J. Phys. Chem. 1985,89, 5202-5206 0-
Table I. We are continuing to explore the effect on the dissociation energy of basis set size/composition, 3s, 3p differential effect, and level of correlation.
A
I IO
-
I I I I
20 -
I I
30 40
-
50
-
E
\
52.4
I
I
103.0
I
101.0
I I I
60-
s
I
I I
= 0 1
Conclusions
3
I I
4
I
I
I
I
120
t-
Figure 7. Computed dissociation energies of various combinations of Sc+ and two H atoms relative to the separated ground state atoms. The dotted horizontal lines (Do) are the Dc(s corrected for zero-point vibrational energy.
equilibrium geometry. In particular we increased the number of active orbitals in the MCSCF (we used 6al, 7al, 8a1, 3b2, 4b2, 3b1, la2) to allow for correlation perpendicular to the molecular plane and increased flexibility in the *un system. While the resulting MCSCF energy was lowered by 6 mhartrees the MCSCF+ 1+2 was essentially unchanged from that reported in
The calculations permit the following conclusions: a. The ground state of ScH+ is of 2A symmetry, has an essentially covalent bond (with the Sc component to this bond being approximately 68% sp and 32% dJ, and has a substantial bond energy. Our calculated Do of 52.7 kcal/mol is in good agreement with the two experimental values of 54 f 4 and 55 f 2 kcal/mol. b. The 211 and 2Z+ are low lying and we estimate they are within 4.8 and 5.9 kcal/mol of the ground state. c. The equilibrium structure of the ground 'Al state of ScH2+ is nonlinear (0 = 106.7') with a bond length of 1.75 A. This bond length is shorter than in any of the three ScH+ states studied and reflects the larger d character in the ScH2+bonds. d. Sc contributes to the bonds in ScH2+ via the 4s f 3d,, hybrids. e. We estimate that the second bond in ScH2+ is almost as strong as the first (a De of 51.7 vs. 54.7 kcal/mol) but do not calculate it to be as strong as experiment suggests (DoI 50 or equal to 65 kcal/mol). f. From the summary of the calculated energetics shown in Figure 7 we anticipate that the reductive elimination of H2 from ScH2+will be endothermic. While the calculated endothermicity is only 2 kcal/mol we do expect our differential correlation error to favor the 'Al state of ScH2+and thus increase this calculated endothermicity. In addition, since this calculated endothermicity is with respect to the spin forbidden process ScH,+('AI)
-+
S C + ( ~ D+) H2('Zg+)
the spin-allowed process (in which Sc+ is in the ID state) would be endothermic by at least 9 kcal/mol. Acknowledgment. We thank Professor P. Armentrout for sending us his unpublished data on ScH+ and ScH2+ and the Argonne Theoretical Chemistry group for providing the QUEST-164 codes. Registry No. ScH', 83018-00-2; ScH,', 93383-01-8.
Ab Initio Calculations Including Relativistic Effects for Ag2, Au2, AgAu, AgH, and AuH Richard B. Ross and Walter C. Ermler* Department of Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, New Jersey 07030 (Received: June 7, 1985)
The ground electronicstates of Ag,, Auz,AgAu, AgH, and AuH are investigated in ab initio self-consistent field and configuration interaction calculations. Relativistic and nonrelativisticeffective potentials are employed to replace core electrons, and extended basis sets comprised of Slater-type functions are used to describe valence electrons. Electronic properties of each species are calculated and compared to experiment, other effective potential calculations, and relativistic and nonrelativisticall-electron calculations.
Introduction
Self-consistent field (SCF), multiconfiguration self-consistent field (MCSCF), and configuration interaction (CI) calculations have been performed on the neutral and first ionized states of Ag2 and Au2 and on AgAu, AgH, and AuH. Relativistic effects are important in these systems and have been incorporated through the use of relativistic effective core potentials (REP). Calculations have also been performed with nonrelativistic effective core potentials (NEP) for comparison to all-electron calculations. Advantages of employing the R E P S and N E P s are that they allow for the use of more extended valence basis sets and more extensive C I procedures than comparable all-electron 0022-3654/85/2089-5202$01.50/0
calculations as well as facilitating a reliable estimate of the important relativistic effects in the use of REP's. Several studies have been completed which establish the validity of employing effective potentials in ab initio quantum chemical calculations. In a study employing NEP's, N E P CI calculations were compared to all-electron CI calculations on F2, C12,and LiC1.I It was found that the NEP and all-electron potential energy curves are nearly superimposable. REP's have also been employed in several studies and have ( 1 ) Christiansen, P. A,; Lee, Y.S.; Pitzer, K. S.J . Chem. Phys. 1979, 7 1 ,
4445.
