8329
J. Phys. Chem. 1992, 96, 8329-8336
Origins of the Double Emlsslon of the Tetranuclear Copper( I)Cluster Cu,I,( pyridine),: An ab Inltlo Study' Marcello Vitale, William E. PaUte,* and Peter C. Ford* Department of Chemistry, University of California, Santa Barbara, California 931 06 (Received: April 20, 1992; In Final Form: June 15, 1992)
The Cu(1) tetranuclear cluster Cu414py4(I, py = pyridine), together with several analogues of general formula Cu414L4,presents remarkable photophysical properties, which have been attributed to two poorly coupled emissive excited states of different orbital parentages2 Ab initio calculations at the restricted HartreeFock self-consistent field level on this and related systems have been used to complement the results of the experimental spectroscopic studies. The outcome indicates an iodinatepyridine charge transfer nature for the state(s) responsible for the high-energy emission band of I. In contrast, the low-energy emission band is assigned to a transition with both iodine-to-copper charge transfer and metal centered 3d 4s promotion within the Cu414cluster core; thus this band is labelled a cluster-centered (CC) transition. The lack of communication between the two excited states is explained by different respective distortions relative to the ground state, as indicated by excitation-induced changes in the calculated bond orders. Calculations are also described for the hypothetical cluster Cu414(NH,),, as a model for compounds like Cu414pip4(pip = the saturated amine piperidine) for which only CC emission has been observed.
-
Introduction A growing interest in the photochemical and photophysical properties of d'O systems, especially polynuclear ones, has been manifested in recent years.*-17 Such interest has resulted in the synthesis and characterization of a plethora of new compounds, the further study of known compounds and a number of theoretical studies. All of these approaches have been used within this laboratory in an effort to clarify the photophysics of copper(1) compounds of the type Cu4X4L4(where X = C1, Br, I; L = a N, P, or As bound base) and particularly of the representative compound Cu414py4(I, py = pyridine).2 This paper will present the results of theoretical studies centered on Cu414py,. Ab initio studies of molecules such as I containing heavy atoms have been recently made possible by the development of relativistically corrected core potentials and programs that employ them.18-21 Even with these recent advances, calculations on molecules as large and complicated as Cu414py4are limited to the restricted Hartree-Fock self-consistent field (RHF-SCF) level. The results obtained should be regarded as a qualitative illustration of the phenomena under examination. Indeed, since assignments of spectra and other interpretations of the photophysical properties of metal complexes are, by necessity, rather qualitative, calculations at the RHF-SCF level, while still qualitative, can provide valuable new insight into the character of the relevant orbitals and excited states (ES). In particular, the computations reported herein suggest a previously unreported explanation of the emission properties of I. Tetrameric adducts of Cu(I), halides and P or N bound bases (Cu4X4L4)have been long known,27and Hardt et al. first drew attention to their luminescence properties.13 Several subsequent efforts have given a thorough portrayal of the photophysical properties of I and its analogues, but spectroscopic interpretations are still contr~versial.~J~-'~ Reviewed briefly below are the photophysical properties of I and of some analogues. A more complete discussion of these has been presented.2 The structure of I (Figure 1) as determined by X-ray crystal diffraction1Iashows it to have a "cubane" Cu414core, consisting of a tetrahedron of copper atoms enclosed in a larger tetrahedron of iodine atoms, with each iodine situated above a face of the Cu4 tetrahedron. The pyridines form another, even larger, tetrahedron, with one py bound to each Cu. The Cu-Cu distance is 2.69 A in versus a Cu-Cu distance of 2.556 A in copper and a Cu-Cu distance of 4.28 A in crystalline cuprous iodide.28bAn isomeric form of (CuIpy), which can be obtained by varying the synthetic conditions, is a polymeric "stair" formed by an infinite chain of steps.14b Also possible are related compounds with different stoichiometry, such as dimers C U ~ X ~ L . , . ~ ~Such JI*'~ species possess features that warrant separate theoretical study.
The cluster I luminesces blue at 77 K, both when solid and in solution, but at room temperature (RT) its emission is yellow from the solid and red from toluene solution, manifesting what has been called "luminescence thermochr~mism".'~This phenomenon is due to the presence of two emissions of different energy, a lowenergy (LE) emission band, dominant at RT and responsible for the yellow color, and a high-energy (HE) emission band, dominant at 77 K and responsible for the blue color (Table I). Such luminescence thermochromism is the norm for Cu414L4when L is an aromatic nitrogen heterocycle; however, only the LE band is observed when L is a saturated amine. The HE band blue shifts when T decreases, while the LE band red shifts. However, when Tis below the glass point of the solvent the LE band sharply moves to the blue. The energy of this band is consistently higher in solid samples than in fluid solution; thus, these properties indicate a steep rigidochromism. The stair compounds are emissive only when L is aromatic, and their emission resembles closely the HE band of the cubane analog. The two emissions present substantially different, although overlapping, excitation spectra: the obtained while monitoring the LE emission is at higher energy than that of the HE emission. Thus, the Stokes shift for the LE band is very large (up to 16.3 kK for I in toluene solution at RT), while that for the HE band is smaller (7.6 kK in the same case).2d The excitation bands do not find any correspondence in the solution absorption spectrum, indicating that the involved transitions are symmetry and/or spin forbidden. Moreover, such excitation bands are at lower energy than any resolved absorption feature. The lifetimes of the two emissions are different as well, implying that the communication between the responsible states is poor. The independent natures of the two emissions are also indicated by the differential quenching of the HE and LE emissions. The former is quenched by Lewis bases such as pyridine and highenergy acceptors such as naphthalene; the latter is quenched by acceptors with an ES lower in energy than the P O of the LE state itself and by electron-transfer acceptors with a reduction potential less negative than -1.4 V (vs ferrmenium/ferrocene in CH2C12).2f The cluster I and in general its analogues do not show irreversible photochemistry under any of the above experimental conditions. Since the X-ray crystal structure of solid I is well characterized,11athe two emissions, at least for the solid, must originate from two nonequilibrated excited states of the same compound. The close parallelism between solid and solution behavior points to the same conclusion for the solution case as well. Thus,there are three questions to which the experimentalresults have given only partial answers:
ex
0022-3654/92/2096-8329%03.00/0 0 1992 American Chemical Society
8330 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992
Vitale et al.
