J . Phys. Chem. 1991,95,9773-9781
9773
Electronic Properties of Transltlon-Metal Complexes Determined from Electroabsorption (Stark) Spectroscopy. 2. Mononuclear Complexes of Ruthenium( I I ) J. R. Reimers and N. S. Hush* Department of Theoretical Chemistry, University of Sydney, Sydney NS W 2006, Australia (Received: May 1 , 1991)
Perturbation of electronic/vibronic absorption envelopes by application of an external electric field is a powerful potential source of valuable information about the nature of excited and ground states. We discuss here the theory of such effects for the ground and excited states of some Ru(I1) complexes and relate it to the experimental work of Oh, Sano, and Boxer.'*2 In a previous paper (part l), we gave an interpretation of the spectra of some mono- and bisruthenium complexes (including the Creutz-Taube ion) in terms of an approximateSCF theory. Here, we concentrate on the interpretation of the monoruthenium experimental data in terms of molecular parameters and rationalize the results in terms of the simplest possible model for the electronic structure of the complexes. The results provide direct confirmation of the electronic structure of these complexes advanced by earlier workers on the basis of chemical, thermodynamic, and spectroscopic data.
1. Introduction The response of molecules to application of electric fields is an area of great diversity. Perhaps the most commonly considered properties for molecular ground states are one-electron properties such as electronic polarizabilities, with hyperpolarizabilities being increasingly studied owing to their importance for nonlinear optics in molecular electronic devices. These can be calculated by application of perturbation theory. However, calculations to all orders of perturbation theory are more simply and elegantly camed out using finite field techniques, in which a term-pel (scalar product of dipole moment and electric field) is added to the Hamiltonian and the response functions obtained from the relevant energy gradient^.^" In addition, properties which can be calculated as expectation values of the appropriate operator, such as dipole or higher moments, electric field gradients at nuclei, etc, can also be calculated as response functions using finite-field techniques. Since properties are usually determined experimentally from the response of the energy to a given perturbation, finite-field techniques connect most naturally with experiment. Indeed, where the Hellmann-Feynman theorem does not hold (Le., where the wave function is not fully optimized), finite-field techniques are formally correct while the expectation value method is not; a discussion and illustrative calculations for this point are presented in ref 7. In addition to equilibrium properties, gradients with respect to nuclear coordinates can be calculated, leading for example to predictions of infrared and Raman fundamental line intensities. Calculations of both electronic and nuclear gradient properties have been a major interest area in our group for a considerable time (see, e.g., refs 8-1 8 and references therein). Oh, D. H.; Boxer, S.G. J . Am. Chem. Soc. 1990,112,8161. Oh, D. H.; Sano, M.; Boxer, S.G. J. Am. Chem. Soc. 1991,113,6880. Cohen, H. D.; Roothan, C. C. J. J . Chem. Phys. 1965,43,534. Hush, N. S.;Williams, M. L. Chem. Phys. t e f f . 1970,5, 507. ( 5 ) Hush, N. S.;Williams, M. L. Chem. Phys. tetr. 1970,6, 163. (6) Hush, N. S.;Williams, M. L. Theor. Chim. Acra 1972,25,346. (7) Rendell, A. P. L.;Bacskay, G. B.; Hush, N. S.;Handy, N. C. J . Chem. Phys. 1987,87,5976. (8) Gready, J. E.; Bacskay, G. 8.; Hush, N. S . Chem. Phys. 1977,22,141. (9) Gready, J. E.; Bacskay, G. 8.;Hush, N. S.Chem. Phys. 1978,31,375. (IO) Gready. J. E.; Bacskay, G. B.; Hush, N. S. Chem. Phys. 1978,31, 467. ( I I ) John, I. G.;Bacskay, G.8.; Hush, N. S.Chem. Phys. 1979.38,319. (12) John, 1. G.; Bacskay, G. B.; Hush, N. S.Chem. Phys. 1980,51,49. (13) Swanton, D. J.; Bacskay, G. 8.; Hush, N. S.Chem. Phys. 1983,82, 303. (14) Swanton, D. J.; Bacskay, G. B.; Hush, N. S.Chem. Phys. 1984,83, 69. (15) Swanton. D. J.; Bacskay, G. 8.; Hush, N. S . Chem. Phys. 1986,107, 9. (16) Swanton, D. J.; Bacskay, G. B.; Hush, N. S.Chem. Phys. 1986,107, 25. (1) (2) (3) (4)
These include the effects of a lied electric fields on vibrational properties ("Stark tuning")lgJgand, more recently, electric field modulation of switch rate and memory in mixed-valence molecular switches.21 If we turn from ground states to excited states, we find that there has been a surprising lack of both theoretical and experimental activity in the molecular (as distinct from solid-state) area. The study of the effects of electric fields on molecular (including molecular ions) electronic absorption or emission spectra has experimentally been mainly limited to organic charge-transfer complexes, although some work on transitions in single molecules has also been carried out. An example of the latter is the work of Scheps and Lombardi of field-induced perturbations in the s-triazine absorption spectrum.22 Very little work has been carried out on inorganic systems, apart from isolated studies of Stark splitting such as that of the 726-nm 'TIstate of permanganate ion23and the crystal spectrum of KCr03C1.24 This is particularly surprising, since the simplest (crystal field) interpretation of the excited states of transition-ion complexes is basically in terms of Stark splitting of the free ion states, and a natural extension would be to consider the effects of additional perturbations due to externally applied fields. The recent work of D a v i d s ~ o n in ~ ~this .~~ area is more relevant to the topics discussed here. In this paper, a brief outline is given of the major effects of electric field perturbations upon molecular electronic spectra; this forms the basis of electroabsorption (EA) spectroscopy. The theoretical approach originates in the work of Li~tay,~'-~O with modifications such as those of Varma3' and of Lin.32 Considerable simplifications to the general equations are introduced herein, based upon geometrical relationships which are expected to be (17) Cummins, P. L.; Bacskay, G. B.; Hush, N. S.J . Phys. Chem. 1985, 89, 2151. (18) Cummins, P. L.:Bacskay, G. B.;Hush, N. S.;Halle, B.; Engstrom, S.J. Chem. Phys. 1985,82,2002. (19) Hush, N. S.;Williams, M. L. J . Mol. Specrrosc. 1974, 50, 349. (20) Gready, J. E.; Bacskay, G. B.; Hush, N. S.J. Chem. Soc., Faraday Trans. 2 1978. 74. 1430. (21) Hush,". 8.;Wong, A. T.; Bacskay, G. B.; Reimers, J. R. J . Am. Chem. Soc. 1990,112, 4192. (22) Scheps, R.; Lombardi, J. R. Chem. Phys. 1975,10,445. (23) Johnson, L. W. J . Chem. Phys. 1983,79, 1096. (24)Hsg, J. H.; Ballhausen, C. J.; Solomon, E.I. Mol. Phys. 1976,32,
"". . xn7
(25) Davidsson, A. Chem. Phys. 1980,45,409. (26) Davidsson, A. Chem. Phys. Leu. 1983,65,101. (27) Liptay, W. In Modern quanrum chemistry; Sinanoglu, O., Ed.; Academic Press: New York, 1965; Vol. 111, p 45. (28) Liptay, W. Angew. Chem., Int. Ed. Engl. 1969,8, 177. (29) Liptay, W. In Excited slates; Lim, E. C., Ed.; Academic Press: New York, 1974; p 129. (30) Liptay, W. Eer. Eunsenges. 1976,80, 207. (31) Varma, C. A. G. 0. Helu.Chim. Acra 1978,61,773. (32) Lin, S.H. J . Chem. Phys. 1975,62,4500.