0 1985 American Chemical Society
Ground States of Ag2, Au2, AgAu, AgH, and AuH TABLE I: Orbital Energies from REP SCF and All-Electron DF Calculations (hartrees)
atom
orbital
DF
REPSCF
difference
Ag
5s 4d* 4d 6s
-0.237 -0.526 -0.501 -0.292 -0.493 -0.429
-0.233 -0.521 -0.498 -0.284 -0.486 -0.423
0.004 0.005 0.003 0.008 0.007 0.006
Au
5d* 5d
yielded consistent and reliable results. Results for Arz, Kr2, and Xe2, and their respective cations, from S C F and C I calculations employing REP's compared favorably to analogous nonrelativistic all-electron calculations.z The expected relativistic effects, such as a small contraction of Re and slightly less repulsive potential energy curves a t short internuclear separation, were observed. In addition, REP's have been used in calculations on Sn2and Pb2,3 T12,4 SIIO,~Pb0,6 PbH,' SnH,* and TlH9 resulting in spectroscopic constants that are in good agreement with available experimental values. Applications of REP's of this form have been reviewed by Pitzer,Io Krauss and Stevens," and Christiansen, Ermler, and Pitzer.12
Calculations REP's and NEP's were calculated for silver and gold such that the effects of the innermost 36 electrons in silver and 68 electrons in gold were replaced leaving only the outermost 10 d electrons and a single s electron to treat explicitly in both cases. REP's and NEP's were also calculated such that the outermost 19 electrons were treated explicitly. The REP's were generated according to the prescription of Lee at a1.13 using shape consistent pseudooribta1s.l They were incorporated in the form of numerical functions U,j(r). Appropriate weighted averages of the two components of the Ub(r) corresponding to values of the angular quantum number 1 were formed to generate averaged relativistic core potentials (AREP). The employment of AREP's permits the use of standard electronic structure computer programs based on the assumption that the L-S coupling scheme is sufficient for describing the symmetry of the various states studied. Triple { s, double { p, and double [ d basis sets consisting of 6s, 6p, and 5d Slater-type functions (STF) were optimized for Au in atomic SCF calculations employing the AREP's to represent the core electrons. The p STF's were optimized for the lowest 2P state of Au. In addition, a basis set that included double { STF's for the 5s and 5p shells was optimized for Au in which an REP replacing the effects of the innermost 60 electrons was employed. Similar basis sets were optimized for Ag employing 4s, 4p, 5s, 5p, and 4d STF's. Triple [ s, double { p, and triple { d basis sets were also optimized for each atom. For calculations treating 19 valence electrons, double { 4s and 4p STF's were included. For w - w coupling molecular calculations employing the REP's, the same STF's are used to represent atomic orbitals with the same I but different j quantum numbers. S C F calculations were carried out employing both AREP's and REP's. The formalism for REP S C F calculations in terms of the w-w coupling scheme is described by Lee et al.I4 MCSCF and C I calculation were performed on Ag,, Au2, and (2) Christiansen, P. A.; Pitzer, K. S.; Lee., Y. S.; Yates, J. S.; Ermler, W. C.; Winter, N. W. J. Chem. Phys. 1981, 75, 5410. (3) Balasubramanian, K.; Pitzer, K. S. J . Chem. Phys. 1983, 78, 321. (4) Christiansen, P. A. J. Chem. Phys. 1983, 79, 2928. (5) Balasubramanian, K.; Pitzer, K. S. Chem. Phys. Lett. 1983, 2 0 0 , 273. (6) Balasubramanian, K.; Pitzer. K. S. J . Phys. Chem. 1983, 87, 4857. (7) Balasubramanian. K.: Pitzer, K. S. J. Phvs. Chem. 1984. 88. 1146. (8) Balasubramanian, K.; Pitzer, K. S. J. Mo/:Spectrosc. 1984, 203, 105. (9) Christiansen, P. A.; Balasubramanian, K.; Pitzer, K. S. J . Chem. Phys. 1982, 76, 5087. (IO) Pitzer, K. S.Inr. J. Qunnrum Chem. 1984, 23, 131. (11) Krauss, M.; Stevens, W. J. Annu. Rev.Phys. Chem. 1984, 35, 357. (12) Christiansen, P. A.; Ermler, W. C.; Pitzer, K. S.Annu. Rev. PhYs. Chem. 1985, 36. 407. (13) Lee, y,s,; Ermler, w, c,;Pitzer, K, s, J , =hem, phys, 1977, 67,
5961.
(14) Lee, Y. S.;Ermler, W. C.; Pitzer, K. S . J. Chem. Phys. 1980,73,360.