TABLE I: Relevant Experimental Results“
294 Kb cu414PY4c
solid toluene solution
Cu414PiP4d
ps.
X I E X
77 Kb r
GYX 619 438 583
XEX
580
380
11.1
690
325
10.6
HE
480
352
0.45
436
32.9
590 680
330
12.3 0.1 1
590 638
13.4 19.8
,
330 365 311 (329 sh
r
LE HE LE
solid toluene solution
OData from ref 2d. b X ’ s are in nm, 7’s in
G?x
::(
25.5 23.2 26.5
sh
‘py = pyridine. dpip = piperidine.
c
i
A
Figure 1. Cu414py4(I), picture drawn with ChemX using crystal structure data from the Cambridge Structure Database.’Ia The coppers’ tetrahedron is outlined with dashed lines.
(I) What is the nature of the LE transition(s)? The experimental results suggest transitions involving solely the Cu414core, since this emission seems to depend on the cubane structure and is not much influenced by the nature of L. (11) What is the nature of the HE transition@)? These transitions present all the characteristics of charge transfers to the ligand, especially since they are present only when L is aromatic. They do not seem to be influenced by the structure of the CUI backbone, being very similar in the cubane and the stair cases. (111) Why aren’t the two excited states coupled? The different Stokes shifts suggest that differing distortions of the excited states may be responsible for their lack of communication. The ab initio calculations described here were initiated with the goal of addressing the unresolved aspects of these questions. Calculation Method Ab initio calculations were performed on VAX computers (Vaxstations 3100 and 3540) using the ARGOS (or COLUMBUS) set of programs developed mainly at the Ohio State University and the Argonne National Laboratory18J9and modified by us to include bond order analysis. The molecules we are studying are extremely large, and two important features of the ARGOS programs enable ab initio computations on such systems. These programs allow one to replace the core electrons of each atom by an effective potential that includes electrostatic, orthogonality, and relativistic Thus a calculation can be restricted to the valence electrons only. The other useful feature of the ARGOS programs is their efficient use of symmetry. All integrals (overlap, kinetic energy, nuclear attraction, core potential and electron repulsion) are computed over symmetry-adapted combinations of atomic basis functions and stored. The subsequent Hartree-Fock SCF computations can be carried out for whatever electronic states are of interest, by using the previously evaluated integrals. Restricted Hartree-Fock wave functions are used, so, in the absence of
spin-orbit coupling, the wave functions are pure spin states. The total energy is calculated in terms of shell-averaged coulomb and exchange integrals; therefore, an SCF calculation is possible only for configurations whose energy is expressible in this way, i.e. all closed-shell and many open-shell case^.^^^^^ In the latter case, coefficients for the open shell-open shell and open shell-closed shell interactions must be input.’8d Different electronic configurations can be described in terms of the same shell-averaged integrals in this procedure, so the integral evaluation has to be performed just once for all the available electronic states of a molecule. The SCF calculation usually converges to the lowest state of any given multiplicity and symmetry. However, when the energy of the lowest state is relatively flat as a function of the MO coefficients being optimized, a higher, steeper state can be sometimes reached instead. Variation of some operational parameters (namely, the damp and level shift coefficients and the initial guess for the molecular orbital coefficients) allows in every case the calculation of the lowest state as well (see for example the IB2’s of I). They are the ones of greatest interest in this investigation since they are the most likely to be involved in the excitation transitions observed. Moreover, it is sometimes possible, within the formalism of the program, to calculate states of the same symmetry and multiplicity but different orbital symmetry parentages (e.g., the 3Al’scalculated for I; the corresponding IAI’s are instead not achievable). For each of these states we obtain molecular orbital coefficients, orbital energies, and a Mulliken population analysis26(where the overlap density is equally divided between the overlapping orbitals). A subroutine has been added in this laboratory to calculate bond orders between atoms in the molecule according to the usual formula: Pab = C n k C c j k c i f i j , i k
j,i
where Pab is the bond order between atom a and atom b, k runs over the molecular orbitals, n k is the number of electrons in the MO k, j runs over the atomic orbitals of atom a and i over the AOs of atom b, C j / j , k are the coefficients of the AOs j or i in the MO k, and Sjs is the overlap between A O j and A 0 i. Such bond orders correspond to half the Mulliken overlap populations.26 The comparison of the bond orders in the ground and excited states gives an indication of excitation-induced changes in structure as well as the contributions of individual MOs to each bond order. The geometrical parameters were not optimized in the calculations. Unless otherwise noted, they were derived from the ground state (GS) structure of I, as determined from X-ray diffraction.”” Since GS structures were used for the calculations, the resulting ES were Franck-Condon states, the products of vertical excitations. Calculations were first carried out on C U ~ I ~ ( N(11) H~)~ [ Td,D2d](in square brackets are the symmetries imposed to the molecule) and the fragments C U ~ I ~ ( N [H C2,], ~ ) CuINH3 ~ [C,], and NH3 [C,,], as a model for the compounds with saturated ligands. The N-H bond length in the complexes was taken as equal to that in free NH3, and tetrahedral arrangement of the atoms around N was assumed. Subsequently the whole cluster Cu414py4(1) [D2dl and its fragments Cu212py2[Chi, CuIpy [GI,
The Journal of Physical Chemistry, Vol. 96,No. 21, I992 8331
Double Emission of a Tetranuclear Cu(1) Cluster CU414 [Td,Du],c U 4 [ T d ] , 1 4 [Tdlr CUI [ c m ] , and Pyridine [cbl were treated. It was not possible to carry out calculations of all the attainable ES of I because of the large size of the data files (-37 X lo6 integrals are stored) and the long time needed for the SCF convergence of each state (about 10 days of CPU time). Calculations were also camed out on a CuJ, [ Td]tetramer whose geometrical parameters were those of crystalline C U Iand ~ ~on~ a Cu4C1, [ T,,]tetramer whose geometry was derived from the GS structure of C U , C ~ ~ ( N E ~ ~ ) ~ . ' ~ ~ The core-valence sets used included Cu = (Ar) 3d,4s,4p; I = (Kr 4d) 5s,5p; N = (He) 2s,2p; C = (He) 2s,2p; H = 1s. The noble-gas symbols in parentheses indicate the inner cores evaluated as effective potentials. The Cu 4p orbital was represented as a single Gaussian function optimized for the dimer Cu212(NH3), as reported previously,2cand STO-3G functions were used for the H 1s orbital. With these exceptions the core potentials and the contracted gaussian basis sets were those of Christiansen et al.,21 the valence orbitals being represented as double-{ by making independent the most diffuse gaussian of each basis set.