0022-365419 1/2095-9713%02.50/0 0 1991 American Chemical Society
9774 The Journal of Physical Chemistry, Vol. 95, No. 24, 1 9’91 applicable for metal to ligand and intervalence transitions of inorganic complexes.1*2In a subsequent paper” on the electroabsorption of bismetal complexes, we extend the theory to include the electroabsorption of states which arise from coupled degenerate localized excitations. There, the transition and dipole moment become functions of the nuclear coordinates and so the basic Liptay approach does not apply. Recent experimental work on the electric field perturbed spectra of biological and transition-metal complexes by Boxer’s group at S t a n f ~ r d I * ~isJcausing ~ ~ ’ a resurgence of interest in the potential of such measurements. In particular, we concentrate upon the results presented2 by Oh, Sano, and Boxer (OSB) and an earlier preliminary communication1 which describes the EA of complexes Ru”(NH,),L, where L is pyrazine (pz), pyrazine-H+ (pzH+), 4,4’-bipyridine (bpy), and 4,4’-bipyridineH+ (bpyH+), as well as the appropriate R U ~ ~ ( N H ~ ) , L R U ~ ~and ( N HR~U) ,” ( N H ~ ) ~ L Ru111(NH3), bisruthenium complexes. Here, for the monoruthenium complexes only, we present an independent analysis of their averaged raw data that concentrates on different aspects of the problem. OSB concentrated upon presenting the most reliable values for the EA spectra in 50% glycerol/water and interpreted their results using the most likely model of the spectroscopy. Thus, the error limits that they present represent the precision of their experimental technique. We, however, concentrate upon the molecular properties that are deduced from the spectra. Our analysis is based upon averaged experimental data, and so our error limits do not reflect the experimental precision; rather, we consider both the effects of the solvent and of different interpretations of the spectroscopy upon the deduced molecular properties; our error limits thus reflect the accuracy by which these parameters are deduced. The deduced molecular parameters are rationalized using the simplest possible analytical model for the electronic structure of the complexes. For the monoruthenium complexes, this is a two-level model comprising of only the Ru-d, level and the ligand LUMO level: subsequently,” for the bisruthenium complexes, we use a three-level model comprising of the two Ru-d, levels and the ligand LUMO. In all, three parameters per complex are introduced and used to describe up to six properties per complex. Inspiration for the model comes from our previous full-r electronic structure calculations for some of these complexes presented in part 1 38 and from calculations of the spectroscopic properties of ruthenium c o m p l e x e ~ . ~ ~ . ~ Numerical data are generally given in atomic units (au) or in wavenumbers (cm-I). Conversion factors for those most commonly occurring are as follows: field strength, 1 MV/cm = 0.000 194 5 au; energy, 1 cm-’ = 4.558 X IO” au; dipole moment, 1 D = 0.2082 e A = 3.336 X IO”O C m = 0.3935 au; length, 1 A = 1.8897 au; polarizability, 1 A3 = 6.7483 au; electroabsorption D, m2/V2 = 2643 au; electroabsorption F, IO4 C m2/V2 = 6.063 au; electroabsorption H,10- C2 m2 = 0.01391 au. 2. Classical Theory of Electroabsorption
We first assume an isotropic sample, with an isolated absorption envelope corresponding to a single molecular electronic transition. A perturbing external electric field is applied, such that the vector internal field at the molecular site is Fint;the relation between the internal field Fintand the external applied field Fappis usually assumed to be Fint
=Fapp
(1)
(33) Reimers, J. R.; Hush, N . S.J . Phys. Chem., manuscript in preparation. (34) Lockhart, D. J.; Boxer, S.G. Chem. Phys. Left. 1988, 144, 243. (35) Lockhart, D. J.; Goldstein, R. F.; Boxer, S.G. J . Phys. Chem. 1988, 89, 1408. (36) Boxer, S.G.; Goldstein, R. A.; Lockhart, D. J.; Middendorf, T. R.; Takiff, L. J . Phys. Chem. 1989, 93, 8280. (37) Oh: D. H.; Boxer, S. G. J . Am. Chem. Soc. 1989, 111, 1130. (38) Reimers, J. R.; Hush, N. S.In Mixed valence sysfems: Applications in Chemistry, Physics. and Biology; Prassides, K., Ed.; Kluwer Academic Publishers: Dordrecht, 1991; pp 29-50. (39) Reimers, J . R.; Hush, N. S.Inorg. Chem. 1990, 29, 3686. (40) Reimers, J . R.; Hush, N . S.Inorg. Chem. 1990, 29. 4510.
Reimers and Hush The proportionality constantf is the local field c ~ r r e c t i o n ; ~this l*~ is generally greater than unity. For a spherical cavity in a dielectric material, this is given by the Lorenz equation4’ florcnz
= (e + 2)/3
(2)
where, in eq 2, t is the dielectric constant. For the polar polymeric or glass matrices used in the work of OSB,2 a reliable estimate for f is not yet available: however, it is likely to be in the range 1 I f I 1.3.2 In their paper,2 OSB chose to present the most accurate results possible; thus, they reported, e.g., fAp rather than A p itself. Here, we are concerned with the significance of the physical parameters; we thus assume that f = 1 .I 5 f 0.15 and report Ap itself, etc. There are four principal effects arising from the electric field perturbation: 1. At finite temperature in a fluid solvent, the molecular distribution will become anisotropic where the molecule possesses a dipole moment an&/or has anisotropic polarizability. Experiments on highly charged ions, of the kind we are concerned with here, will however generally be carried out in rigid matrices such as poly(viny1 alcohol) or glycerol/water films. In this case we can make the infinite-temperature approximation and assume that the original isotropic distribution is maintained in the presence of the field. 2. The transition moment vector M may be modified. 3. The energies of initial and final states may change. 4. The shape function S(v) of the absorption envelope may change. A second assumption is that the changes mentioned in effects 1 and 4 are zero, so that effect 3 gives the absorption spectrum t(Fint)in the presence of a field of magnitude Fin,= IFintlas the isotropic sample average of v M2(Fint) S(v - vm(Fint))
(3) where v,,,(Fint)is the frequency of the absorption maximum, the Stark shift Av is given by the isotropic average of hAv(Fin,) = hv,(Fint)
- hv,(O) = -ApFint - f/zFint.Aa.Fin, (4)
and Ap and Aa are, respectively, the changes in dipole moment and polarizability on going from ground to excited state. It is assumed that all sublevels of the initial electronic state have the same dipole moment and polarizability; a similar assumption is made for the final state. The transition moment in the presence of the field (effect 2) can be expressed to the second order as M(Fint) = M
+ A*Fint+ Fint.B.Fint
(5)
where A and B are, respectively, the transition polarizability (second-rank) and hyperpolarizability (third-rank) tensors. We calculate the isotropically averaged perturbed spectrum t(Fht)for the experimental situation in which the linearly polarized light passes through a sample held between two electrodes in a configuration such that the propagation vector of the light is perpendicular to the direction of the field, with the electric polarization vector e making an angle x with the direction of the field. If the angle between the vectors M and Ab is 5; we then define a sensitivity function R ( x ) as R(x) = [5
+ (3 Cos2 f -
1)(3
COS*
x
- 1)]/15
(6)
In their experiments,* OSB used a range of values of x and deduced for several complexes considered herein that M and Ap are parallel, implying { = 0. Subsequently, we assume that { = 0 for all of the complexes considered herein. Thus, when the mutual orientation of polarization vector e and field direction is the magic angle x = cos-’ 3-II2, R ( x ) reduces to the value The results of OSB2 which we quote herein are obtained at the orientation x = 90°,giving R ( x ) = Further, for the systems discussed here, we extend the { = 0 assumption. While a general solution for the spectroelectric effect (41) Bottcher, C. J. F. Theory of electric po1arizafion; Elsevier: Amsterdam, 1973; p 176.
