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 M C P F 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 M C P F values reported in this Comment. While our M C P F 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 M C P F 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 M C S C F (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 M C P F 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 S C F / M C P F 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 S C F / M C P F method. The 32e-MRSDCI gave 5.2 and 6.9 cV. rcspcctivcly, for Ag, and A u , . ~ , ~Hence, BLP's S C F / 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 S C F / M C P F 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 S C F 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 S C F / 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
8380 The Journal of Physical Chemistry, Vol. 94, N o . 21, 1990
Additions and Corrections
TABLE I: Vertical Ionization Potentials and Binding Energies (eV) of M, and MAa MRSD M
CI
cu
70
jig
6.7 8.5
nu
1 P( M2) MRSD CI-D
72 6.9 8.6
~
MRSD
De(M2) MRSD CI-D
expt
CI
79b 7.6'
16
18
1.3 2.0
1.5 2.1
~~
IP(M4) ~
expt
SDCl
SDCI-D
208b 1.6hd
56 5.5
58 2.7
2.3d
6.9
1.1
expt
72zt08b (7.9'
-
De(M4) MRSD MRSD CI CI-D
17 I .2 I .7
18 1.3 I .9
MRSD CI
49 3.8 5.1
AWMd MRSD CI-D
55 4.2 6.2
expt 563b
+
M R D C l and M R S D C I - D refer to multireference singles + doubles CI and niultirefercnce singles double CI with Davidson's correction. 2 M 2 . Reference 5 . e Reference 7. Reference 8. e Reference 6.
De( M4) rcrcrs to thc cncrgy required for M4
BLP use a scaling factor of 1.2 since their SCF/MCPF De and IP of Cuz are in 17% error compared to the experiment. Our CAS/MRSDCI values are 8-1 3% lower than experimental values. The scaling factor of BLP is based on a comparison with expcriment on dimers and not on any a b initio procedure to account for the missing electron correlation effects in the S C F / M C P F nicthod. Electron correlation effects are different for the three group I B clusters and in fact vary as a function of size. Hence the usc of a single scaling factor for all three clusters of all sizes to represent a complicated missing many-body electron correlation cffect is questioned. Consequently, we disagree with their claimed accuracies of scaled results and comparison of their scaled results with our unscalcd fully a b initio results. I t is more appropriate to compare their unscaled results with our unscaled results. Hence we disagree with BLP's claim that our values are too small. Our rcsults arc the most accurate results obtained to date, directly from a n a b initio study without introduction of any scaling factor. The IPS of Cu,. Ag,, and Au, at the 44e SDCI-D level are 5.8. 5.7 and 7.1 eV compared to BLP's 6.16, 5.86. and 7.32 eV. The cxpcrimcntal IP(Cu,) obtained by Jarrold and CreeganS is 7 . 2 f 0.8 cV. Both theoretical calculations suggest that the lower error bar is reasonable but BLP's SCF/MCPF results for the IPS arc superior to our SDCI-D results. We could not do MRSDCI for thc ions due to too many configurations. The previous pre-
diction? that IP(Au4) >> IP(Ag,) was confirmed by an experiiiicntal htudy of Cheng and Duncan.6 They, however, have only a n upper limit of 7.9 eV for the I P of Au,. I t is concluded that 44e CASSCF/MRSDCI-D study yields more accuratc AEs and IPS compared to the SCF/MCPF method and that the previously reported AE(CU,)~is incorrect. We agree w i t h BLP's Au, > Cu4 > Ag, ordering for AEs and IPS but the prcvious incorrect ordering resulted from an error in the Cu, result. Thc prcviously rcported values for Ag, and Au, are within the accuracies of a 32e CI scheme. The present study could be in IO% crror for thc tetramers compared to experimental values since clcctron correlation effects from 44 electrons and basis set errors could still not be fully accounted. Although our CAS/ MRSDCI-D and BLP's SCF/MCPF to a large extent still do not fully account for correlation effects from all 44 electrons, we have not sccn a better agreement for a 44-electron correlation problem N i t h c x pc r i me n t . Registry No. Ag,, 64475-45-2; Au,. 124236-18-6;Cu4, 65357-62-2.
Depurfi)ieiir oj C'heiprrsrry 4rizona Srntr Linirervitjs i e m p e , Arizona 85287- 1604
ADDITIONS AND CORRECTIONS 1987, Volume 91
John H. Kiefer* and Jatin A. Shah: Cnimolecular Dissociation of Cyclohexene a t Extremely High Temperatures: Behavior of the Energy-Transfer Collision Efficiency. Page 3026. Equation I, which contains the normalization correction of Gilbert et al. (Ber. Bunsen-Ges. Phys Chem. 1983, 87, 169, eq 4.7), is incorrectly evaluated a t high temperatures. Here the Whitten-Rabinovitsch approximation was used for molecular state densities; since this is inaccurate for low E , the integrals of the form J p f ( E ) d E were evaluated as I - J&J(E) d E . Although these integrals are always accurate to within a few percent with this approximation, this is inadequate for the evaluation of ( I ) at very high temperatures where the denominator appears as a small difference of large numbers. We have replaced the above approximate evaluation with a more accurate procedure using direct-count densities. The results are now in complete agreement with the calculations on cycloheptatriene presented by Gilbert et al. and with cyclohexene calculations using an independent program provided by R. Shandross. With this new evaluation. the calculated rate constants for cyclohexene above 1600 K are substantially altered: a fixed cy = (.lEjdown = 550 cm-' now generates a good fit to the dissociation data for all conditions. When the weak-collision formulation of Gilbert et al. is correctl! applied to this problem, it is actually a fixed ( .lE)do,,nrather than a fixed ( AE)all which most accurately describes the c>clohcxcne data.
K. Balasubramanian* Kalyan K . Das
