J. Phys. Chem. 1986, 90; 255-260 region in going from diethyl ether to T H F solution. (Probably the weak infrared band at 1584-1581 cm-' corresponds to the intense Raman band at 1583-1582 cm-'.) It may be concluded from these observations that bulk solvent effects do not contribute to the downshifts from group I to 11. Raman and Infrared Spectra of Chl b. Like Chl a, Chl b also showed shifts of the Raman and infrared bands, depending on the solvent used. In Figure 8 are shown thc; Raman spectra of Chl b in the region of 1800-1470 cm-' observed in eight kinds of solvents, which were also used to observe the Raman spectra of Chl a. Chl b was more fluorescent than Chl a when excited with the He-Cd 441.6-nm line. The fluorescence was so strong from CCI, and pyridine solutions that no Raman spectra could be obtained from these solutions. The solubility of Chl b in n-hexane was too low to observe the Raman spectrum in this solvent. As shown in Figure 8 the C-9 keto carbonyl and the C-3 formyl carbonyl stretchings are observed, respectively, at about 1700 and 1666 cm-' in non-hydrogen-bonding solvents. These bands shift, respectively, to about 1675 and 1648 cm-l in ethanol and methanol, which form hydrogen bonds with the above carbonyl groups. Under the present experimental conditions, Chl b does not seem to form self-aggregates in all these solvents including nonpolar
cs2.
The patterns of the Raman spectra of Chl b in the 162015 10-cm-' region can be classified in the same way as for Chl a. The spectra from CS2, diethyl ether, acetone, ethyl acetate, and ethanol solutions belong to group I and those from THF, dioxane, and methanol solutions to group 11. The 1607-cm-' band in group I shifts to 1596-1594 cm-' in group 11, although these bands are extremely weak in some solvents. A difference between Chl a and Chl b is found in the 1570-1 540-cm-' region; the group I band
255
at 1566-1564 cm-' of Chl b is replaced by a doublet at 1559 and 1551-1549 cm-' in group 11. The origin of this doublet is not clear at present. It is conceivable that the group I band at 1566-1 564 cm-' consists of two overlapping components which give rise to the doublet in group 11. The band at 1523-1520 cm-' in group I shifts to 1519-1516 cm-' in group 11. The infrared spectra of Chl b were also observed in diethyl ether and THF solutions. A medium-intensity band observed at 1610 cm-' in diethyl ether solution clearly shifts to 1597 cm-' in T H F solution. This downshift is very similar to the results obtained for Chl a (Figure 4). The above results indicate that Chl b behaves in the same manner as Chl a with respect to the axial coordination by solvent molecules. Conclusion
The resonance Raman and infrared spectra of Chl a and Chl b in various solvents are usually classified into either group I or 11. Group I is correlated with a system in which the five-coordinated species (one axial ligand to Mg) is dominant, whereas group I1 is correlated with that in which the six-coordinated species (two axial ligands) is the major fraction. However, spectra intermediate between the two groups may be obtained, as exemplified by the cases shown in Figure 3, for systems in which the five- and six-coordinated species coexist with comparable concentrations. Acknowledgment. We are grateful to Dr. Hidenori Hayashi for his technical guidance in sample preparations. This work was supported by a Grant-in-Aid for Special Distinguished Research (No. 56222005) from the Ministry of Education, Science, and Culture.
Electron Correlation Effects in Ligand Field Parameters and Other Properties of CuF, Sergei Yu. Shashkint and William A. Goddard III* Arthur Amos Noyes Laboratory of Chemical Physics.1 California Institute of Technology, Pasadena, California 91 125 (Received: July 24, 1985)
The effect of electron correlation on ligand field splittings in CuF2 is examined. We find that charge-transfer (CT) effects play an important role in stabilizing the z2g+and states (but not 2Ag) and that electron correlation enhances the CT, raising ligand field splittings by about 20%. Electron correlation has an important effect on the g tensor but not on geometry and vibrational frequencies. Simplified configuration interaction schemes that should be practical for much larger clusters are suggested and tested.