+
TABLE II: Contributions to the Molecular Orbitals of C U , I ~ ( N H ~ ) ~ (II), Point Group Tda MO E (eV) Cu sob.' Cu db*' I sbqc I vbq4c Lb.' 9.70 85.6 0.0 12.4 1.6 0.4 7.67 7.25 5.37 5.23 3.56
64.4 68.0 81.7 24.9 30.2
0.4 0.7 0.2 2.9 1.9
11.6 0.0 3.4 2.1 27.3
-8.24 -8.63 -8.96 -9.66 -1 1.55 -1 1.84 -12.06 -12.11 -12.57 -12.78 -13.03 -13.10 -13.44 -14.73 -15.25 -18.56 -18.57 -18.57 -22.64 -22.96 -32.56 -32.57
4.2 3.1 6.4 10.5 24.9 5.4 5.1 0.6 0.0 0.2 0.7 3.5 0.7 1.8 5.7 -0.1 0.0 0.1 2.1 2.7 -1.3 -1.7
13.2 7.5 22.3 0.5 2.9 60.4 47.7 97.3 99.2 94.4 98.6 87.4 83.9 29.3 44.3 1.3 0.9 1.o 2.1 0.4 0.2 0.2
0.1 0.0 0.3 0.0 2.1 0.5 1.8 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.2 0.1 0.0 0.0 95.3 95.8 0.1 0.0
18.1 30.3 8.7 51.7 38.5 80.5 89.3 63.6 88.8 51.7 16.9 17.1 1.1 0.4 5.4 0.0 8.7 11.3 0.5 0.8 0.0 0.1 0.2 0.4 1.0 0.0 0.1
5.5 1.o 5.9 2.0 2.0 2.0 0.1 7.5 0.3 2.0 16.8 28.2 1.o 0.4 0.0 0.6 0.4 2.0 68.5 48.9 98.7 99.0 98.7 0.2 0.1 101.0 101.3
Results and Discussion Before tackling the three questions presented in the Introduction, it is useful to examine some aspects of the ground states of I and the NH3 analog I1 described by these calculations. Ground-State Properties of Cud& Clusters. A value of -39.8 kcal/mol for the enthalpy, per stoichiometric unit, of the reaction leading to the formation of I (AH of CuI(s) + py(gas) I/,Cu414py4) was obtained by subtracting from one-fourth of the calculated GS energy of I (-405.713 hartrees; Table V), the sum of the calculated GS energies of CUI (-61.453 hartrees) and "Note: numbers are given for all filled and for the lowest energy pyridine (-39.912 hartrees). The corresponding calculated value empty orbitals. For empty orbitals, the numbers given are relative to for I1 (AH of CUI@) NH3(gas) '/,CU~I~(NH,)~) was -40.4 the sum of the square of the relevant coefficients for the symmetry kcal/mol, obtained by using the calculated GS energy of I1 orbitals in the molecular orbitals. Since the overlaps are completely (-291.605 H) and that of NH, (-11.384 H). The computed neglected, these numbers have only a very qualitative value. cFor filled orbitals the numbers given are the percentage of the electrons in each enthalpies are in good agreement with the experimental value for MO that is attributed to that particular atomic orbital type by Multhe pyridine cluster, found through thermogravimetric analysis liken's population analysis. (-35.9 k c a l / m ~ l ) ,especially '~~ considering that no intermolecular interactions were included in the calculations. The slightly larger stability of I1 would be expected, owing to the greater basicity between those of the monomers and those of the tetramers (0.445 and 0.422 for L = py and NH,, respectively), as covalency's of ammonia respect to pyridine. These results are a good indication that the closed-shell GS are described satisfactorily at this calimportance increases. In each case the ligands turned out to be slightly positive, and the increase in charge separation upon ligand culation level and that their energies are not much influenced by addition is due to a smaller degree of covalency between copper electron correlation. To have a single-value measure of the ionic component of the and iodine. Cu-I interaction, charge separation will be defined as the average The MO correlation diagram presented in Figure 2 and the composition of the MOs of I1 reported in Table I1 show clearly of the absolute values of the charges on copper and iodine. While the covalent interactions described. While the splitting of the the absolute sizes of the charge separation values presented could be disputed, owing to the shortcomings of Mulliken's population iodine 5p and Cu 3d sets of orbitals can be mainly attributed to analysis26on which they are based, their variation within series interaction between sets of identical orbitals coming together in of closely related species is undoubtedly meaningful. The same a tetrahedral arrangement, the change of their average energies is true for the calculated bond orders defined in the previous must be due to the mixing of orbitals with different energies. Any section. The charge separation so defined was calculated to be of these interactions yields a bond or repulsion between the involved 0.521 in a Cu414unit with the geometry of crystalline C U Ibut ~ ~ ~ atoms, but opposing results could nearly cancel each other. For only 0.205 when the assumed geometry was that of the core of example, the weak calculated Cu-N bond (bo = 0.02 in