The Journal of Physical Chemistry, Vol. 89, No. 24, 1985 5203 TABLE 11: Molecular Constants of Ag2 and Ag,'
Re, %, Go, cm-' Ag, AREP S C F 2.76 72.6 AREP SCFb 2.74 71.7 AREP SCFc 2.74 74.4 REP SCF 2.76 72.7 MCSCF 2.81 62.0 CUI) 2.76 78.5 CW) 2.72 78.4 CI(2) + Qd 2.71 71.9 expt 2.47' Ag2+ AREP S C F 2.99 49.9 REP SCF 3.02 48.2 CUI) 2.92 53.4 calcn
we, cm-'
' use,cm-' De, eV
145.4 143.4 149.4 145.6 123.9 146.3 157.2 143.6 192.4' 100.0 96.4 107.1
0.45 0.39 0.74 0.45 0.39 0.48 0.57 0.55 0.66 0.37 0.40 0.70
0.68 1.08 1.658
"Double ( basis set for the 4d shell and REP's due to 11 valence electrons. *Triple {basis set for the valence d-shell. 'Triple {basis set for the valence d-shell plus a set of f-type STF's. dEffect of quadruple excitations (ref 16). 'Reference 17. fSradanov, V. L.; Pesic, D. S. J . Mol. Spectrosc. 1981, 90, 27. gGingerich, K. A. Faraday Discuss. Chem. Soc. 1980, 14, 109. TABLE III: Molecular Constants of Au2 and Au2+
calcn A U ~ AREP S C F REP SCF MCSCF CI(1) CI(2) CI(2) Qb expt Au2+ AREP S C F REP S C F
+
R..
A
2.65 2.65 2.69 2.65 2.64 2.64 2.47< 2.82 2.82 2.76
Gn. cm-'
cm-' 160.1 161.2 140.1 159.1 162.1 159.4 191' 107.8 109.0 129.7
w..
80.0 80.5 69.9 78.5 80.9 79.6 53.8 55.3 64.8
ax.. cm-'
D.. eV
0.42 0.42 0.54 0.46 0.42 0.43
1.11 1.58 2.31d
0.59 0.58 0.42
1.71
'Double ( basis set for the 5d-shell and REP's due to 11 valence electrons. Effect of quadruple excitations (ref 16). 'Reference 18. dKordis, J.; Gingerich, K. A.; Seyse, R. J. J . Chem. Phys. 1960, 33, 1284. TABLE I V Molecular Constants of AgAu"
calcn AREP S C F REP S C F
MCSCF CI(1)
Re, A 2.69 2.69 2.73 2.64
Ge cm-'
cm-I 161.5 161.9 143.7 176.7
w.,
80.7 80.8 70.7 88.2
w x , , cm-' 0.47 0.47 0.58 0.57
D.. eV
1.00 1.47 2.08b
expt
" Double ( basis for the 4d and 5d shells and REP'S due to 11 valence electrons. bGurvich, L. V.; Karachevstev, G. V.; Kondrat'yev, V. N.; Ledbedev, Y. A.; Mendredev, V. A.; Potapov, V. K.; Khodeev, Y. S. "Bond Energies, Ionization Potentials, and Electron Affinities"; Nauka: Moskow, 1974. TABLE V Molecular Constants Derived from SCF Results for AgH and AuH"
AgH -
AuH
calcn NEP all-electronb REP all-electron' exptd NEP all-electronb REP REPe all-electron' exptd
Re, A 1.76 1.77 1.70 1.70 1.62 1.82 1.82 1.59 1.59 1.64 1.52
we, cm-'
upx,,cm-'
1538 1452 1537
21 22 22
1760 1520 1475 2100 2029
34 32 19 45 18
2305
43
"Triple ( basis set for the Ag 4d shell and the Au 5d shell and 11 valence electron EP's. bReference 21. 'Reference 32. dReference 34. 'Double (basis set for the 5d shell.
