

 

 

 

 

 

 

 

 

 

16000
14000 A
12000 A A
‘ A
A . C
10000 ' ’
'a .
fl 8000
>\
3°
8
m 6000
4000
- I
2000 h l
I I
0 r

 

 

 

 

 

 

 

0 15 30 45 60 75 90
Twist Angle (x) (degrees)

Figure 111.]. Energies of 3A2“ (solid squares), 1A;" (solid triangles) and the difference
of the two energies (solid circles). Data from Reference 50

53

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slope = 2.05
1.5 —
’33
8
B
5 ..
E:
cl
DD
.9.
1 .—
0.5 l l l I l l l
2 2.25 2.5 2.75 3

log (Laser Power)

Figure 111.4. Power Dependence plot for MozCl4(PMe3)4. The instrument was

configured for vertically polarized light and he,“ = 860 nm. Power depencences were
taken at 10 nm intervals using both polarizations, across the spectral range scanned and
similar results were obtained for each.

56

 

 

 

 

 

2
. Slope = 2.0
3 1.5 _
g .
8
E.
E .
:l
on -
.0.
1 _
1 l 1 l 1 l 1
0.5
2 2.25 2.5 2.75 3

log (Laser Power)

Figure 111.5. Power Dependence plot for cis-MozC12(mhp)2(PMe2Ph)2. The instrument
was configured for vertically polarized light and hem = 840 nm. Power depencences

were taken at 10 nm intervals using both polarizations, across the spectral range scanned
and similar results were obtained for each.

57

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58

excitation spectrum. The two absorption maxima in the one-photon spectrum are
assigned as indicated in Chapter I; the maximum at 445 nm is l(rt-8") and the maximum
at 585 nm is 1(8-8"). There is a single maximum observed in the two-photon spectrum, at
455 nm. To aid in assignment of the two-photon transition, it is necessary to consider all
reasonable electronic transitions (those that might be expected to occur around 455 nm).
As mentioned in the introduction, Hay has made extensive calculations on the RezClgz'
anion and determined the energies of many of the electronic transitions (both single and
double excitations)5. While the numerical values of the transition energies will not be the
same (RezClgz' and the molybdenum compound of interest here, M02C14(PMe3)4), the
relative energies can still be used to eliminate those transitions with unreasonably high or
low energy. Several of the calculated transitions and their respective energies are shown
in Table 111.1.

The polarization ratio, 9, is particularly useful in determining the symmetry of
the states involved in a two-photon transition. (2 is plotted as a function of laser
excitation wavelength in Figure 111.7. The polarization ratio is constant and less than 1
across the observed band. This indicates that the observed excitation envelope represents
a single electronic state and is not a convolution of several bands (unless all of the
transitions have the same symmetry). Furthermore, in the D2d point group, the
polarization ratio can be less than one only if the symmetry of the excited state is the
same as the symmetry of the ground state (see Table 1.2 and Table 1.3 in the
introduction). Since it has been well established that the ground state symmetry of
M02C14(PMe3)4 is A‘, the excited state must also be of A1 symmetry.

There are only four reasonable (those excitations that involve either the 0' or 0*
orbitals are presumed to be much higher in energy than the transition observed at 455
nm) electronic transitions that meet the requirement of an Al ground state and an A]

excited state. These transitions are listed in Table 111.2. By comparing these transitions

59

Table 111.1. Selected singlet state energies for the RezClsz‘ anion. From Reference 5.

 

Transition (state)

Energy with S-O* (eV)

Energy without S-O* (eV)

 

Single Excitations

 

 

 

 

 

 

 

 

 

 

5 — 6* ('AZU) 1.8 1.8

n — 5* ('Eg) 2.6 2.5

5 — 1" (‘Eg) 3.4 3.4

n — 11*(1Alu) 4.4 4.1

n —— 11* (1132,) 4.9 4.5
Double Excitations

88 — 8*8* (‘A,g) 2.2 2.0

118 -— 8*8* ('Eu) 3.6 3.4

88 — 5*n* (‘13,) 4.8 4.4

 

 

 

* S-O indicates spin-orbit coupling

60

 

 

030.5”

 

 

 

400 420 440 460 480 500

Wavelength / nm

Figure 111.7. Polarization ratio , Q, for MozCl4(PMe3)4.