I, in the cluster I.28c Simultaneously,the calculated bond order (bo) agreement with the experimentally determined ligand labilityu) between a single copper and a single iodine atom went from 0.1 1 derives from the reciprocal annihilation of large contributions from to 0.15, with smaller changes in the homoatomic bonds, which filled bonding and antibonding orbitals. The net bonding is deindicates a more efficient covalent interaction in the latter case. termined by the mixing into the Cu-L* orbitals of some iodine The geometry of the Cu414core in I appears to maximize covalent p and copper s character. interactions while keeping the ionic contribution relatively small. It should be no surprise that the iodine p levels appear above When the ligands L were introduced to give Cu414L4,the charge the copper d orbital energies. This is the situation one has to expect separationswere found to increase, to 0.383 in I and 0.365 in 11, from an analysis of the ionization potentials (IP) and electron while Cu-I bo's decreased to 0.10 and 0.12, respectively. The affinity data available for the atoms and ions in the gas same relation between covalency and ionicity can be appreciated as shown in Figure 3. The effective charge separation in I or by looking at monomeric units. The computed charge separation I1 signifies a situation intermediate between atoms and monovalent was 0.452 in an isolated CUIunit and went up to 0.518 in CuIpy ions, so that the iodine p orbitals must lie at higher energy than and 0.522 in CuINH3. At the same time the splitting between the Cu d's. This energy order is suggested also by the first IP the Cu-I bonding orbital (whose main component is iodine 5p) of the clusters Cu414(g)and Cu,Cl,(g), which are, respectively, and the other iodine 5p orbitals decreased from 0.71 eV in CUI 8.7 f 5 and 9.9 f 5 eV.30 The electron is therefore likely to be to 0.47 eV in CuIpy and 0.49 eV in CuINH,, as another measure extracted from an orbital centered mostly on the halogens. The of the decreased Cu-I covalent interaction therein. Charge values obtained in our calculations for the HOMO energies, which separation in the dimers CuzIzL2assumes values intermediate represent a fmt approximation of the ionization potential according +
+
-
8332 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992
Vitale et al.
TABLE III: Reeults of the SCF Csilculatioas for the Excited States of CII,I~(NH,)~ (II), Point Croup Td statea AE (kK)b XMCT‘ ’Tz 52.1 55 IT2 55.5 44 56.6 66 ’TI 57.9 65 ,TI 68.9 ,A1 14.6 12 ’TI12 IO ‘TI,, 75.9 ’E 83.0 96 ,E 84.3 91
-
Cud-sp’
LMCTC
1 I
44 48 35 35 84
16 8
20
-
21 4 3
9
-
-
“Transitions: Tz = t2 a,; T , = t l a , ; A, = a , a,; E = e a,; T!,? is an average of T2 and T I states originating from a t2 t2 transition, which can be calculated by reducing the point group sym+
metry to D2+ bExcited-state energy relative to the ground state assumed as zero, in IO3 cm-’ (kilokaisers). ‘The nature of the excited states is represented as percent contributions of ‘elementary” transitions to the total change in charge distribution. For example, the values reported for XMCT are the percentage of the charge added to the Cu s and p orbitals that is subtracted from the iodines. XMCT = halogen-to-metal charge transfer; LMCT = ligand-to-metal charge transfer.
t
‘lo
.,3 5
I
ccnn d
-----I -- __a
___----:------
d
(/I
CUINH~ C u4I4 (NH3)4 (11) Figure 2. Partial molecular orbital correlation diagram of the monomer The arrows connect the CuINH3 and the tetramer C U , I ~ ( N H , )(11). ~ MOs whose natures are most similar. The symmetry labels noted are for point group Td to which I1 belongs. E tcVl Bi p ,;’
I I, ,I I ,
,’,’ ,’ ,’,‘ ,’ ,’,’ ’ ,‘,, ,I
-14 -12
i m+
M
X
X
Figure 3. Energies of the valence orbitals of CI, Br, I, Cu, and Ag, derived from gas-phase spectroscopy and thermodynamic data. For the halogens, the energies of the p orbitals in the neutral atoms are equal to the first ionization potentials changed of sign, while those in the mononegative ions are the electron affinities. For the elements of group l, the energies of the s orbitals in the neutral atoms are equal to the first ionization potentials changed of sign, those of the d orbitals are this value minus the spectroscopic d s gaps, and the energies of the d orbitals in the monopositive ions are equal to the second ionization potentials changed of sign. The connection lines are purely indicative. Ionization potentials and d-s gaps are from ref 29a, electron affinities from ref 29b.