1. Introduction Cluster models have proved useful in theoretical studies of the electronic structure of crystals containing transition-metal ions: for example, the use of the cluster [NiF,]" to model KNiF3. These studies have generally been at the Hartree-Fock (HF) level, and the discrepancies with experiment are generally attributed to electron correlation (many-body) effects. For instance, the is calculated crystal-field splitting parameter 1ODq for about 80% of the experimental value.'S2 As the initial step in a program for investigating the role of electron correlation in electronic properties of such systems, we examined the electronic structure of the linear molecule CuF2. The geometry and energy spectrum of CuF2 have previously been Permanent address: Physics Department, A. M. Gorkii Ural State University, Sverdlovsk, 620083, U.S.S.R. *Contribution No. 7256.
0022-3654/86/2090-0255$01.50/0
studied within the framework of molecular orbitals (MO) using ab initio HF, multiple scattering X,, and semiempirical INDO method^.^,^ Limited configuration interaction (CI) studies5,, for a fixed geometry have also been performed recently. In order to determine the influence of electronic correlation on ligand field splitting, we carried out various C I calculations on the ground and excited electronic states of CuF2. We find that charge-transfer (CT) configurations play a particularly important (1) Moskowitz, J. W.; Hollister, C.; Hornback, C. J.; Basch, H. J . Chem. Phys. 1970, 53, 2570. (2) Wachters, A. J. H.; Nieuwpoort, W. C. Phys. Reu. B 1972, 5, 4291. (3) Basch, H.; Hollister, C.; Moskowitz, J. W. Chem. Phys. Let?. 1969,
., .,.
d IO
(4) de Mello, P. C.; Hehenberger, M.; Larsson, S.; Zerner, M. J . Am. Chem. SOC.1980, 102, 1278. ( 5 ) Larsson, S.; Roos, B. 0.;Siegbahn, P. E. M. Chem. Phys. Let?. 1983,
96,436. (6) Ha, T.-K.; Nguyen, M. T. Z. Naturforsch. A 1984, 39, 175.
0 1986 American Chemical Society
256
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986
Shashkin and Goddard
8
8
(4)
while the 'A, state has one singly occupied d6 orbital on the Cu2+
8
X
x
(5)
Of course this description as F C u 2 + Fis idealistic, and significant neutralization of the above schemes 3-5 is expected. The Mulliken population analysis leads to a valence electronic configuration on Cu of 3d9.144s0.354p0.32 and formal charges of Cu' 19+ and Fo59for the 'ZBf state (RCu+= 1.79 A), One cannot, of course, take such Mulliken charges too literally since the Cu 4s, 4p orbitals overlap the ligand orbitals much more than do the 3d orbitals, leading to 4s, 4p Mulliken charges that should be partially attributed to the ligands.' These neutralization effects ere visualized in terms of VB configurations involving CT of one electron from ligands to the copper
'd
for 'Z,+ and
Figure 1. Amplitude contours for various valence orbitals of CuF, from average-ofanfiguration (AC) calculations (RhF = 1.79 A). The lowest and highest contours are 3~0.3au; contour separation is 0.03 au. The boxes are 7 X 5 A.
role and have developed simplified schemes that make the corresponding calculations practical for large clusters of transition metals (e.g. [CuF,le). These simplified CI approaches were used for calculations of the geometry, vibronic frequencies, and g tensor for CuF2. The results are summarized and discussed in section 2 and the details of the calculations described in section 3.
for 'II,, respectively. However, there is no analogous C T configuration for 2Ag. In MO language, the transitions from ground to C T configurations 6 and 7 are
2. Results and Discussion
(.,,)'(.d'
2.1. Wave Functions. The wave functions for the low-lying states of CuF2 can be thought of as based on F C u 2 + Fwith the Cuz+in the d9 configuration. For the linear geometry this leads to 'E,+, 'II,, and 'A, states. The molecular orbital configuration of the ground state ('8,') is ( 1a,)
'. ..(6a,)'(
'
7 a,) ( 1a,)
'. ..( 5 a,)
'( 1
2nJ4( 1a,)
'. ..