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9775
Ru(l1) Electroabsorption Spectroscopy SPECTRA
DIFFERENCE f 5
W
Figure 1. Left: Field-free absorption e' a t / u (solid line) and the change (translation or scaling at constant band shape) of this band in response to an applied field. The response of the A and A p terms is proportional to F and the short- and long-dashed curves indicate the response to fields orientated parallel and antiparallel. The response of the Band Aa terms is proportional to P and is given by the dashed curves. Right: Averaged difference spectra proportional to either the absorption band strength t' or its first or second derivatives.
This description of the anticipated results of electric field perturbation of absorption band envelopes is based on the assumption that the shape function S(u) does not change so that eq 3 is valid. As described in part 13* and demonstrated in part 333for bismetal complexes this is not necessarily so because the parameters M , Ap, etc, become strongly dependent upon a nuclear coordinate. In such cases, the classical Liptay equation, eq 7, is not appropriate. Recent work of Liptay et al.424 on centrosymmetric systems leads to similar conclusions. A further expected feature of interest in the electric field perturbation effect is that bands of extremely low intensity in the unperturbed absorption spectrum may appear as distinct features in the perturbation difference spectrum, thus providing useful information about the location, identification, and properties of possibly hitherto unknown states. This should be a most useful feature but may also lead to difficulties in analysis when there is close overlap of bands with strong electric field response.
3. Electronic Structure Model In part we performed full r-electron calculations for some of these complexes. Often, the simplest possible model for the electronic structure, a model containing just two molecular orbitals, gave very similar results to the full r-electron calculation for the in terms of all of the tensor components of M,A, B,Ap, and A a properties considered therein. As such an analytical model presents is easily obtained, we assume that all of the electronic properties a concise, chemically intuitive picture of the complexes, it is of the metal to ligand transitions of these transition-metal comemphasized here in preference to more extensive electronic plexes are dominated by only one component, M,,A,,, B,,, Ap,, structure calculations. Models of this form were suggested by and Aaz,, respectively, of each of the tensors; we write this comZwickel and C r e u t ~ . ~ ~ ponent as M , A, B, AM,and A a , respectively. Here, the positive The two orbitals considered are the metal tZgorbital of d, z direction is taken to be the direction from the metal to the symmetry and the ligand's LUMO orbital. Initially, these orbitals aromatic ligand (note that this convention sets the direction of are separated in energy with the ligand orbital lying e,, above the the electric field vector and hence the sign of A p and A). Possible metal orbital. They are then coupled together by an interaction contributions from other tensor components are discussed, when matrix element 8. A third parameter r is introduced as the appropriate. With the above assumptions and conditions, the L i p t a ~ ~ ' - ~ * effective distance through which an electron is transferred during the M L transition of the uncoupled orbitals (the associated equations simplify so that the observed EA response A d can be dipole moment change is Ap = -r). Naively, one would set r to expressed in terms of the field-free extinction coefficient as ro, the distance between the metal atom and the center of the ligand; as is shown later, however, this effective distance is modified by the presence of the nearby ammonia ligands and solvent molecules. Finally, the Hamiltonian for monoruthenium comwhere the normalized absorption spectrum t' is given by plexes in the presence of an external field is given b ~ ~ " * ~ ~
-
and the EA response functions are given by
Diagonalization of this matrix gives the absorption maximum at (9)
+
hum = (eo2 4j32)1/2
(13)
and the transition moment as
H = Ap2 (11) The electric field perturbation is thus a superposition of three terms. To illustrate their origin, we plot in Figure 1 a field-free absorption band, its change in turn due to the terms A, B, Ap, and Pa in eqs 5 and 4 when a field is applied parallel and antiparallel to the dipole direction, and the resulting averaged difference spectra. The first term, D, has the shape of the unperturbed band envelope and will thus be referred to as the "constant" term. It is influenced only by the transition moment polarizability A and hyperpolarizability B; see Figure 1. The second term, F, has the shape of the first derivative of the unperturbed absorption envelope. It is influenced by the polarizability change (see Figure 1) and a cross-term between the transition moment polarizability and the dipole moment. The third term, H. has the shape of the second derivative of the unperturbed absorption envelope and is proportional to the square of the dipole moment change Ap; see Figure 1. Some of the spectra presented later are expected to show no dipole moment change, and the fitted value for H is found to be small but negative. In such cases, we set H to zero.
Given experimental M and u,, it is easy to invert these two equations and obtain expressions for leal and 181:
The sign of p is immaterial, but the sign of eo is important as it determines the sign of A and Ap: For all complexes considered herein, electrochemical evidence indicates that eo is positive." In (42) Liptay, W.; Wortmann, R.; Schaffrin, H.; Burkhard, 0.;Reitinger, W.; Detzer, N . Chem. Phys. 1988, 120,429. (43) Liptay, W.; Wortmann, R.; Bohm, R.; Detzer, N. Chem. Phys. 1988, 120, 439. (44) Wortmann, R.; Elich, K.;Liptay, W. Chem. Phys. 1988, 124, 395. (45) Zwickel, A. M.; Crcutz, C. Inorg. Chem. 1971, 10, 2395.
9776 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991
this fashion it is possible to express all of the EA response functions in terms of the experimentally well-determined properties M and u, as well as the adjustable parameter r. This gives Ap
= -sign (e,) X (9 - 2 h f ) ’ / 2
-
-A= -
M
(17)
(18)
hum
where a is the coefficient of the metal orbital in the bonding molecular orbital. Thus, the EA response functions become
D= F=
3r2 - 8M
h2um2
(23)
2AAp -- -2Ap2
IPI*
IO3 cm-’ 8.0 9.39 4.05 3.31
a
4,. e
0.896 0.726 0.976 0.978
0.39
pzH+ 1.oo 0.95 17.2 0.10 bpy 14.7 0.09 bpyH+ ‘The uncertainty in r reflects the uncertainty in the experimental data to which r is fitted and implies uncertainty in the other quantities.