to Koopmans’ theorem, are 9.9,8.2, and 7.9 eV for Cu414,Cu414(NH3)4,and Cu414py4,respectively. The number calculated for Cu4C14is 10.19 eV, in the correct energy order. These values compare well with the experimental result reported above and confirm the reliability of the ground-state description obtained. Sizable contributions of the Cu 3d AOs to the mainly iodine 5p higher energy occupied MOs are also apparent in Table 11. Such Cu d components can be seen as partially resulting from the kind of Cu-Cu interaction hypothesized by Lee and TroglerI% for the complex [Cu(Z-NPh-phen)], (a compound with a Cu-Cu distance of 2.600 A). Their Xa-DV calculations found that the interaction between the Cu d orbitals gives a high energy u*
orbital. In our case, such an orbital would be practically isoenergetic with the iodine p’s and would therefore heavily mix with them. The presence or absence of a Cu-Cu bond in these and in other polycentric compounds has been subject of dispute, with contradictory theoretical and experimental r e s u l t ~ . ” J Z ~The ~ J ~present calculation indicates an exceedingly weak C u 4 bond (bo = 0.01 in I) arising from the counter balancing of the dlo-dIorepulsion (usually the only interaction considered in a Cu(1) first approximation model) and a residual s-s bonding contribution. This result is essentially in agreement with previous calculations, from the extended Htickel theory of Hoffmann et al.lZB-b to the more complete ab initio of Kblmel and Ahlrichs,12fthe two interactions being in a balance that varies from species to species. The above Cu-Cu bonding contribution can be traced in I1 to the Cu 4s components of the Sal Cu-I bonding orbital. This orbital gives the greatest contribution (0.019) to the calculated Cu-Cu bond order. Its exceptional stabilization upon cluster formation is apparent in Figure 2. Its separation from the 8t2 orbital, which is also involved in the formation of the Cu-I bond, is quite large (2.59 eV). The splitting between the corresponding Cu-I* orbitals is similar in dimension and equal in direction, with the 6aI orbital being lower in energy than its lotz companion. These energy differences can be easily explained considering that the a1 orbitals are Cu-Cu bonding in nature, while the t i s are Cu-Cu nonbonding or slightly antibonding. Indeed the Cu 4s atomic orbitals of the four Cu’s all contribute to the a1MOs with the same sign. Thus, electronic population of the Sa, or 6a1 orbitals contributes to Cu-Cu bonding (this has other important consequences, as seen below). Electronic Transitions of Cu;GL4Clusters. The C U ~ I ~ ( N H ~ ) ~ model species I1 was studied to address the first of the questions put forth in the Introduction: W3ar is the nature of the LE transition? The MO diagram on the right side of Figure 2 and the values reported in Table I1 suggest the HOMO to LUMO transition to be largely an iodine 5p copper 4s charge transfer. Indeed the 9t, HOMO and the following 4t1, 8t2,and 4e orbitals all are mainly iodine 5p in character, such AOs making up between 64% and 89% of these MOs. The 6a, LUMO, by far the lowest energy empty MO (1.67 eV from the next one), has comparable copper 4s and iodine 5p components. Table 111, which summarizes some results of the calculations for the excited states of 11, gives a slightly different answer with greater emphasis attributed to the Cu 3d to 4s transition than the MO diagram would suggest. In the lowest excited state, the HOMO LUMO )T2, only 55% of the charge moved to Cu 4s and 4p orbitals comes from iodine while the other 44% previously resided in Cu 3d orbitals. To explain this seeming discrepancy, one could envision the vertical excitation as initial electronic
-
-
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8333
Double Emission of a Tetranuclear Cu(1) Cluster
TABLE I V Contributions to the Frontier Molecular Orbitals of C ~ J ~ ( p y r i d i n e(I), ) ~ Point Group Dw c u spa.6 Cu daqb I sa.6 MO E, ( e v ) I p"*b 17al loa2 26e lobi l6b2 25e 16al
3.94 3.41 3.39 3.34 2.66 2.65 2.63
27.0 3.5 0.2 5.1 0.6 1.3 0.9
15b2 24e 23e 9% 14b2 22e 15a, 9bl 21e 8% 8bl 20e 13b2 14a1 13al 19e 12b2 12a,
-7.86 -7.92 -8.20 -8.29 -8.55 -8.68 -9.1 1 -9.31 -9.88 -9.88 -9.88 -10.75 -10.88 -10.93 -1 1.05 -1 1.28 -11.37 -1 1.64
3.5 4.1 2.9 3.0 5.4 5.5 9.2 10.0 0.0 0.0 0.2 0.1 0.6 1.3 19.3 4.7 4.6 9.0
2.5
23.7
0.0 0.0
0.0 0.0 0.0
0.1 0.3 0.4 0.2 12.8 12.7 7.2 7.3 21.8 22.1 1.O
0.4 0.3 0.4 0.1 18.1 5.8 6.5 8.3 45.6 43.9 29.3
0.0 0.0
39.9 0.1 0.1 0.1 0.6 0.2 0.6 81.3 81.7 88.1 88.2 63.0 64.2 83.3 86.6 0.3 0.6 1.8 0.5
0.1 0.0 1.o 0.4 0.4 2.8
5.8 31.2 16.5 18.6 37.9
0.3 0.0 0.0 0.1 0.1 0.0
0.0 0.3 0.3 0.0 0.0 0.0 0.0
P F 6.9 99.7 99.6 99.4 98.1 98.1 98.3 2.4 1.4 1.8
1.5 9.5 7.9 6.6 3.0 99.4 99.0 98.0 81.3 92.4 86.4 40.3 32.8 32.5 21.1
1.1
PY p" 1.2 99.6 98.2 95.3 97.9 97.9 98.2 2.0 1.2 1.5 1.2 7.6 6.3 6.6 2.0 99.4 99.0 98.0 81.2 92.0 86.4 32.5 26.1 26.8 17.0
"For empty orbitals, the numbers given are relative to the sum of the square of the relevant coefficients for the symmetry orbitals in the molecular orbitals. Since the overlaps are completely neglected, these numbers have only a very qualitative value. bFor filled orbitals the numbers given are the percentage of the electrons in each M O that is attributed to that particular atomic orbital type by Mulliken's population analysis. CThecolumn labeled py gives the values defined above summed over all the A 0 types of the atoms part of the pyridine ligands. The column labeled py p gives the same values summed only over the p orbitals of all the atoms part of the pyridines. Since the s orbitals do not contribute to T and r* orbitals, orbitals with large and equal or nearly equal values in both this columns will have mainly pyridine r or r* character.