61

Table 111.2. There are twelve metal-based transitions which satisfy the criteria of an A1
excited state and an A1 ground state. The four transitions listed are expected to occur in

the near UV or visible region of the spectrum. The remaining eight transitions involve
either the 0’ or 0* orbitals and should not occur in the near UV or visible region of the
spectrum.

 

 

 

 

 

 

Ground State Excited State Transition
Configuration Configuration Symmetry
621t452 lAl 621t4808*2 lA, 86—5*6* (A, -A,)
621:462 1Al 621t4801t’1‘2 lA, 88—1c*1t* (Al —A,)
0210182 ‘Al 0211:2525’l‘2 1A, m—8*8* (Al —Al)
621:482 1A, 621:2821t*2 1A, 88—1t*1c* (Al —Al)

 

 

 

62

 

with the energies determined by Hay, and the energies of the one-electron transitions for
MozCl4(PMe3)4 it can be shown that the only possibility is 82 —> 8'”, i.e., the hitherto
unseen transition in the 8 manifold. Assuming that two-electron transitions are higher in
energy than their one-electron counterparts allows dismissal of all the transitions but
82 —) 8'“2 (since the one-electron transitions 1: —> 1c*, 1: —-> 8*, and 8 -—) 11:" all occur to
higher energy than the observed 82 —> 8'“2 transition). This assumption is further
supported by Hay's calculations that indicate that the 82 —) 8'“2 transition occur between
1: —> 8* and 8 —> 8* and indicate that the 8 —-> 11?“ and 1t —) 1t* transition occur at much
higher energy than either of these two transitions. Also, Hay has calculated the energy of
the 1:8 —> 8'”2 transition and it also lies to higher energy than the 82 —) 8'“2 transition. The
1:8 -) 8’“2 transition would provide a lower limit to the energy for the 11:2 -) 8'“2
' transition. Similarly, Hay has calculated the energy of the 82 —> 8*1c* transition; this
transition would provide a lower limit for the 82 --9 1t'"2 transition energy. Assuming that
the observed transition is 82 -—> 8‘“2 it is possible to determine the energy separating the
two zwitterionic states (188* and 8”). If one assumes similar Franck-Condon factors for
the 1(8 —> 8*) transition and the 82 —) 8’“2 transition, an energy separation of 4800 cm'1 is
calculated.

That the two-photon maximum falls so close to the l(rt-8’“) transition observed in
the one-photon spectrum is of some concern. As shown in Table 111.3, the l(rt—>8”)
transition is an allowed two-photon transition. However, the transition would be of the
Al-E type and its polarization ratio would be expected to be 1.5, rather than the observed
value of 0.7. Moreover, for the transition to be allowed, two linearly polarized photons
with perpendicular planes of polarization would be required (since the basis function for
the E operator in the DZd point group is xy), whereas the polarization of the two photons

in this experiment are necessarily parallel.

63

Table 111.3. Four possible two-photon transitions, their symmetry and the expected
polarization ratio, (2.

 

 

 

 

 

 

 

 

 

Transition Symmetry Q :
'(82 —> 5“) A, —A, <1 E
1(1t—> 8*) A, — E 3/2
1(8—> 6*) A, - B2 3/2
l(8—> n*) A, -— E 3/2

 

 

64

The two-photon excitation spectrum of cis-MozC12(mhp)2(PMe2Ph)2, shown in
Figure 111.8, is consistent with these assignments. There are two peaks present (A = 390
nm and 420 nm) in this excitation spectrum. The lower energy band has a polarization
ratio of ~0.7 as shown in Figure 3.10, while the polarization ratio of the higher energy
band is ~l. The lower energy transition is assigned as 82 -—> 8”, while the higher energy
band is assumed to be ligand based. This is reasonable since
cis-M02C12(mhp)2(PMe2Ph)2 has such low symmetry (C2), that a great deal of intensity
borrowing may occur, thus making the ligand based transitions two-photon allowed. The
energy separating 188* and 8’“2 in this compound is ~5,000 cm".