(3%)4(16,)4 (1)
with a hole in the 70, orbital. The 'IIg and 2A, excited states have 7agdoubly occupied and the hole in either the 2 r g or 16, orbitals, respectively. These 7ag, 2ng, and 16, orbitals are all d-like orbitals on the Cu (see Figure 1) and will be denoted as b d = 7ag ?fd
= 2ag
6d
= 16,
(2)
The valence bond (VB) visualization of the 'Zg+ state is (3)
where only the pertinent doubly occupied p, orbitals of the two F and the singly occupied d, orbital of the Cuz+ are shown. Similarly, the important a-orbitals in the 211gstate can be visualized as
-
(a,,)l(.d'
for 'Eg+
(8)
and (*~g)~(*d)~
-+
(*~g)~(Td)~
for
2ng
(9)
where we denote the F 2p-like orbitals as up, = 6a, apu= 50, apg= la, apu= 3a,
This notation is only qualitative since the F 2p-orbitals mix considerably with the Cu d-orbitals (the apgand apgorbitals are plotted in Figure 1). 2.2. Geometries. We find equal bond distances of 1.78 A (CI) for 'Eg+and 211swith 2Ag longer by 0.024 A. This indicates the importance of CT for both 2Zg+and 211gstates. H F calculations lead to a slightly larger bond distances for 'Zg+ and 'Ag (by 0.005 and 0.006 A, respectively) and a more distinct increase in the 'IIg bond distance (by 0.016 A), indicating a somewhat poorer description of CT for the 'II, state at the HF level in comparison with that for 'Eg+. 2.3. Vibrational Frequencies. The antisymmetric stretch vibrational frequency (v3) for %,+ is 761 cm-' from the CI, which (7) Polak, K.; Malek, J. Czech. J . Phys., Sect. E 1972, 22, 1232.
Electron Correlation Effects in CuF2
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 257
I-
2 W
W
f
W
I .8
2.0
2.2
BOND DISTANCE (A) Figure 3. The distance dependence of CuF, ligand field splittings. The CI-SD(2) results are most reliable.
respectively, in qualitative agreement with our values of 1865 and 1385 cm-I. The CI-SD calculation6 leads to tn = 409 cm-I and ez = 654 cm-', demonstrating a general inability of this approach to describe the important correlation stabilization of 211gstate. The experimental data on the CuF2 d-d absorption bands are not yet available (these optical absorption bands were not detected in ref 8) so that no comparison between theory and experiment can be made. 2.5. Bond Energies. From H F wave functions the directly 2F Cu) is 6.90 eV. This calculated atomization energy (CuF, is artificially large (for the H F level of estimation) because our contracted bases were determined for F and CuZ+.An alternative procedure for making a best estimate of experimental atomization energies is to use theory for calculating the energy to dissociate CuF, into Cuz+and two F (this should be fairly accurate since CuFz has character similar to F-CuZ+Fand hence differential electron correlation effects should be small) and then to use the experimental values of fluorine electron affinity, 3.4 eV,'O and copper double ionization energy, 28.0 eV," to correct the infinite limit, obtaining neutral Cu and F atoms. The resulting atomization energy is 5.8 eV at the H F level. These estimates may be compared to an (indirect) experimental value of 7.9 eV.12 It is less reliable to use our CI results for estimate of bond energies since the CI-SD calculation is not dissociation consistent. Nevertheless the results are (i) a direct atomization energy of 9.06 eV (the basis restriction should lead to too large a value while the inconsistent level of correlation would tend to yield a too small value) and (ii) an empirically adjusted atomization energy of 6.8 eV. 2.6. g Factors. We also estimated the influence of correlation effects (and the electron delocalization connected with these effects) on the magnetic g factors of CuF, ground state. The electronic Hamiltonian including spin-orbit and Zeeman interactions has the form
-
% = %o
+
+ Y, + Y, =
+ x[t(rk)(lk'Sk) + FH*(Ik + 2.0023sk)I k
(12)
Diagonalizing the 7f matrix in the basis of ten CI wave functions l i p ) [ i = 2Eg+,211g(xz,yz),2A,(x2- y z , xy), m = in the presence of a small magnetic field H directed along the x or z axis, we obtain the g,,, g,, factors from the ratios of 6E/fiH, where 6E is the ground state splitting value. The gois diagonal with matrix elements corresponding to the C I energies E(i). For the calculation of the spin-orbit interaction and orbital part of Zeeman
(8) Kasai, P. H.; Whipple, E. B.; Weltner, W. J. Chem. Phys. 1966, 44, 258 1. ( 9 ) Hougen, J. T.; Leroi, G. E.; James, T. C. J . Chem. Phys. 1961, 34, 1670.