promotion, with the MOs "frozen" in their ground-state form, followed by electronic reorganization. Only conclusions about the first step can be strictly drawn from the coefficients of the GS MOs. The electronic reorganization in the ES releases charge from the copper centers to the iodines, so that the overall charge separation has only slightly decreased, to 0.302. Thus,since neither the XMCT nor the d s metal-centered label alone can describe the lowest excited states, a better designation would be that the resulting transitions are cluster centered (CC), characteristic of the Cu414core and involving significant charge transfer from iodine to copper.* This result seems to agree very well with Jansen's proposal of a XMCT (and subordinately Cu d s) nature for low-energy Cu(1) transitions.12cThe small LMCT components found for some states (Table 111) derive from the mixing of some Cu-L* character in all the highest occupied MOs. The small influence of L is confirmed by calculations on the Cu414cluster core alone, which gave percentages of XMCT character between 57% and 75% for the lowest T2 and TI states. Figure 4 and Table IV provide some insights regarding question two: What is the nature of the HE transition? This emission band was observed only for the complexes with aromatic ligands. The MO diagram of I (Figure 4) is very similar to that of I1 (Figure 2), with two obvious differences: the presence of a and T* levels of the pyridine ligands and the decrease in degeneracy of the orbitals common to the two cases, owing to the change from Td to D u symmetry. The HOMOs have almost exactly the same composition, in terms of A 0 contributions, of their correspondents in 11, that is, they are mostly iodine 5p. Only the MOs at energies lower than the pyridine a level show a greater mixing with these a orbitals than is possible with the orbitals of a saturated ligand. The LUMOs are pyridine r * in character but the next higher LUMO is nearly identical to the LUMO of 11, as is its symmetry, a]. The existence of two different types of low lying unoccupied MOs allows for two Werent types of excited states of close energy, originating from the same HOMOs. The calculated results for I are best compared with the excitation spectra, since the calculations were camed out at the ground state equilibrium geometries to give Franck-Condon states. As noted above, the excitation maximum of the HE emission occurs at lower energy than that of the LE emission. Thus,the ES energy
-
-
7 5 8
..
8 5
..
9
..
9 5
..
1
0
10 5
I
/
I _ _ _ _I_p Ip
- I----- -I _ _ _ _ _
cP-H b.
I---- I P
f2
tl t2
e
-. ..
1 1
-.
11 5
.-
12
-
-
_ _ _pyridine _. f
-- _ - - - Cun-I b.
=I----can-IL+
a, t2 a1
order suggested by Figure 4 agrees with the excitation energies, despite the LE and HE labels drawn from the positions of the emission bands. The lower energy absorption (corresponding to the excitation of the HE emission band) would involve electron promotion from one of the frontier occupied MOs to a a* ligand orbital. This would be in essence an iodine to pyridine charge transfer, or XLCT. The second absorption would involve excitation from a frontier-occupiedorbital to the empty Cu-I* MO and would correspond to excitation of the CC transition also observed and calculated for Cu414L4with saturated amine L's.
8334 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992
Vitale et al.
TABLE V Selected Results of the Ground and Excited State Calculation8 for C U I I ~ D(I), Y ~ Point Group D , Cub dC SC Ib state transition -energy" PC 0.360 39.879 405.713 0.863 1.820 -0.406 "4, 1.178 1.941 0.301 39.678 405.476 -0.345 b2 a1 'B2 405.463 1.169 1.970 0.302 39.652 -0.353 a, b2 0.958 1.972 -0.203 0.337 39.723 IB2 b2 a1 405.447 0.337 39.721 0.957 1.975 -0.203 'E b2 e 405.447 0.957 1.97 1 -0.202 0.337 39.723 IE b2 e 405.446 1.976 0.956 -0.204 I b2 b2 405.446 0.337 39.722 0.910 1.802 -0.218 0.351 39.884 'Al al a1 405.398
----
Nb -0.075 -0.074 -0.073 -0.116 -0,116 -0.116 -0.115 -0.113
Lb 0.046 0.044 0.051 -0,134 -0.134 -0.135 -0.133 -0.133
Ae0.44 0.44 0.81 0.81 0.82 0.81 0.75
"Calculated energies in hartrees. bColumns labelled Cu, I, and N give the calculated charge on one of the respective atoms and L that on one whole pyridine, as fractions of one electron, from Mulliken population analysis. CColumns labelled d, s, and p report the Mulliken electronic wDulation of the respective orbitals of all four comers. dAmount of charge transfer in each excited state, calculated as the sum of the charge
'O-
-'4
4:
X
T
X
T
5b
---
'A,
5
54
--
3 4
9
16
74
-2
--
'E
9
I6
75
?E
9
16
71
55
60
95
TABLE VI: Calculated Bond Orders in the Ground and Excited States of I and 11" state CuCu Cu-I Cu-N CU4I4PY4 !Al G.S. 0.01 0.10 0.02 'B2 0.13 -0.04 0.03 IB2 0.13 -0.04 0.03 9 2 0.0 1 0.10 0.08 'E 0.00 0.11 0.09 'E 0.00 0.11 0.09 'A, 0.01 0.10 0.08 'Al 0.01 0.09 0.08 C U ~ I ~ ( N H ~ ,A, ) ~ G.S. 0.00 0.12 0.01 'T2 0.15 -0.03 0.01 IT2 0.15 -0.03 0.02 IT1 0.15 -0.03 0.01 'TI 0.15 -0.03 0.01 'Al 0.11 0.02 0.02
Calculated bond orders correspond to the electronic population in the orbital overlaps between two atoms (one-half of Mulliken's overlap population). As a reference, N-H bo in N H 3 is 0.36. States are listed in increasing energy order starting with the respective ground states at the top. /-
1 I
increasing Cu-I distance decreasing CU-Ndistance decreamg Cu-Cu dictance
Figure 6. Hypothetical cross section of the potential energy surfaces of the ground state and the first excited states of I and its unsaturated analogues. Solid arrows correspond to LE emission and excitation, dotted arrows to H E emission and excitation.