The experimentally observed triplet state energies and 188* and 8'“2 energies are
collected in Table 111.4. By analyzing these values, it can be seen that the VB model is
indeed an appropriate representation of the energies of the states of the 8 manifold. The
VB model predicts that the energy separating the zwitterionic 188* and 8'"2 states should
be equal to the triplet state energy. This is observed: 8’“2 - '88* = 4800 to 5000 cm";
388* = 4840 cm". Also, the experiments performed by Cotton and coworkers showed
that the energy separating 388* and '88“ is essentially independent of twist angle, as

predicted by the VB model.

Table 111.4. Comparison of the 2‘A,g — lAZu energy gap as determined by two-photon
spectroscopy with the 3A2u — lA,g energy gap as measured by Cotton in Reference 50.

 

 

 

 

 

 

Compound 3A2u — lA,g (cm'l) 2'A1g - 1A2“ (6111'!)
M02C14(PM63)4 4840 4800
M02C12(mhp)2(PMe2Ph)2 5000

 

65

 

 

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1.50

 

 

 

 

1.00 _
a .-
0.50 _.
0.00llllllllllllllLllllllllllll
340 360 380 400 420 440 460 480

Wavelength / nm

Figure 111.9. Polarization ratio, (2, for cis-M02C12(mhp)2(PMe2Ph)4.

67

 

Appendix 1

Using the states as defined in Chapter I:

52:51(1)51(2)811132-1310‘2 }' lAlg (AI-a)
3 55. ={51(1)52(2)'52(1)51(2)}81152+1310‘2}3A2u (AI-b)
155‘ ={51(1)52(2)+52(1)51(2)}{0‘1132—13102}’-1A2u (AI-C)

.2
5 =52 (1)52 (2)10‘152‘1310‘2} ZlAlg (AI-d)
And employing the Hamiltonian, also described in Chapter 1:
HT=H(')+H(2)+~1— (AI.2)
r12

it is possible to determine the energy of each of the states.

The energies of lA,g and 21A,g can be determined by developing the matrix
elements of the Hamiltonian. The diagonal elements represent the energy of the states
and the off-diagonal elements determine the extent of mixing between the states

(configuration interaction) The matrix elements for the Hamiltonian operator are:

HT=[H” H12] (A13)
H21 H22
The elements on the diagonal are.
H,,= (82 [11462) (AI.4a)
H22=<5*2 11.45“) (Al.4b)

 

The off-diagonal elements are given by:

H,2=<62 IHT|8*2>=H2,= (8*2 IHT|82> (A15)

68

The energies of these Hamiltonians are:

H,, -_-(82|H“>[82>+(82|H(2>|82)+(82|ri|82> (A1.6a)
12
=(51<1>61(2>|H‘”|61(2>81(1))+<8.(1)61<2)IH‘2’l6.<2>8.(1))

+<61<1)61(2>|ri|6.(2)6.(1)) (AL6b)
12

where the first term represents the energy of electron 1 in 82 and the second term
represents the energy of electron 2 in 82. The third term represents the repulsive energy
between the two electrons in the same orbital (82). This is known as the Coulomb

repulsion energy J , ,. The energy for this state is then:

H11=w1(1)+wl(2)+-111(1,2)=2W1+Jl1 (AI-7)

 

where W,(l) is assumed equal to W,(2) and the electron labels have been left off.