-
experimental data. In Table I the values of u,, M , and r used to describe the M L spectra of the RU”(NH,)~complexes of pz, pzH+, bpy, and bpyH+ are given. The uncertainty given for r in this table indicates the range through which it may be varied without significantly affecting the comparison between observed and calculated properties.
All of the experimental data analyzed in this paper are taken from the results of OSB2at x = 90’. For the absorption spectra, the normalized spectral line shape e’ 0: t ( u ) / u is constructed so that its maximum value is unity (eq 8). Small amounts of noise present in the experimental spectra make differentiation of this function difficult; hence, it is first fitted as the sum of a number of curves of Gaussian shape; i.e., we construct
- u - Umi)2
hum
e’
and hence this two-level model predicts that the two contributions to F i n eq 10 always have opposite signs. Note, however, that for large ligands like bpy with closely spaced virtual orbitals, excitations arising from the LUMO orbital may cause Pa to become positive.38 Whenever 0.466 < a < 0.888, B / M is expected to be negative and thus the two contributions to D in eq 9 would also have opposite signs. Thus, estimating bounds for Aa, A, and E based entirely upon experimental D and F information (as attempted in ref 2) is a very hazardous procedure. A useful quantity is the charge involved in 7r back-bonding qT, which is given by
- a2) = 1 - sign (e,)
3.2 i 0.3 3.1 16 6.3 i 0.6 7.9 f 0.8
IO’ cm-’ 12.2
Data
2r2 - SM2 hvm
Note that the cross-term in eq 10 is predicted to always by positive
qT = 2(1
PZ
e,*
r,‘ au
4. Extraction of Molecular Parameters from Experimental
H=r2-2hf
M
TABLE I: Parameters r , e,,, and /3 Used in the Electronic Madel of the Monoruthenium Complexes (Deduced Metal Coefficient on the Occupied Orbital, a , and the Charge Transferred to the Ligand via I Back-Bonding, q.* Also Given)
ligand
-2Mz
Aa =
Reimers and Hush
x
( y)”, 1-
(25)
The reduction of IApl below r embodied within eq 17 may be viewed as being a consequence of this back-bonding. The metal atom has in fact three orbitals oft,, symmetry: the d, orbital, which interacts strongly with the ligand, and two other orbitals, which point away from the ligand and therefore interact weakly. For ruthenium and osmium complexes, this weak interaction may produce weak absorption bands either in the red tail of the main absorption band or, for the pzH+ complex, in the far-infrared r e g i ~ n . ~ ~ ~Within ~ ’ ” ~the framework of the above electronic model, the absorption frequency of this band is given by hut,# = (eo + hvm)/2 (26) Ligand field effects, however, introduce a tetragonal splitting to the tzs orbitals which is expected to reduce this frequency slightly. The effective distance r is treated as a free parameter, its value chosen to give the best agreement of Ap, D, F, and with (46) Ford, P.;Rudd, D. F. P.; Gaunder, R.; Taube, H. J . Am. Chem. Soc. 1968, 90, 1187. (47) Lauher, J. W. Inorg. Chem. Acto 1980, 39, 119. (48) Creutz, C.: Chou, M.H. Inorg. Chem. 1987, 26, 2995. (49) Winkler, J. R.; Netzel. T. L.;Creutz, C. C.: Sutin, N. J . Am. Chem. Soc. 1987, 109, 2381. (SO) Magnuson, R. H.; Taube, H. J . Am. Chem. Soc. 1975, 97, 5129.
= .a,exp[ i
( 2a:
]
(27)
where ai is the intensity of the ith Gaussian whose center is a t umi and whose standard deviation is ai.A typical root-mean-square error for this procedure is 0.01-0.1% of the absorption maximum, but this is related to the noise level of the experimental data. We choose a Gaussian curve because such a bandshape is predicted by the central-limit theorem in the case that the Franck-Condon envelope is constructed from a large number of slightly displaced oscillators and because this functional form is well suited for the representation of non-Gaussian bands. In fact, for the inorganic complexes considered herein, the observed line shapes are noticeably non-Gaussian; alternative methods for handling this, such as the use of skewed Gaussians, contain regions of their parameter space which are nonphysical, and so can be difficult to work with. Also, the observed spectra usually show contributions from bands attributable to different electronic transitions. As each such electronic transition will have associated with it its own particular EA response, it is important to deconvolute the observed absorption spectrum before fitting of Liptay’s equation can commence. Thus, after constructing the component Gaussians in eq 27, we sum Gaussians together to form bands and then sum these bands to form the total absorption spectrum. While this partitioning of the absorption into bands is somewhat arbitrary, it is performed using chemical insight and the use of Gaussian functions ensures that the resultant deconvolution is chemically sensible. We quote error bars on extracted quantities which reflect their sensitivity to changes in the Gaussians used in the expansion Gaussians, eq 27, as well as to changes in the partitioning of the Gaussians into bands. Once the absorption is partitioned into bands, the bands are differentiated analytically and the unknown coefficients in eq 7 are determined by constructing the least-squares solution to the overdetermined set of linear equations which result. For all of the complexes considered herein, the observed absorption spectra show similar features: Three absorption bands are discernible of which the central band is strong and the two side bands are weak. Always, the upper side band shows no EA response and is thus ignored. Failure to correctly extract this component leads to extra features in the fitted spectra at high frequency, but this is not a problem as the calculated EA response
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9777
Ru(I1) Electroabsorption Spectroscopy
TABLE 11: Deduced Values of the Liptay CoeMcients W ,W ,and HP Obtained from the Averaged Experimental Data of Oh, Sam, and Boxer' for the Strong Band9 ligand transition Y, IO3 cm-l D/*,IO3 au Ff2, IO3 au Hf2, au DJH, au FJH,au DJF, au DZ M-L OSB 20.1 -3.4 f 3.4 0.055 f 0.04 4.45 f 1.4 0.07 f 0.04 4.7 f 0.8 -500 f 1500 12 f 5 -100 f 200 20.1 -2 f 6 obs
pzH+
$--
$+
pzH+
tZ8-$+
bPY
M-L
bpyH+
model ZlNDO OSB obs-A obs-B obs-C obs-C obs-D obs-D obs-E obs-E model obs OSB obs model OSB obs model
M-L
[20.1] [20.2] 18.8 20.1 20.1 18.1 20.0 17.5 19.0 17.9 19.4 [18.8] 9.9 19.2 19.0 [ 19.01 16.0 16.1 [16.1]
0.8 f 0.3 1.5 f 0.4 0.40 f 0.19 Of6 -12 8.6 -28 -72 -10 70 -40 -1.8 f 0.6 -77 8.7 f 2.1 l2f7 16f6 1 9 f 11 Of35 3 7 f 13
4.9 f 2 12.2 f 4 0 0 f 0.01 0 f 0.01 0 f 0.01 0 f 0.01 0 f 0.01 0 f 0.01 0 f 0.01 0 f 0.01 0.0003 4.9 38.4 f 1.0 40 f 1 4 4 f 15 6 0 f 13 67 f 2 71 f 24
0.063 f 0.022 0.013 f 0.005 -0.23 f 0.04 -0.25 f 0.05 -0.18 -0.28 -0.22 -0.30 -0. IO -0.35 -0.35 -0.075 f 0.025 0.35 1.37 f 0.06 1.3 f 0.1 0.96 f 0.3 2.4 f 0.6 2.6 f 0.1 1.9 f 0.6
12
150 94
12 90
1
0 f 20 70 -30 130 240 100 -200
I IO -.I 6000
23 -220
72
320 f 180 370
32 f 4 22
0 f 500 520
39 f 1 26
IO* 5 17
O f 15 20