AgAu. For calculations labeled CI(l), the set of configurations includes those arising from single and double excitations from the sug and suu valence orbitals and single excitations from the d-type valence orbitals into virtual orbitals. This corresponds t o the
5204 The Journal of Physical Chemistry, Vol. 89, No. 24, 1985 TABLE VI: Comparison of 19 and 11 Valence Electron SCF Calculations
AuH
calcn REP 11-electron 19-electron
all-electron Dirac-Fock" expt Ag,
NEP 11-electron 19-electron
all-electron Hartree-Fockc expt
Re,A 1.59 1.61 1.64 1.52b 2.9 1 2.88 2.79 2.4Id
cm-' 2100
w.,
2062
2305b 121 122 129 192e
Reference 32. bReference 34. 'Reference 21. dReference 17. 'Sradanov, V. L.; Pesic, D. S . J . Mol. Spectrosc. 1981, 90,27. procedure used by Ermler et al. in calculations on Au2.1S The second type of C I calculation, labeled CI(2), involves all single and double excitations with respect to the S C F ground-state configuration. The CI(2) calculations were limited to values of internuclear separations near equilibrium (Re). Dissociation energies are reported only for those calculations that dissociate properly. An approximate correction for the quadruple excitations (unlinked clusters) was added to the CI(2) energies by using the where Co Langhoff-Davidson formula, AEquad= (1 - Co2)AEDE, is the coefficient of the SCF configuration and hEDEis the energy - EsCF.16 lowering Ecrc2) Orbital energies for the valence s, d*, and d atomic orbitals obtained through R E P S C F calculations for silver and gold are shown in Table I together with those due to all-electron numerical Dirac-Fock (DF) calculations. Spectroscopic analyses for Ag, and Ag2+ are given in Table 11, for Au, and Auz+ in Table 111, for AgAu in Table IV, and for AgH and AuH in Table V. Table VI contains a comparison of 19 and 11 valence electron S C F calculations.
Discussion Orbital energies for the valence orbitals (s, d*, and d) obtained though relativistic atomic S C F calculations employing the REP'S and the optimized basis sets are in good agreement with those calculated through all-electron DF calculations. As shown in Table I, the maximum energy differences between D F and R E P S C F calculated orbital energies are 0.005 and 0.008 au for Ag and Au, respectively. The close agreement between D F and REP S C F orbital energies is one indication that the effects of the core electrons are being accurately reproduced by the R E P S . Values calculated for the equilibrium bond lengths of Agz and Au, through both 1 1-electron AREP S C F and 11-electron R E P S C F calculations are 2.76 and 2.65 A, respectively, as shown in Tables I1 and 111. Experimental bond lengths for Ag, and Au2 are 2.4717and 2.47 A,'* respectively. The value reported for Ag, was not obtained directly, but was estimated from spectroscopic relations among molecules containing Cu, Ag, and Au. The calculated values show relativistic contractions when compared to the present NEP SCF calculations on Ag, (2.91 A) and to NEP S C F calculations by Christiansen and Ermlerlg on Au, (3.01 A). As expected, the contraction in Au, is considerably larger than that found in Ag,. In a previous 11-electron REP SCF study by Lee et al. on Au,, employing a (2s 2p 2d) STF valence basis set, Re was calculated to be 2.50 The fact that their value for the equilibrium bond length is shorter than the present value is not surprising in that a Phillips-Kleinman type of effective potential was used. Such E P s have been shown to seriously underestimate the repulsive portions of potential energy curves leading to interatomic distances (15) Ermler, W. C.; Lee, Y.S.; Pitzer, K. S. J. Chem. Phys. 1979, 70,293.
(16) Langhoff, S. R.; Davidson, E. R. Int. J . Quantum Chem. 1974,8, 61. (17) Brown, C. M.; Ginter, M. L. J. Mol. Spectrosc. 1978, 69, 25. (18) Ames, L. L.; Barrow, R. F. Trans. Faraday Soc. 1967, 63, 39.
(19) Christiansen, P. A.; Ermler, W. C. Mol. Phys., in press. (20) Lee, Y.S.; Ermler, W. C.; Pitzer, K. S.; McLean, A. D. J . Chem. Phys. 1979, 70, 288.
