8378
J . PhY.Y. Chew. 1990. 94, 8378-8379
in conjunction with the well-established generator matrix metho d ~this , ~set~of parameters can be used to rationalize the optical anisotropy, ( - y 2 ) , of polyesters that contain phthaloyl, isophthaloyl, or terephthaloyl groups. lncorportion of the end-to-end vector and dipole moment vector in the analysis will permit calculation of (rT&r) and(pT&p) for the same polymer, and hence the rationalization of their stress-induced and electrically induced bi-
refringence^.'^ (19) Florq, P. J . Macromolecules 1974, 7, 381.
Nevertheless, it is difficult to dismiss the possibility that dimethyl phthalate might have conformations described by the four-state model, with 0 < 90°, and a set of optical parameters different from those found in the planar molecules methyl benzoate. dimethyl terephthalate, and dimethyl isophthalate. Acknowledgmenr. This research was supported by National Science Foundation grant DMR 87-06166, by DGICYT grant PB88-0152, and by the Comunidad de Madrid. Registry No. M B , 93-58-3; DMT, 120-61-6; DMI, 1459-93-4; DMP, 1 3 1 - 1 1-3
COMMENTS Comments on “Bindlng Energies and Ionization Potentials of the Tetramers of Cu, Ag, and Au”
TABLE I: Summary of the Atomization Energies (eV) MCPF” scaled* B F(scaled) expt I .74 ( I .73) 2.09 2.078‘
Sic This Comment refers to the recent work of Balasubramanian
and Feng (BF)I on the geometries and energy separations of the low-lying electronic states of the homonuclear tetramers of the group 1B elements. In this work they reported the atomization energies (AEs) and ionization potentials (IPS). They reported AEs of 9. I I . 5.20, and 6.94 eV for Cud, Ag,, and Au,, respectively. Further they claimed that these values should be 80-90% of the true values due to limitations of both the one- and n-particle treatments. The experimental AEs of the dimers2 and bulk metals3 follow the trend Au > Cu > Ag as do the AEs for the trimers from accurate ab initio calculation^.^ In this Comment we show that the AEs for the tetramers also follow this trend and that the recent values reported by BF for the tetramers, which follow the trend Cu > Au > Ag, are incorrect. These comments also apply to the tetramer IPS reported by BF. The same computational approach is used as in our previous study of the dimers and trimers of the group IB elements-see ref 4 for details. The self-consistent-field (SCF)-based modified coupled-pair functional (MCPF) method is employed to account for electron correlation among the 44 valence d and s electrons for the tetramers. For Au and Ag we employ a relativistic effective core potential (RECP). The same Gaussian basis sets are used as in our previous study of the group IB trimers., For the trimers we consider only the equilaterial triangular geometries, and increase the AEs by the relatively small JahnTeller stabilization energies computed previ~usly.~ For the tetramers we consider only the lowest energy rhombus structure with both degrees of freedom optimized at the MCPF level. Our optimal structures are in reasonable agreement with those of BF; the angles and bond lengths are within 4’ and 0.06 A, respectively. I n Table I we compare our MCPF AEs for the dimers, trimers, and tetramers with previous theoretical and experimental work. For the dimers and trimers we have found that f polarization functions have little effect on the computed AEs and this is the case for Au, here. Therefore, f functions were not included in the tetramer calculations for Cu or Ag. BF also did not include f functions in their calculations based on their finding5 that f ( I ) Balasubramanian, K.; Feng, P. Y. J . Phys. Chem. 1990, 94, 1536 and references therein. ( 2 ) Rohlfing, E. A.; Valentini, J. J. Chem. Phys. Leu. 1986, 126, 113, for C u i and Huber, K. P.; Herzberg, G. Constants of Dioromic Molecules: Van Nostrand Reinhold: New York, 1979, for Ag, and Au,. ( 3 ) CRC Handbook of Chemistry and Physics, 6Sth ed.; Weast. R.C.. Ed.: CRC Press: Boca Raton. FL, 1984. (4) Bauschlicher, C. W.; Langhoff, S. R.; Partridge, H. J . Chem. Phys. 1989, 91. 2412, and references therein.