Similarly for H22, the energy of this element is:
H22=W2(1HW2(2)'1'122(1,2)=2W2+122 (A13)

where W2 represents the one-electron energy of an electron in the 8" orbital and 122
represents the Coulomb repulsion between the two electrons in the 8* orbital.
The energy of the off-diagonal terms is given by:
8.. =(52|H<1>;a*2).(52 lam 5*2>+<82|;1—
12

=(61<1>81(2)|H‘”|6208320))+(81(1>6.(2)|H‘2’|62(1)82(2)>
+(51(1)51(2)lr—1-I52(l)52(2)) (AL9b)
12

 

 

6*2) (AI.9a)

The first two terms are zero (since (8,(1)8,(2) I 82(1)82(2)) = 0). The remaining term is
the exchange energy ,K,2. This energy represents the energy required to move electron l
and 2 from 8, to 82 (and vice versa).Therefore, the energy of the off-diagonal elements

are:

H12=H21=K12 (ALIO)

69

Including the off-diagonal elements in the secular determinant allows the energies
of the states to be determined:

2W,+J,, —}\. K12
K12 2W2+122 -}»

E. 1 .
A,g,2 Alg

 

l=0 (AI.11)

Using the definitions and assumptions given in Chapter I, this secular determinant

reduces to:

— AW 4. K,2 1
=0 (A112)

 

El 1 I
A182 Alg

Solving the secular determinant leads to the energies of the states:

13. Am:- ,le2+Aw2 (AI.l3a)

E

 

2.Alg=+ 1(9sz (A1.l3b)

The next two states,3A2u and 1A2“, those with one electron in each orbital can also
be determined using the same types of integrals. The only new integral to be encountered

is one in which there is a Coulomb repulsion between the electrons in different orbitals:

(81(1)62(2)|;1-|61(2)62(1))=Jn(1.2) (A114)
12

These energies of these remaining two states are then determined to be:
El 2 =W|+WZ+J12+K12 (AI.153)
E3 2 =Wl+W2+le—K12 (AI.15b)

A

A

70

10.
11.

12.
13.
14.

15.

16.

REFERENCES

. (a) Cotton, F.A. Science 1964, 145, 1305; (b) Cotton, F.A., Inorg. Chem. 1965, 4, 334

Cowman, C.D.; Gray, H.B. J. Am. Chem. Soc., 1973, 95, 8177

Bratton, W.K., Cotton, F.A., Debeau, M., Walton, RA. .1. Coord. Chem. 1971, l, 121
Benard, M. J. Am. Chem. Soc, 1978, 100, 2354

Hay, P.J., J Am. Chem. Soc., 1982, 104, 7007

This is a typical value, for RezClsz‘, the distance is 2.24A, for more specific values,

see for instance Cotton, F.A.; Walton, R.A., Multiple Bonds Between Metal Atoms,
1993, Clarendon Press, Oxford, and references therein

Trogler, W.C.; Gray, H.B. Acc. Chem. Res. 1978, 11, 232
Mulliken, R.S., J. Chem. Phys, 1939, 7, 20

Bino, A; Cotton, F. A., Angew. Chem. Int. Ed. Engl, 1979, 18, 462
Hopkins, M.D.; Gray, H.B., Polyhedron, 1987

See any general chemistry text such as McQuarrie, D.A.; Rock, P.A., General
Chemistry, 1984, WH. Freeman and Company, New York

Mulliken R. S. Phys. Rev. 1936, 50, 1017;1028
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71

 

17.

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See any introductory quantum mechanics text such as Atkins, P.W., Molecular
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72

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39. (a) Monson, P. R.; McClain, W. M. J. Chem. Phys, 1970, 53, 29; (b) McClain, W. M.
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43. Turro, C. Ph.D. Dissertation, Michigan State University, 1992

44. Similar long-lived transients are also seen for M02C14(dmpm)2 (1: = 100 us)

73

 

45. M02C14(PMe3)4: Cotton, F. A.; Extine, M. W.; Felthouse, T. R.; Kolthammer, B. W.;
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46. Yu, J. Ph. D. Dissertation, Michigan State University (1990)

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2104.

74