"Key: OSB,results as given in ref 2, the error bars representing the precision of the experimental data; obs, results obtained herein, error bars indicating uncertainties arising from ambiguities with the interpretation of the experimental data as well as from solvent effects; A-E, obtained using the interpretations of the absorption spectrum given in Figure 4; model, calculated from the electronic structure model, error bars reflecting the experimental uncertainty in f 2 and brackets indicating values treated as parameters in the model; ZINDO, results of preliminary ZINDO5I calculations. TABLE 111: Deduced Values of Molecular Parameters for the Well-Resolved Bands As Obtained from the Averaged Raw Data of Oh, Sano, and Boxer2 (Assumed Values Enclosed within Brackets) ligand transition Y,, IO3 cm-l M,au Ap: au Aa, au A, lo3 au B, lo3 au PZ M-L obs 20.1 1 .8b -1.9 f 0.5 ZlNDO [20.2] 2.1 -3.5 -I 80 -0.032 0.99
pzH+
$--$+
pzHt
bzp
bPY bpyH'
M
-
L
model obs model obs obs model obs model
[20.1] 18.8 [ 18.81 9.9d 19.0 [ 19.01 16.1 [16.1]
[ 1.81 2.2c P.21 0.48e 1
.sr
v.91 2.2f [2.21
-7 1 -400 f 200 -1 IO
[-1.941 0 f 0.1 -0.02 -3.2 f 1.6 -5.4 f 0.9 [-5.71 -7.2 f 0.9 [-7.261
-0.004
0.1 1 Of6 -1.4
-83"
-0.13
7.3
-1 3V
-0.22
-0.038
PI
20
"Signs of observed Ap's are set to those given by the model. bFrom ref 49. See also refs 46 and 48. The half-width and transition moment reported in ref 59 appear to be in error. From ref 49. d9.9 f 0.2 from the model eq 26. CEstimatedusing M for Ru"(NH,),pz and OSBs intensity ratio. This band is enhanced compared to room-temperature solution spectra for which M = 0.27 a ~ . /Estimated '~ using Y, and t data from ref 62, approximating the bandwidth by temperature scaling the spectra of OSB.2 "ull *-electron calc~lations~~ indicate that an addirional contribution of -+300 au arises from a T* T* transition within the ligand of these complexes.
-
of the strong band is insensitive to this effect. The identity of the non-EA-active component of the absorption is uncertain. Only for the pzH+ complex is the lower band fully resolved. Analysis of this band is, in general, difficult, but analysis is consistent with the notion that his band is the tzs L band, displaying slightly enhanced Ab and significantly enhanced either Aa,A, and/or B. Also, for the pzH+ complex, the EA spectra indicate that the strong central band itself consists of two different components. When two bands with different EA responses overlap, analysis is difficult because assumptions made as to the deconvolution can change dramatically values deduced for the smaller terms. This is true even when one band is rather weak. Usually, however, the dominant term of the dominant band is well determined and invariant to the analysis method. The deduced EA response parameters D,F, and H for the resolved bands are given in Table 11; calculated properties for these bands are given in Table 111. In Table IV is given available information for the poorly resolved low-frequency tails: As these parameters are speculative, no error bars are estimated. Insufficient information is available to resolve uniquely both the constant ( D ) and linear (F)terms for these shoulders: The results given in this table are all obtained assuming that the first-derivative term is more significant than the constant term for the poorly resolved bands. Reversing this assumption can give equally good fits to the EA response but changes the sign of the constant
-
TABLE I V Deduced Values of the Liptay Coefficients W ,W , and IApl (Assuming f = 1.15 f 0.15) Obtained from the Averaged Experimental Data of Oh, Sano, and Boxel3 for Weak Bands Overlapctine the Primarv Band ulh, io3 cm-' Of2, Ff2, IArl, ligand transition model obsd IO3 au IO'au au tz8tZgtz8
-
PZ
bpy
L L
16.2 18.0 15.4
17 16.1 13.4
[O]" [O]" [O]"
0.9 -0.3 -0.6
3.2 5.9 8.5
L bpyH+ " Insufficient information is present in the data to determine uniquely both D and F; alternative interpretations with D large and F small are possible.
contribution to the EA of the main central band. Thus, values for D for the main band are very difficult to determine reliably. 5. M
-
L Absorption of R u * ~ ( N H ~ ) ~ ~ z The observed2 absorption spectra are shown in the lower panels of Figure 2 taken in two different matrices at 77 K. In the other panels of this figure are given the observed difference spectra a t x = 90'. We fit this to eq 7 assuming that the first and second components have different EA responseswhile the third component is not EA active. Two rather different fits per solvent are given in this figure: The upper fits correspond to the results given in
9778 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 50% GLYCEROL/H&
PVA
I
Reimers and Hush Excellent agreement is seen between the deduced and model values for A p = -1.9 au as r is adjusted essentially to fit this observable. Values of D f and F f are consistent, but a better test for accuracy of the calculated weak components is to compare the ratios D / H and F / H . These ratios are not affected by the value offand are given in Table 11. Good agreement is seen for F / H , but it is too difficult to determine D / H accurately from experiment because of the sensitivity of this ratio to assumptions made about the weak low-frequency shoulder. It is not possible to extract uniquely values for the molecular properties Pa,A, and B from the experimental data because only two independent pieces of information, D and F, are available. Values of the molecular properties calculated from the model are given in Table I11 and are expected to be quite reliable. As suggested earlier, F is given as the difference of two quite large numbers from eq 10, and D is given as the sum of two small terms from eq 9. Results from the preliminary ZINDO calculations are encouraging and present the same qualitative description of the electronic structure of this complex as does our model. ZINDO predicts a larger A p of -3.5 au, but given the complex nature of the origin of this term discussed later, the prediction of such a small value by ZINDO is encouraging. The small value of F predicted by ZINDO (see Table 11) arises perhaps due to an overestimation by a factor of 2 of the polarizability change Pa, giving rise to an accidental cancellation of the two (large) terms in eq 10. It is difficult to draw conclusions concerning the properties given in Table 1V for the weak band at ==17000cm-'. Evidence to suggest that this is the tZg L band comes from eq 26, which predicts the frequency of this band at 16000 f 1000 cm-I (see Table IV; the error bar here is derived from the uncertainty in r), and from the conclusion that Ap for this band is slightly larger than that for the strong M L band. The all-valence ZINDO calculation contains all of the d and u orbitals and is in principle capable of interpreting this band. Unfortunately, this is not a simple task because the ZINDO results are somewhat model and solvent dependent and the number of states of similar energy makes polarizability, etc., calculations hazardous. The tZg L transitions can obtain intensity from both Franck-Condon and vibronic mechanisms and would be expected to have the same orientational properties as for the main transition, as observed by OSB.2 It is not known to what extent the results given in Table IV can be trusted, but such transitions should have large polarizabilities and transition moment hyperpolarizabilities due to the presence of very close lying additional excited states. The value fitted for the free parameter r for this complex is 3.2 f 0.3 au, considerably less than the distance from the metal atom to the center of the ligand, ro = 6.6 