(10) Hotop, H.; Lineberger,.W. C. J . Phys. Chem. Re$ Data 1975,4, 539. (11) Moore, C. E. Natl. Stand. Re$ Data Ser., Natl. Bur. Stand., 1971, VOl. 2. (12) Kent, R. A,; McDonald, J. D.; Margrave, J. L. J . Phys. Chem. 1966, 70,874.
Shashkin and Goddard
258 The Journal of Physical Chemistry, Vol. 90, No. 2, 1986
TABLE I 1 The Basis for F (Valence Double ,O
TABLE I: Calculated Values of g Tensor for the *ZB+State HF" CI-S(2)a-b CI-SD(2)Oab exptl' 2.656 2.601 g.r* 2.866 2.582 1.903 1.913 gz, 1.906 1.938
basis function 1s
"AC results. bMVS results. 'Reference 8
interaction matrices, we neglected all small contributions to the C I wave function except the main d-shell and C T terms, Le., we used the approximate two-configuration C I wave function li,m) = [Cyli,d-shell)
+ C,CTli,CT)]lm)
2s
12.67 1.376 0.4063
2s'
0.1120
2P
22.67 4.984 1.349 0.3477
2P'
0.0760
(13)
The one-center approximation was used for evaluating the oneelectron matrix elements (pI{(r)ll$), where cp and $ are MO's (see ref 13, pp 271-275). Thus we considered the fir) as strongly localized functions and neglected all two-center contributions to (cpl{(r)il$). We also neglected the terms of (ppx~d/dx~cps) type in the (cplil$) matrix elements. The atomic spin-orbit parameters C3,, = 830 cm-' and = 220 cm-I were used. The use of one set of average of configuration molecular orbitals (see section 3) for all ligand field states simplifies the calculation of all necessary matrix elements. Our results are g,, = 2.656, g,, = 1.903, in good agreement with the experimental values8 of 2.601 and 1.913 (see Table I). The value for gxxseems particularly sensitive to electron correlation (HF leads to 2.866). This can be qualitatively understood in terms of simple perturbation theory. Spin-orbit interaction mixes the (*II,,m)and 12X,+,m)states [defined by (1 3)], giving the ground state wave function of the symbolic form I2Z,+,m) XI2IIg,m'), where X is a small coefficient. The 1, operator has nonzero matrix elements within 211gstates only, while the I, has nonzero matrix elements only between 2Zg+and 211gstates. Therefore, the correlation contributions to the I, matrix elements (and thus to the Zeeman splitting of the ground state at H directed along the z axis) will be proportional to X2CyTand (XC:T)2 assuming Cp 1. On the other hand, the correlation contributions to the I, matrix elements will be proportional to XCja and X(Cim)2,leading to a much larger influence of C T on g, value in comparison with
+
-
(13) Sugano, S.;Tanabe, Y.; Kamimura, H. "Multiplets of TransitionMetal Ions in Crystals"; Academic Press: New York, 1970. (14) Huzinaga, S. 'Gaussian Basis Sets for Molecular Calculations": Elsewer: New York. 1984. (15) Huzinaga,'S. J . Chem. Phys. 1965, 42, 1293. (16) Dunning, Jr., T. H. J . Chem. Phys. 1970, 53, 2823. (17) Gladney, H. M.; Veillard, A. Phys. Reu. 1969, 180, 385. (18) RappC, A. K.; Goddard 111, W. A,, to be submitted for publication.
coefficient 0.020499 375 0.141 169622 0.479 134791 0.500751 943 -0.089 483 034 0.485 444 147 0.592 476 983 1.o
0.040 962 756 0.214 233 464 0.459 730 668 0.455 963 289 1.o
TABLE 111: Orbital and Total Energies (in au) of F for Various Basis Sets
contraction scheme
ref
oresent work
(431/41)
1 17 14 2 23
(53/41) (222/ 1) (43/4) (5212/42)
.