to the different nature and strength of the interactions, for example, of Cu with iodine, the ligand L and the other copper atoms, which cannot be described by just two @ (interaction) factors for copper, one referring to the sp shell, the other to the d shell. Starting from these poor foundations, the CI failed to approximate the known features of the electronic spectrum. The third question was, Why HE and LE are not coupled? The answer may lie with the calculated bond orders reported in Table VI for various states of I and 11. The calculated excited states can be immediately divided in two groups. One group shows a large change (0.11-0.15) in Cu-Cu and Cu-I bond orders with respect to the ground state. The other states (in I only) present variation of the Cu-N bo (-0.08) along with bond order changes within the pyridine rings but no effect on the Cu-Cu bond orders. These two groups exactly correspond to those states designated CC and XLCT. Examining the calculated bo changes leads one
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8335
Double Emission of a Tetranuclear Cu(1) Cluster to conclude that the CC states are much more distorted than the XLCT states, since a larger bo change occurs in the cluster core. The different distortions of the excited states involved in the LE and HE transitions of I are illustrated in Figure 6. To a first approximation, excitation into the XLCT manifold should not result in emission from the CC states without a thermal activation to surmount the bamer represented by the curve crossing between the two states. Similarly, the Franck-Condon state resulting from the excitation into the CC manifold is also likely to thermally deactivate rapidly to an energy below the crossing point. The trajectories of the distortions involved, as suggested by the calculated bond order changes, may also be factors in ensuring that the individual Franck-Condon states relax to the respective XLCT and CC states responsible for the HE and LE emissions. Such a scheme also accounts for the energy inversion between the positions of the excitation and the emission maxima. The calculated singlet-triplet splittings of the CC states are certainly larger than those of the XLCT states (Tables I11 and V), but are not yet sufficient to produce the experimentally observed Stokes shift. The large Stokes shift of the LE system is therefore connected to the distortion of the responsible CC excited states. The same distortion would be the logical explanation of the reported rigidochromism of the LE emission band, since a more rigid medium would certainly increase the energy of a very distorted excited state.
Conclusions The use of ab initio calculations has provided valuable new insights into a complicated photophysical system. Early assignments of the observed transitions, some of these from our laboratory, are in only partial agreement with the present resdlts. The states involved in the HE transitions can be labeled, with good confidence, as XLCT. The calculations tend to confer a much greater emphasis on the halogen’s contribution than it was usually thought and do not find much direct evidence of the more traditional MLCT parentage. The other type of state observed, originating from orbitals of bonding or antibonding character between all of the atoms in the cluster core, does not conform to any of the usual labels. We have used, as a best approximation, cluster-centered, and it can be also sp b c r i b e d as a mixture of XMCT and metal centered d transitions. At the root of the observed double emission are Cu-Cu and Cu-I interactions in the cluster core, which are deeply affected in the CC states but are essentially undisturbed in the XLCT ones. Acknowledgment. We thank Prof. Russell M. Pitzer for providing us the COLUMBUS computer programs and Dr. Chong Kul Ryu for his continuous comments and suggestions. This work was supported by National Science Foundation grants (CHE90-24845 and CHE87-22561) to P.C.F.
-
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F.; Christiansen, P. A. J . Chem. Phys. 1985, 82, 2664-71. (b) Hurley, M. M.; Pacios, L. F.; Christiansen, P. A.; Ross,R.B.; Ermler, W. C. J . Chem. Phys. 1986, 84, 6840-53. (c) LaJohn, L. A.;
8336
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Christiansen, P. A.; Ross, R. B.; Atashroo, T.; Ermler, W. C. J . Chem. Phys. 1987.87.2812-24. (d) Ross. R. B.: Powers. J. M.: Atashroo. T.: Ermler. W. C.; LaJohn, L. A,; Christiansen, P. A. J . Chem. Phys. 1990, 93, 6654-70. (22) Raffenetti, R. C. J . Chem. Phys. 1973.58, 4452-8. (23) Dupuis, M.; Rys, J.; King, H. F. J . Chem. Phys. 1976, 65, 111-6. (24) (a)-McMurchie, L. E.; Davidson, E. R. J . Comput. Phys. 1981,44, 289-301. (b) Pitzer, R. M.; Winter, N . W. J . Phys. Chem. 1988,92,3061-3. (25) Roothan, C. C. J . Reo. Mod. Phys. 1960, 32, 179-85. (26) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1833-40, 1841-6. (27) (a) Arbusow, A. E. J . Russ. Phys. Chem. SOC.1906,38ii, 293. (b) Mann, F. G.; Purdie, D.; Wells, A. F. J . Chem. SOC.1936, 1503. (28) (a) For copper metal, Cu-Cu bond length = 2.551 A: Lide, D. R. CRC Handbook of Chemistry and Physics, 71st ed.; CRC Press: Boca Raton,
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G. In Handbuch der Praeparatiuen Anorganischen Chemie; Ferdinand Enke Verla : Stuttgart, 1975. (c) For I, crystallographic bond lengths: Cu-I = 2.70 C u C u = 2.69 A; 1-1 = 4.51 A; sce ref 1la. (29) (a) Moore, C. E. Atomic Energy Levels; 1971; Nat. Bur. Stand. US. Circ.; vol. I-III,467. (b) Cotton, F. A.; Wilkinson, G . Advanced Inorganic Chemistry, 5th ed.; Wiley-Interscience: New York, 1989. (30) Rosenstock, H. M.; Sims, D.; Schroyer, S. S.; Webb, W. J. Ion Energetic Measurements. Part 1,1971-1973, in National Standard Reference Data System, Sept 1980. (3 1) Vanquickenborne, L. G.; Coussens, B.; Postelmans, D.; Ceulemans, A.; Pierloot, K. Inorg. Chem. 1991, 30, 2978-86.