au. Such a small value may seem surprising, but it is not unreasonable in light of the fact that the value necessary to fit the ZINDO values of EML(II), M, and Aa is r = 4.3 au. In order to locate the cause of such a reduction in the effective charge separation, we examine the effects of the NH3 ligands. Each of these has an associated polarizability; corrections to the non-back-bonded dipole moment change A p = -ro arise from interaction of the electric field with the ligand polarizability inducing a ligand dipole moment which interacts with the metal-ligand permanent charge distribution. The result is that the M L transition energy changes proportionally to both the applied electric field and the ammonia polarizability. Such a contribution thus modifies r in eq 12. Other contributions arise from the interaction of an induced dipole within the metal-ligand system with the permanent dipoles of the ammonia ligands. In total, we consider the following interactions of the chromophore with the ammonia ligands: (1) induced Ru charge interacting with five ammonias, (2) induced ligand charge interacting with collinear ammonia, (3) induced ligand charge interacting with four perpendicular ammonias, (4) induced axial ammonia dipole moment interacting with permanent Ru and ligand charges, (5) induced perpendicular ammonia dipole moments interacting with ligand charge, and (6) induced Ru charge
-
Figure 2. Field-free absorption spectrum t' 0: t / u (resolved into two bands) and the EA difference spectrum Ad of Ru"((NH,),pz in poly(viny1 alcohol) (PVA) and in 50% glycerol/water at 77 K and x = 90°. For A d , the solid line is the spectrum of Oh, Sano, and Boxer2 and the short-dashed line is the total of the Liptay fit to both bands, while (0) long dash and ( 0 )are the constant, first- and second-derivative components, respectively, of just the strong M L band. Two different fits per solvent are given; the bottom fits are unconstrained while the top fits are constrained so that the weak band has no constant component.
-
Tables 11-IV and are obtained by constraining D = 0 for the weak bands; the lower fits have no such constraint. Note how variations of the solvent and of the fitting technique cause considerable changes to the deduced contributions of the weak constant and first-derivative terms of the main band. Large uncertainties are thus quoted for these parameters and the properties derived from them. Alternatively, the dominant second-derivative nature of the observed EA response is somewhat solvent dependent but quite stable with respect to details of the band deconvolution. The parameters deduced by OSB2 for the strong band based upon the assumption both it and its low-frequency tail have the same EA responses are also given in Table 11. Note that their error bars are set to reflect the precision of the experimental data in 50% glycerol/water given just one possible spectral interpretation. The precision of the experimental technique is considerably greater than is its ability to yield accurate molecular properties. Molecular properties and EA responses evaluated using the two-level electronic structure model are also given in Tables I1 and 111. Further, for this complex only, we give some preliminary results obtained using the Z1ND05'*52program. This is an allvalence semiempirical molecular orbital technique which includes explicitly the ammonia ligands and includes via reaction field techniques the effects of solvent. Neither details of the calculation nor a thorough application of the technique is presented herein as the optimum values for the parameters of the second transition series are currently under review by the wider scientific community (e.g., refs 52 and 53). (51) Zerner, M.; et al. ZINDO Quantum Chemistry Package, University of Florida, Gainesville. FL. (52) Anderson, W.P.; Cundari, T. R.;Drago, R.S.;Zerner, M. C. fnorg. Chem. 1990, 29, I .
-
-
-
~
(53) Cundari, T. R.; Drago, R. S. fnorg. Chem. 1990, 29, 487.
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9179
Ru(I1) Electroabsorption Spectroscopy
PYRAZINE
interacting with permanent ligand dipole moment. The ligand-free complex’s polarizability Pa’ induces a dipole moment change of A d F , which we represent as induced charges -A9id and A9id on the Ru atom and the ligand center at distance r, respectively. Note that we assume that the polarizability change ha’ is associated with transitions out of or into the metal orbitals: We shall see later that while this appears to be an adequate approximation for the pyrazine complex, it will not be so for larger acceptors, and so this approach is too simplistic to be applied to bpy complexes. We estimate Pa’ using eq 18 with M evaluated from eq 14 with r = ro and v, increased by the electrostatic interaction of the dipole moment change with the ammonia ligands. This gives A d = -130 au and hence the induced charges are A9ind = Aa’F/ro (28) The interaction of the Ru-induced charged with the five ammonias is IC(NH#-Aqind) AEI -5 - 5ll”~~IAff’F (29) R2 roRZ where R is the ammonia Ru-N bond length. Using the values I+(NHJ.= 0.51 au,54 ro = 6.6 au, and R = 3.8 auSSgives a contribution of -3.55 au to the effective r. The energy of interaction of the induced ligand charge with the axial ammonia is
giving a contribution to r of +0.10 au. Similarly, the energy of interaction of the induced ligand charge with the four perpendicular ammonias is
PYRAZINE-H+ Ill*
JIFigure 3. Upper frame: Weak bonding between the Ru tD orbitals and the ligand LUMO (L) orbital in Ru’i(NH,)5pz. The final orbitals show weak mixing between the LUMO and d, orbitals. Lower frame: Strong bonding within Ruli(NH,)SpzH+. The final orbitals reflect near-equal mixtures of the LUMO and d, orbitals. Arrows indicate the observed absorption bands. B
A
C
E
giving a contribution to r of +0.42 au. If the axialplarizability of NH3, ( a N H J risr ,16.3 au (free molecule value ) and the estimated change in charge on the metal L excitation is A9Ru= 1 - 9 , =, 0.61 e, atom during the M then the energy of interaction of the induced axial ammonia dipole with the Ru and ligand charges is
-
AE4 = (ffNH,)zzAqRuF[R* - ( R + rO)-’] (32) which gives a contribution to r of 0.51 au. The interaction of the induced dipoles on the four perpendicular ammonias is r(-A9Ru)(ffNH,)yf AEs = 4 ( R 2 r 2 ) 3 / 2 (33)
+
where the perpendicular polarizability of ammonia, (aNH3),,), is 13.9 au.54 This gives a contribution of -0.48 au to r. Minor effects such as interaction of induced ligand charge with the ligand permanent moment are ignored. The estimated value of r is thus r = 6.6 - 3.55 + 0.10 0.42 0.51 - 0.48 = 3.6 au, much closer to the fitted value r = 3.2 f 0.3 au (Table I) than is warranted from this highly simplified approach. In conclusion, we see that the appropriate value of r in general will be the result of a number of terms of varying magnitude and sign, which cannot be estimated by inspection, and whose relative contributions to a theoretical value calculated by rigorous methods will be difficult to disentangle. The consequence of this reduction in r is a dramatic reduction in the electric properties M and Ap leading to similar reductions in the EA response. functions. It is not possible to model these properties without modification to the charge separation distance r.