,
I
uncontracted
orbital energies
total
1s
2s
2p
-25.7843 -25.8016 -25.7812 -25.7625 -25.7599
-1.0784 -1.0789 -1.0142 -1.0992 -1.0519 -1.0700 -1.0744
-0.1825 -0.1825 -0.1562 -0.1735 -0.1555 -0.1812 -0.1808
-25.8295
energy -99.31 11 -99.3240 -99.3311 -98.5219 -99.2852 -99.4473 -99.4594
TABLE IV: The Basis for Cu2+(Valence Double t) basis function exponent coefficient Is 10730.0 0.020 104 649 1618.0 0.139 350022 365.5 0.482 783 133 0.496 184 256 99.53 ~
2s
gzz.
3. Computational Details 3.1. Basis Sets. For fluorine, a variety of Gaussian basis sets are a~ailable.~~~~'"" One calculation6 for CuF2 used the Huzinaga double {basis set optimized for neutral fluorine atom15 (in spite of the ionic character of CuF2). Another calculation5 on CuF2 used the Dunning contraction of the neutral fluorine basisI6 extended by a set of diffuse p orbitals, leading to a total of four s functions and three p functions in the S C F calculations. Other contracted basis sets have been developed for the negative fluorine ion13zJ4917 but without the diffuse valence functions that may be important for the chemical bond in CuF,. Since our objective was to obtain a basis adequate for F and simple enough for large clusters, we developed a new contracted valence double {basis for F- as follows. We started with the FOURS primitive basis ( 7 ~ 4 ~ )(optimized " for neutral fluorine atom) and supplemented this basis with sets of diffuse s and p Gaussians appropriate for describing F. Using this 8s5p basis, we obtained contraction coefficients from H F computations on F. The final contracted basis is given in Table 11, and Table I11 compares various energies with other calculations. The FOURS basis was developed to provide a good valence double f description for valence electrons while minimizing the number of core functions. Thus we see in Table I11 that the 2s and 2p
exponent 992.8 149.5 33.48 8.963
143.1 23.64 9.200
-0,125412309 0.450 163 130 0.640 084 138 -0.242 356495 0.532 602028 0.619435279
3s
14.42 2.823 0.9866
4s
1.450
1 .o
4s'
0.1030
1 .o
2P
48 1.O 112.3 34.49 11.71
0.030 082 440 0.191 890008 0.521 068 172 0.430471 873
3P
8.115 3.559 1.084
0.064 423 133 0.542 793 902 0.508 730 68 1
4P
2.981
1.O
4P'
0.1579
1 .o
3d
3d'
43.66 11.97 3.916 1.222 0.3066
0.039 501 242 0.200 227 022 0.43 1 024 455 0.490 441 820 1 .o
orbital energies are in excellent agreement with rather complete bases, but the limited description of the Is orbital leads to a poor value for the total energy. There are several previous basis sets for c ~ p p e r , 'but ~ . ~all~ were optimized for the neutral first-row transition-metal atoms. In (19) Basch, H.; Hornback, C. J.; Moskowitz, J. W. J . Chem. Phys. 1969,
5 1 , 1311.
(20) Wachters, A . J. H. J. Chem. Phys. 1970, 52, 1033.
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 259
Electron Correlation Effects in CuFz TABLE V: Orbital and Total Energies (in au) for Cu2+ state
IS
2D(3d9)'
2D(3d9)
(3ds4s),,
(3d84p),,
-329.768 -41.805 -5.983
-329.190 -41.749 -5.975
-329.687 -42.255 -6.365 -0.986
-329.691 -42.259 -6.369
2p 3P 4P
-36.604 -4.287
-36.579 -4.289
-37.084 -4.663
-37.090 -4.671 -0.757
3d
-1.472
-1.480
-1.865
-1.873
totalb
-8.0834
-6.389 304
-6.029 238
-5.800570
2s 3s 4s
'Reference 23. gies.