0022-3654/90/2094-8378$02.50/0
2.73 (2.86) 4.9 I
3.28 5.89
9.1 (10.4)’
1.35 (1.34) 2.00 ( I .99) 3.76
I .62 2.40 4.52
I .3 ( I .6)h 2.1 (2.7)h 5.2 (6.9)‘
I .90 ( I .87) 2.93 (2.94) 5.30 (5.25)
2.28 3.52 6.36
2.0 (2.3)h 3.3 (3.9)h 6.9’
3.0Y 3.50 f 0.01g I .66 f 0.03‘ 2.62‘ 2.95 f 0.0Ih 2.31‘ 3.80‘ 3.82 f 0.02s
“The values in parentheses are obtained with f functions included in t h e basis set; some of the results are taken from ref 4. bScaled by a factor of I .2; see the text. ‘Reference 2. dThe MCPF values include the Jahn-Teller stabilization energies from ref 4 of 0.03, 0.06, and 0.07 eV for Cu3, Ag,, and Au3, respectively. Weltner, W.; Van Zee, R. J. Annu. Rec. Phys. Chem. 1984, 35, 291. ’Reference I . gReference 3. hBalasubramanian, K . ; Feng, P. Y . Chem. Phys. Lett. 1989, 159, 452. ‘Reference 5. TABLE 11: Ratio of Atomization Energies with Experimental Results in Parentheses dimer trimer tetramer bulk Cu/Au Ag/Au
0.916 (0.900) 0.711 (0.719)
0.932 0.683
0.926 0.723
(0.917) (0.774)
functions have little effect on either the AE of Au2 at the correlated level or the geometry of Au, at the complete-active-space S C F level. The size-extensive MCPF approach in conjunction with the flexible Gaussian valence basis sets employed in this work is expected to provide a nearly equivalent treatment of all three metals and all cluster sizes. The computed MCPF binding energies for the dimers are about 82% of experiment. Therefore, in Table I we also give AE values for all clusters scaled by the factor of 1.2, which should give results close to the true values. Our scaled AEs for Ag,, Au,, and Cu, are about 0.6, 0.6, and 3.2 eV smaller than the directly computed values of BF. Since our scaled values should be accurate to within several tenths of an electronvolt, the AE values reported by BF, especially for Cu,, are too large. The ratios of the atomization energies for CuJAu, and Ag,/Au, are given along with the bulk values in Table 11. We find both ratios to be nearly constant for all cluster sizes including the bulk. This is particularly true for the CuJAu, ratio, which varies only over the narrow range of 0.924 f 0.008. I n contrast, ( 5 ) Balasubramanian, K.; Feng, P. Y.; Liao, M. Z. J . Chem. Phys. 1989, 91. 3561
1990 American Chemical Society
J . Phys. Chem. 1990, 94, 8379-8380 BF obtain 1.3 1 for the ratio of the AEs of Cu4 and Au,. This also strongly suggests that their computed AE value, at least for Cu,, is in error. The vertical IPS of Cu,, Ag,, and Au, shown in Figure 7 of BF follow the trend Cu > Au > Ag. Considering that the IP of Ag atom6 is only 0.1 5 eV less than Cu atom, it is particularly surprising that their vertical IP of Ag, is about 2 eV less than for Cu,. Our MCPF vertical IPS (eV) are Cu, (6.16). Ag, (5.86). and Au, (7.32). These are expected to be 88-90% of the true values based on the computed atomic IPS. In contrast to BF, our tetramer IPS follow the same trend (Au > Cu > Ag) as the atomic I Ps. The MRCl + Q AEs reported in the reply by Balasubramanian and D ~ swhich , ~ are 3.6. 1.O, and 0.7 eV smaller than his previous results for Cu,, Ag,, and Au,, respectively, support the MCPF values reported in this Comment. While our MCPF AEs are smaller than their MRCl + Q values, our scaled MCPF AEs are slightly larger, which is consistent with the fact that our values are scaled based on experiment, while the MRCl Q results are expected to be too small due to limitations in both the one- and n-particle treatments. We feel that it is valid to scale the MCPF results, because they are size extensive and the nature of the bonding is very similar in the different sized clusters. The fact that the MCPF IPS are larger than the SDCI + Q values' can probably be attributed to the lack of size extensivity in the SDCI + Q method. Our scaled AE value of 5.9 eV for Cu, is consistent with the upper bound of 6.3 eV given by Jarrold and Creegan,* and we feel that the scaled MCPF AE values should be the most accurate and consistent set available. Thus we conclude that the MRCl calculations reported in the reply by Balasubramanian and Das7 fully support our MCPF calculations, which show that the bonding in the group IB tetramers is completely consistent with that for the dimers, trimers, and bulk. Registry No. Ag,, 64475-45-2; Au,, 124236-1 8-6; CU,,65357-62-2.
+
+
( 6 ) Moore, C. E. Atomic Energy Leoels; U S . GPO: Washington, DC, 1949; Natl. Bur. Stand. Circ. No. 467. (7) Balasubramanian, K.; Das, K. K. J . Phys. Chem.. following paper in this issue. (8) Attributed to M . F. Jarrold and K . M. Creegan in ref 7.