+
+
Figure 4. Field-free absorption spectrum t’ a t / v (lower panels) and the EA difference spectrum A d (upper panels) for RU”(NH,)~~Z in 50% glycerol/water at 77 K and x = 90°.* Five different resolutions of the absorption spectrum into bands are given (lower panels, dashed curves), and the corresponding Liptay fits (upper panels, dashed curves).
simultaneously increases the coupling of the d, orbital to the nitrogen T orbital. Thus, the result is that these two orbitals mix nearly equally and split apart in energy forming two molecular orbitals $+ and Two transitions thus result: a weak solvent-dependent (hence large AM)low-frequency transition from the non-d, t2&orbitals to $+ and a strong solvent-independent (hence small Ap) transition from $- to $+. All of these effects are describable by our electronic structure model: the three parameters of this model are constrained to fit the observed M and Y, for the $- $+ transition and utli (via eq 26) for the tZg J.+ transition. The weak bonding within Ru1i(NH3)Spz is contrasted to the strong bonding within R U ~ ~ ( N H , ) ~ ~inZFigure H+ 6. M L Absorption of Ru”(NH,),pzH+ 3. The absorption spectrum of this complex is w e l l - k n o ~ n . 4 ~ - ~ ~ In Figure 4, frame A, is given the entire observed absorption spectrum of OSB along with the corresponding observed EA According to the Magnuson and Taube assignment,m protonation response. The strong band has a weak EA activity, which shows of the pz ligand reduces the energy of its LUMO orbital and no trace of any second-derivative component (hence, Ap = 0), while the weak band shows considerably enhanced EA activity. (54) Werner, H. J.; Meyer, W. Mol. Phys. 1976, 31, 855. Frame A is obtained by fitting the observed EA spectrum to two ( 5 5 ) Gress, M.E.;Creutz, C.; Quicksall, C . 0.J . Am. Chem. Soc. 1981, 20, 1522. sets of Liptay parameters, but fitting only up to Y = 18 000 cm-I.
-
~
$-.48950
-
-
9780 The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 The deduced parameters and properties are given in Tables I1 and 111. respectively: error bars indicate the sensitivity of the deduced parameters to small changes in the fit cutoff frequency. Clearly, a first-derivative response represents the lower half of the strong band very well, but major deviations occur for the upper half of this band. This suggests that the strong band itself is made up of two components displaying different EA responses. Data for the weak band are very noisy, and all of the band is not observed by OSB, making it difficult to obtain reliable parameters. Clearly, a large constant term is involved, but the value obtained for 1Ap1 is, however, quite reasonable, being of the order of the dipole moment change observed for the tzg L transition of (NH,),Ru"pz. Thus, the observed EA spectra support the existing theory of the structure of (NH3)5R~"pzH+.48-50 Frames B-E give four different interpretations of the experimental data for the strong absorption band. In B, one set of Liptay parameters is used to describe the entire band; the fit produced could well be thought to be quite adequate, but the excellent fit to the lower portion of the band seen in A suggests that B is too simplistic and that multiple bands are involved. Also, interpretation B would be enhanced by the inclusion of an imaginary Ap term, but a theoretical interpretation for such an effect is unknown. Frames C-E show three different deconvolutions of the observed absorption spectrum into two bands. In all cases, it is possible to get near-perfect agreement with the EA spectra, though the nature of the deconvolved bands varies dramatically from C to E. This highlights the difficulty in interpreting experimental data and raises the possibility that undetected effects in the absorption spectrum can cause marked effects in the EA spectra. Intuitively, D and E are unlikely because the final EA spectrum is given as the small difference between two much larger spectra, and the deduced molecular properties differ by orders of magnitude from the ones estimated using our model. One possible cause for the appearance of two bands is the presence of an equilibrium of isolated complexes and ion pairs in the sample. Ion pairing is known to become important in 0.1 M CI- solutions of transition-metal complexes56 and is also important for this ~omplex.~' The spectra from the paired and unpaired species would be expected to show similar orientational properties but could display different EA responses. Repeating the experiments using triflate as a counterion could largely eliminate ion pairing and may lead to simpler spectra. An alternative cause for the appearance of a second band is the possibility that another tzr L transition lies almost degenerate with the main band and gains intensity either through weak Franck-Condon or vibronic coupling with the strong band. Again, two such bands would be expected to show similar orientational properties but different EA responses. In this case, the sum of the squares of the two transition moments, M I 2+ MZ2, is conserved independent of the applied electric field, and assuming that A , = A2 = 0, this condition enforces
Reimers and Hush BPY-H+
1
;i 8
-
-
8I
The results labeled E are obtained by optimizing a parameterization of the absorption into two bands such that the EA spectra show the same A a and obey the constraint in eq 34. Hence, it is possible to interpret the observed data on the premise that another degenerate band is involved; the particular interpretation presented here is unlikely, however, due to the large values of the deduced molecular parameters. From the results given in Table 111 it is apparent that the electronic model underestimates Aa for the intense transition: The Acu is -400 f 200 experimentally and -1 10 from the model. It is possible that effects not taken into account in our simple model account for this difference; alternatively, this difference may arise from solvent effects. The observed value of Aa for the pz complex is apparently solvent dependent (see Figure 2), and solvent de( 5 6 ) Basolo, F.; Pearson, R. G.Mechanisms of Inorganic Reactions, 2nd ed.; Wiley: New York, 1967; p 34. ( 5 7 ) Lay, P. A. Private communication.
1
Figure 5. Field-free absorption spectrum c' a c / v (resolved into two bands) and the EA difference spectrum A& of Ru"(NHJ5bpy and of Ru1*(NH,)5bpyH+ in 50% glycerol/water at 77 K and y, = 90°. For A&, the solid line is the spectrum of Oh, Sano, and Boxer2 and the shortdashed line is the total of the Liptay fit to both bands, while (0)long
-
dash and ( 0 )are the constant, first- and second-derivative components, respectively, of just the strong M L band. pendence of A a for transitions within the Creutz-Taube ion is p o ~ t u l a t e d . lOne ~ ~ cannot ~ ~ ~ ~make ~ ~ a comparison between the observed and model values for B or D because of the large uncertainty in the experimental value of this minor contribution; see the values of D/F given in Table 11. The values used for r, eo, and 0 (see Table I) are all quite reasonable. Increasing the metal-ligand bond order will shorten the metal-nitrogen bond length and thus cause an increase in 6 from that seen in the pz complex. Ab initio calculations58indicate that the structure of the isolated pz ligand's LUMO orbital does not change significantly when one end is protonated, and hence no great change to the electrical length r is expected.