1;
A Theoretical Study on the Assignment of Fundamental Frequencies of o-Benzyne Ruifeng Lh,* Xuefeng Zhou, and Peter Pulay Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, Arkansas 72701 (Received: May 4, 1992)
The geometry and quadratic force field of o-benzyne are calculated by the recently developed unrestricted Hartree-Fock natural orbital complete active space (UNO-CAS) method. The force field, after an empirical scaling by scale factors of the UNO-CAS force field of benzene, satisfactorily reproduces the matrix IR frequencies of o-benzyne and its deuterium and I3Cisotopomers. On the basis of the calculations, earlier assignments of the fundamentalsof o-benzyne, o-benzyne-d4, and 1,2-I3C2C4H4 are discussed. The conclusion that the frequency of the formal triple bond stretching is at around 1860 cm-I instead of 2080 cm-l is confirmed. The matrix IR frequencies at 1627, 1607, 1598, 1596, 1307, 1271, 1055, and 838 cm-' are concluded to be. not fundamentals of o-benzyne, those at 1411, 1198, 1112, 1029, 679 and 616 cm-I are concluded to be not fundamentals of o-benzyne-d4,and those at 1298, 1266, 1040, and 835 cm-l are concluded to be not fundamentals of 1,2-I3C2C4H4.Reassignments on some of the normal modes are proposed.
Introduction Since the first matrix infrared (IR) identification of obenzyne,'J IR studies on this molecule have been conducted in several group^.^" However, only a small number of frequencies have been recorded and many questions were raised in the vibrational assignments. Representative of these is the assignment of the formal carbon-carbon triple bond stretching frequency. Early studies unambiguously assigned a strong band at 2080 c m - I to this vibrati~n.l-~It was challenged seven years ago by a gas-phase photodetachment study which assigned 1860 cm-' to this vibration.' Theoretical calculations6.*-" with both semiempirical and ab initio methods including MNDO, restricted Hartree-Fock (RHF), two-configuration SCF (TC-SCF), and second-order Moller-Plesset perturbation (MP2) resulted in frequency of this vibration in the range 2190-1930 cm-I. On the basis of results of their calculations at several levels of theory, Schaefer et a1.I0 concluded that this frequency cannot be higher than 2010 cm-I. Thus, the photodetachment conclusion is in line with theoretical results. However, because of strong electron correlation and basis set truncation errors, none of the pure ab initio studies successfully reproduced observed frequencies quantitatively. For example, the recent study of Scheiner and Schaefer" used MP2 in conjunction with triple [ plus two sets of polarization functions (TZ2P) and obtained a frequency 1943 cm-l for the CC triple bond stretching vibration.'l The size of their calculation is perhaps the largest at this level, but the result is still about 100 cm-' higher than the photodetachment result.' Recently, the conclusion of the photodetachment study was confmed experimentally. In a neat matrix 1R study, a weak band at 1846 an-'was detected and attributed to this vibration: The origin of the frequencies at around 2085 cm-I in the matrix IR spectra of o-benzyne was also found. Laboratory studiesI2J3 concluded that cyclopentadienylideneketene has a strong IR absorption at 2085 cm-I. This molecule or molecules with similar structural units are believed to be byproducts or unstable intermediates in the reactions generating o-benzyne in matrices.I"
Although the controversialassignments of the stretching vibration is apparently resolved, the assignment and interpretation of the experimental IR spectra are still not complete; e.g., results of the most recent matrix IR study6 differ in several aspects from previous experimental studies. To clarify the remaining problems, we used an empirically corrected ab initio technique in this study. On the basis of the results of our calculation, detailed discussions on the assignment of the matrix IR frequencies of o-benzyne, o-benzyne-d,, and 1,2J3C2C4H4are given.
Method For o-benzyne, the simple restricted HartreeFock (RHF) method is apparently not appropriate because of the presence of strong (nondynamic) electron correlation. The most straightforward way to treat strongly correlated systems is multiconfiguration SCF (MC-SCF) method, i.e., the optimization of molecular orbitals in a limited configuration interaction (CI) wave function. It is now generally agreed that the most satisfactory MC-SCF wave function should include all possible configurations in the active space, i.e., the space of strongly correlated orbitals. This FORS (full optimizul reaction space) concept was introduced by Ruedenberg and co-~orkers'~ and further developed by Roos et al.Is as the complete active space SCF (CAS-SCF). Up to now, the only multiconfigurational method applied to this molecule is two-configuration SCF (TC-SCF).9Jo Such a wave function can describe only the biradical nature of the formal triple bond. However, it has been our experience that, in conjugated radicals, the whole *-electron system is involved in resonance, leading to strong correlation effects. This predicts an eight-orbital active space, consisting of the bondingantibonding pair of the in-plane 7 orbitals on the formal triple bond, as well as the six out-of-plane .rr orbitals of the ring. Indeed, the unrestricted Hartree-Fock (UHF) natural orbital criterion16gives exactly this active space. To strike a compromise between computational expense and accuracy, an alternative to CAS-SCF, the recently developed unrestricted HartreeFock (UHF) natural orbital complete active
0022-3654/92/2096-8336%03.00/0 0 1992 American Chemical Society