NASA Ames Research Charles W. Bauschlicher, Jr.* Center Stephen R. Langhoff Moffett Field, California 94035 Harry Partridge
Reply to Comments on "Binding Energies and Ionization Potentials of the Tetramers of Cu, Ag, and Au" Sir: In response to the previous Comment by Bauschlicher et al. (BLP),' we point out that the focus of the previous article2 is the geometries and energy separations of low-lying electronic states of Ag, and Cu4. We computed the ionization potentials (IP) and atoniizution energies (AE) mainly for qualitative comparison with thc corresponding values of Au,. Nevertheless, the results of 44-electron multireference singles + doubles CI (MRSDCI) containing 1.4 million configurations after complete active space MCSCF (CASSCF) calculations are reported below. We start with a CASSCF method which distributed the four outermost electrons in all possible ways among the metal valence s orbitals. Although excitations of the 40 d electrons were not allowed at the CASSCF stage, the final MRSDCI calculations included excitations of all 44 electrons. BLP' use a single-configuration S C F method to obtain orbitals for their MCPF study. Thc basis set is comparable in the two methods, and note that ( I ) Bauschlicher, Jr., C. W.: Langhoff, S. R.; Partridge. H . J . Phys. Chem.. previous paper i n this issue
0022-3654/90/2094-8379$02.50/0
8379
indeed in a previous CASSCF/CI study on A u ~ IO-component .~ 4f functions were included and the effects of these functions were found to be insignificant. In the previous study, Balasubramanian and Fcng (BF)2 used a CASSCF/32e CI approximation for Cu, and Ag4 mainly because of technical limitations with an earlier version of ALCHEMY I I codes4 that runs with 8 megabytes of iiicmory. However, now an improved version (on an IBM 3090/300) provides 32 megabytes. The 32e MRSDCI was satisfactory for the computation of geometries and energy separations of Ag4 and Cu,, the focus of the previous study? although we were aware that it is less satisfactory for the computation of IP and AE. Nonetheless, this approximation provided reasonable AE and IP for Au, in a previous study.3 The AE reported for C U , ~ was in error. For the dissociated supermolecule, the reference occupations had to be permuted for the MRSDCI since the POLCl natural orbitals which were used for the MRSDCI computations are ordered while the CASSCF orbitals are randomly arrangcd. In doing so, the occupancy of one reference configuration was incorrectly permuted. The IP of Cu, in the previous study was also larger due to an orbital space inconsistency. Table I shows the IPS, Des, and AEs of the dimers and tetramers together with available experimental results from refs 5-8. We havc already discussed the results on trimers9 but Bauschlicher and co-uorkcrsI0 have not recognized this earlier work.9 There is no major disagreement in the results of BLP and ours on trimers, cxccpt that (i) the spin-orbit effects are shown to influence the barrier to pseudorotation by 67% in Auj9 while BLP'O ignored spin-orbit effects and (ii) BLPs MCPF AEs for the trimers are much smaller especially for Au3 than our values and experiment as sccn from Table I of ref I . Theoretical results in Table 1 for the tetramers were obtained through a CASSCF/MRSDCI treatment that included all 44 electrons, all orbitals, and up to I .4 million configurations. In addition, we calculated the effects of unlinkcd quadruples through Davidson's corrections. As seen from Table I, our dimer MRSDCI-D IPS are roughly 9 1 7 of the experimental values. The Des of Cuz, Ag,, and Au2 havc comparable accuracies. We expect the accuracies for the tetramers to be similar to but not identical with those for the dimers. The De obtained in the present study for Au2 (2.1 eV) is the bcst thcoretical value to date. The effect of f functions changed thc De at most 0.05 eV. This corroborates the finding of BLP,' although their SCF/MCPF value of 1.90 eV is 10% smaller than our value. The MRSDCI-D (44e) AEs of Cu,, Ag,, and Au, are 5.5,4.2, and 6.2 eV compared to 4.91, 3.76, and 5.3 eV obtained by BLP' using the SCF/MCPF method. The 32e-MRSDCI gave 5.2 and 6.9 cV. rcspcctivcly, for Ag, and A u , . ~ , Hence, ~ BLP's SCF/ MCPF AEs for Cu,, Ag,, and Au, are 0.59, 0.44, and 0.9 eV, rcspcctivcly, lower than our CAS/MRSDCI results. For the dimers and trimers also their SCF/MCPF values are approximately 4-107; and 5-1 1% lower than our values and 16-24% lower t h a n experimental values. We believe this is due to the inadequacy of the SCF/MCPF method to fully account for electron correlation cffccts sincc thc basis sets are comparable. Furthermore, BLP used a singlc-configuration SCF method to generate orbitals while we use a more accurate CASSCF method. Consequently, the CASSCF/MRSDCI-D values for the dimers and trimers are in better agreement with the experiment compared to the SCF/ MCPF method. ( 2 ) Balasubramanian, K.; Feng, P. Y. J . Phys. Chem. 1990, 94, 1536. ( 3 ) Balasubramanian, K . ; Feng. P. Y.; Liao, M. Z. J . Chem. Phys. 1989, 91. 3561. (4) The major authors of ALCHEMY II are B. Liu. B. Lengsfield, and M. Y os h i mi nc. ( 5 ) Jarrold. M. F.; Creegan, K . M. I n t . J . Moss Specrrom. ion Processes, in press. (6) Duncan, M . , private communications. (7) Hopkins, J . B.; Langridge-Smith. P. R. R.; Morse, M. D.; Smalley, R . E.. unpublished results. (8) Hilpert, K.. Gingerich, K . A . Eer. Bunsen-Ges. Phys. Chem. 1980.84, 739
( 9 ) Balasubramanian, K.; Liao. M. Z . Chem. Phys. 1988. 127. 313. ( I O ) Bauschlicher. C. W. Chem. Phys. Left. 1989, 156, 91. Bauschlicher. C W : I anghoff. S . R.: Partridge. H.J . Chem. Phys. 1989, 9 / , 2412.
0 1990 American Chemical Society