7. M (34)
0
-
L Absorption of R U ' * ( N H ~and )~~~~
Ru"( NH3)sbpyH'
The observed absorption and EA spectra for these complexes are given in Figure 5 , and the observed and model EA responses are given in Tables 11-IV. Qualitatively, the observed absorption and EA spectra are unchanged from those of (NH3)5Ru'ipz. Weak low-frequency tails to the main M L band again makes extraction of the minor EA components for the M L band very difficult. The weak components are identified as the tzg L transitions as their A p is slightly larger than that of the main M L band. Equation 26 underestimates the separation of the M L and L bands by 2000 cm-I, the additional splitting possibly arising from a ligand field tetragonal splitting of the tZg orbitals. No difficulty is experienced obtaining values of r which reproduces the observed A p and negligible D contribution, but it is clear that the model underestimates F / H . All-* electron calculations for the bpy complex38indicate that A a is dominated
--
-
- -
(58) Bacskay, G.B. Private communication.
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9781
Ru( 11) Electroabsorption Spectroscopy TABLE V Coefficients of the Doubkf' Nitrogen Atomic Orbitals on Atoms Nl and N2 to the LUMO Molecular Orbital (Atom N1 Is Never Protonated While Atom N, Is the Atom Protonated in the pzH+ and bpyH+ Molecules) Nl
species PZ pzH+ bPY bPYH+
0.23 0.17 0.19 0.21
N2 0.49 0.35 0.34 0.40
-0.23 -0.27 0.19 0.13
-0.49 -0.55 0.34 0.21
by a large term of ~ 3 0 au 0 arising from a ligand LUMO to higher *-orbital excitation. Addition of this term to F removes most of the difference seen between the observed and calculated F / H ratios for the bpy complex; note, however, that even with this additional contribution to the polarizability change, F is dominated by the cross-term in eq 10. The values used for the parameter 0 are much smaller than the corresponding values for pz complexes, as one expects.s9 This effect is due principally to the reduction of the nitrogen coefficient on the ligand LUMO orbital due to the increased number of orbitals in the 7 system of the ligand. Similarly, r is much larger for the bpy complexes, also reflecting the increased size of the ligand (note that the two rings are strongly c ~ u p l e d ~ ~Pro.~). tonation, however, is seen to reduce r and increase 0 for the pz complex, and vice versa for the bpy complex. The qualitatively different behavior is interpretable based upon the response of the LUMO orbitals of the free ligands to protonation given in Table V. Double-tab initioS8calculations (using a Roos and Siegbahn (7s,3p) basis set contracted to [4s,2p160 for C and N and a Van Duijneveldt (3s) basis set contracted to [2sI6' for H) show that the pz LUMO upon protonation is to concentrate this orbital on the uncharged N atom: hence, r decreases and j3 increases. For bpy, however, these calculations reveal that protonation significantly localizes the LUMO orbital on the charged N atom; hence, r increases and 0 decreases upon protonation, as observed through the increase in Ap. 8. Conclusions
Given the usual geometrical constraints applicable to transitions in coordination complexes, Le., that the electronic transition moment is parallel to the dipole moment change and that the dipole and transition polarizabilities and hyperpolarizabilities have nonzero components only in this direction, Liptay's general equations for the EA response reduce to quite a simple form. Further simplifications arise due to the use on an infinite-temperature approximation appropriate for samples held rigid glasses and not allowed to reorientate under the influence of the applied electric field. One expects that the simplified theory presented herein is applicable to the EA of a very wide range of complexes studied in glasses and thin films. The EA spectra of all four monomeric complexes reported by Oh, Sano, and Boxer2 are interpreted in terms of the simplest possible model for the electronic structure of the complexes. Two bands are seen to dominate the EA spectra: the primary metal to ligand transition and a lower frequency nonbonding t2, to ligand transition which is considerably weaker in absorption but stronger in EA than is the primary band. Only in the case of the Ru"(NH3)5pzH+complex are these two bands resolved in the ab(59) (60) (61) (62)
Richardson, D. E.;Taube, H.J . Am. Chem. Sot. 1983. 105, 40. Roos, B.; Siegbahn, P. Theor. Chim. Acru 1970, 17, 209. van Duijnevcldt, F. B. IBM Tech. Rep. 1971, RJ-945. Lavallee, D. K.;Fleischer, E. B. J . Am. Chem. SOC.1972, 94, 2583.
sorption spectrum, the weak band appearing as a shoulder for the other complexes. Strong evidence is seen to suggest that the intense M L band for the pzH+ complex is itself split into two bands. It is suggested that experiments be performed in order to determine the nature of such possible bands, and the possibility of both ion pairing and vibronic coupling is considered. Molecular electronic properties deduced for the pz and pzH+ are in good agreement with those obtained from chemical, thermodynamic, and other spectroscopic data. Indeed, all of the results obtained are interpretable in terms of the electronic structure models proposed initially by Zwickel and C r e ~ t and z~~ by Magnuson and Taube.% Quantitatively, the difference deduced between the LUMO energies eo of the pz and pzH+ ligands is 11 200 cm-I, close to the value 10 600 cm-' deducedSofor the analogous osmium complex. Agreement is also seen to within 20% for the absolute values of 0 and eo for these c o m p l e x e ~ . 4 ~Most *~ important, we see that conclusions concerning the nature of the dipole moment change upon excitation based upon chemical interpretations of the origin of absorption solvent dependence are verified using EA techniques. While EA spectroscopy provides the opportunity to obtain information concerning electronic states which are weak or hidden in absorption spectra, it correspondingly provides difficulties in the interpretation of its spectra. Analysis is straightforward provided that only one band contributes to the spectrum in any given region, but overlapping bands give rise to complicated EA responses. Qualitatively, the interpretation of these responses usually leads to firm conclusions about the nature of the dominant EA-active features, but it is very difficult to obtain accurate quantitative information because assumptions must be introduced during deconvolution of the absorption band contour. In particular, the minor EA-active contributions from the strong absorption band are very difficult to determine in the presence of an additional poorly absorbing but highly active band. Considerable care must be taken with the interpretation of EA spectra. In a subsequent paper,33we investigate the EA of the bis-metal complexes (including the Creutz-Taube ion) studied by Oh, Sano, and Boxer2 (some preliminary results have been presented in part 138). There, all of the EA responses are interpreted in terms of the same processes seen herein; analysis is complicated, however, because the EA of the main band often decreases while that of the tz8 L transition increases, making the weak band in the absorption spectrum the dominant band in the EA spectrum. Also, the nuclear coordinate dependence of the transition and dipole moment of these complexes leads to non-Liptay behavior, further complicating the spectra. Finally, the simple electronic structure model presented herein is not adequate for describing the electronic properties of the Creutz-Taube ion, due to strong configuration interaction between the intervalence and M L transitions. +
-
-
Acknowledgment. We are most grateful to Prof. S. Boxer and Mr. D. Oh (Stanford University) for providing us with their experimental results and for permission to reproduce extra material; also, we appreciate the many discussions we have had concerning interpretation of the data. We thank Dr. G. B. Bacskay (University of Sydney) for performing some ab initio calculations, Dr. P. Lay (University of Sydney) for help with the inorganic chemistry, and Prof. M. Zemer (University of Florida, Gainesville) for sending us his research ZINDO progiam. J.R.R. is indebted to the Australian Research Council for a Research Fellowship. Registry No. RU~~(NH,),PZ, 19471-65-9; Ru1I(NH,),pzH+, 21-5; Ru"(NH,)Sbpy,
54714-01-1; Ru"(NH,)SbpyH+,
1944136645-25-7.