1630 au are to be subtracted from all total ener-
addition, the minimal (single {) basis sets19 for the first-row transition metals do not contain 4p-type functions, while the Wachters basis setsz0 seem to overemphasize the core orbitals, requiring a large number of contracted functions. We started with the FOURS basis18 for Cu (designed for a double { quality description of both core and valence orbitals but contracted as valence double {) and replaced the four-Gaussian 2) with the five-Gaussian basis of Rapp& et a1." d basis (4 Using these primitive functions, we recontracted the basis for Cuz+ using the ground state zD(3d9) for the 3d contraction and the average-of-configuration excited ion states [ (3d84s),, and (3d84p),] for the 4s and 4p contractions. The final valence double {contracted Gaussian basis set for Cuz+ is given in Table IV and calculated energies are given in Table V. In order to test the basis sets, we calculated fluorine electron affinity (EA), Cu+ ionization potential (IP), and Cu double ionization potential (DIP). The calculated values of EA = 1.79, IP = 17.72, and DIP = 23.65 eV for HF and EA = 2.62, I P = 20.31, and DIP = 24.1 1 eV for C I singles and doubles agree reasonably well with the experimentally determined values of EA = 3.4 eV,I0 IP = 20.29 eV," and DIP = 28.0 eV." 3.2. HF Calculations. Spin-restricted HF calculations of CuFz were carried out for the three states of interest, zZg+,zIIg,and zAg. The Cu-F distance, R = 2.22 A (this is one of the two different Cu-F distances in KzCuF4crystalzz), was chosen for the first series of calculations. For each state, all orbitals were solved self-consistently. The energy differences en and cz are defined in (3). The H F calculations lead to en = 2963 cm-l and cz = 5522 cm-I. Eliminating the diffuse Gaussians on the fluorine basis set and recalculating the energy splittings leads to tn = 3127 cm-' and cA = 5620 cm-' (the ground-state total energy increases by 0.024053 au). This indicates that the energy spectrum is rather insensitive to the diffuse fluorine exponents. 3.3. CI Calculations. For each state of CuF, (at RCudF = 2.22 A), the C I calculations were based on the S C F orbitals for that state. However, no excitations were allowed out of the core orbitals (1s for F; Is, 2s, 2p, 3s, 3p for Cu). We carried out a full singles and doubles excitation C I (CI-SD) from the dominant configuration, with results as in Table VI. The role of the excitations from F 2s-like orbitals was investigated, and we established that these excitations can be ignored (compare the second and third groups of results in Table VI). These C I calculations lead to an increase in by 13% and in cz by 10%. From an examination of these results, it is clear that the primary factors affecting the ligand field splitting are the excitations (8) and (9) to the C T configurations displayed in (6) and (7). This C T admixture is 12.1% for zZgf and about 10.1% for zJIg (see Table VI), but no such term is possible for 'Ag. We expected that the CI-SD calculations would be biased against C T since only single excitations are allowed out of the C T configuration but doubles are allowed from the ground state.
-
(21) RappE, A. K.; Smedley, T.A,; Goddard 111, W. A. J . Phys. Chem. 1981, 85, 2607. (22) Haegele, R.; Babel, D. Z . Anorg. Allg. Chem. 1974, 409, 1 1 .
Consequently, we carried out a series of calculations [CI-SD(2)] where all single and double excitations were allowed from both the ground and CT configurations. As indicated in Table VI, this leads to a doubling of the CI effect on ligand field splitting (total and 18% for ex). Consistent with this balanced of 23% for treatment for CT is a large increase in the CT admixture (to 20.1% for zZg+and 18.7% for zIIg). As a simplification in the calculations, we investigated the use of single excitations [CI-S(2)] from the ground and C T configurations. As indicated in Table VI, this leads to an overestimate of ligand field splittings. For example, with the full basis, c2 = 8406 cm-' from CI-S(2) and 6757 cm-I from CI-SD(2). The main effect seems to be an extra stabilization of the zZg+state in CLS(2) calculations since = 4361 cm