Ross and Ermler that are too As a result, fortuitous agreement with experiment for the equilibrium bond distance was obtained. Spectroscopic analyses of 11-electron MCSCF and CI( 1) potential energy curves of Ag, and Au, are shown in Tables I1 and 111, respectively. The values of we show that the shapes of the calculated potential energy curves agree well with experiment but are shifted to somewhat larger equilibrium bond distances. The shift in Re is of similar origin in both Ag, and Au,. It may be due in part to the lack of additional p- and d-type functions in the basis. McLean?I in all-electron nonrelativistic calculations employing a triple {valence and double { STF core basis set on Ag,, obtained a contraction of 0.07 A in proceeding from S C F to C I calculations. The calculations were based on an excitation scheme similar to that used in the present CI( 1) calculation. No contraction was observed in the AREP calculation in which a double { p and d valence basis set was employed. To investigate the effects of an additional d-type S T F in the basis at the S C F level, AREP S C F calculations were performed on Ag, employing a triple { S T F basis set for the d orbitals. Re was calculated to be 0.02 A shorter than in calculations employing double {d STF's. This effect may be somewhat amplified in the C I calculations. In addition, it is also possible that configurations corresponding to double excitations out of the d shell may be important in the C I calculations. In a nonrelativistic all-electron C I calculation on AgH by McLean, employing a triple { STF valence basis set, a contraction of 0.03 A was obtained when these configurations were included in the CI calculation.2i These configurations were included in the present CI(2) calculations on Au2 and Ag,. The resulting effects were contractions of 0.01 and 0.04 A for Au, and Ag,, respectively. The above-mentioned effects are seen in calculations on Ag, and a contracted Gaussian-type function by B a s ~ h ? ~A?n~AREP ~ (GTF) valence basis with double {d-type GTF's was employed to calculate Re as 2.62 A through a C I procedure that included "energy selected" double excitations from the d shell. In another CI calculation, omitting one of the d-type GTF's and the double excitations out of the d shell, Re was calculated to be 2.68 A. The same AREP was used in both calculations. Comparing the present calculated value for Re for Agz and that of Basch, it is surmised that the differences in the calculated bond lengths arise from differences in the forms of the REP'S employed. In several 11-electron calculations on Ag, and Au the present calculated bond lengths are consistently about 0.10 longer than those calculated by Basch, who employed a modified PhillipsKleinman-type REP. It is also plausible that the inclusion of f-type functions in the basis is important in the correlated calculations. In a previous REP calculation on Au, by Ermler et al., employing a (2s 2p 2d If) S T F valence basis set, a shortening of 0.1 1 A was obtained in proceeding from an S C F to a C I c a l ~ u l a t i o n .The ~ ~ configuration selection scheme employed was the same as that of the present CI(1) calculation. In addition, McLean showed that the incorporation of f-type functions into the basis in calculations on AgH led to a contraction of 0.07 8, in proceeding from an allelectron nonrelativistic S C F calculation to a CI calculation employing a selection scheme equivalent to that in the present CI( 1) procedure.21 McLean found similar results for AuH. It should be noted, however, that when McLean's CI calculations were extended to include double excitations out of the valence d shell, the calculated values of Re were the same with or without f-type functions in the basis. Calculations at the AREP S C F level for Ag, that include a single set of f-type STF's, analogous to the basis used by McLean, resulted in an energy lowering of about 1 mhartree for each internuclear separation. The results given in Table I1 show that there is no effect on Re and small changes in we. C I calculations may show a larger contribution due to the f-type basis functions. (21) McLean, A. D. J . Chem. Phys. 1983, 79, 7 . (22) Basch, H. Symp. Faraday SOC.1980, 14, 149. (23) Basch, H. J . Am. Chem. SOC.1978, 100, 6989.
Ground States of Ag,, Auz, AgAu, AgH, and AuH The effects resulting from correlation of the ( n - 1)s and ( n - l ) p orbitals (where n is the principal quantum number of the outermost s orbital) may also be important. In the present 11electron calculation these orbitals are included in the defined set of core orbitals. A method for the treatment of intershell correlation effects on the alkali dimers has been proposed by Muller et al.24 In another study of the alkali dimers, Partridge et al. have shown that using localized MCSCF MO's and including single and double excitations from the p-shells recovers important core-valence effects on bond lengths.25 It should be noted, however, that in the case of group 1 136molecules the presence of filled d-shells may require a somewhat different approach to treatment of core-valence effects. TO investigate the effect of adding the next inner shell at the S C F level of approximation, 19 valence electron EP's were used in S C F calculations on AuH and Ag,. As can be seen in Table VI, the changes in Re and we for both the hydride and the dimer are very small. Finally, with respect to the differences between calculated and experimental Re values, the present deviations are of the same magnitude as those found in several other recent REP calculations on heavy atom system^.^,^,^,^^,^' Re of Ag, has also been calculated in a nonrelativistic allelectron SCF calculation by Shim and Gingerich.28 Their basis consisted of contracted GTF's and was not as large as McLean's S T F basis,21but their calculated value of 2.77 A is only 0.02 A shorter than that of McLean. Several recent studies on Cu2 have examined the effects of accounting for size consistency when CI calculations are performed with basis sets containing f-type functions. Sunil et al. have shown that including diffuse f functions in CI calculations improves 0, by about 0.1 eV.29 Werner and Martin30 and Scharf et aL3I have calculated Re to within 0.02 A of experiment after accounting for both sizeconsistency and first-order relativistic effects, which were of similar magnitudes. The basis sets employed in the present CI calculations do not include f functions. It is also noted that little effect is seen after accounting for unlinked clusters (CI(2) + Q) via the Langhoff-Davidson correction.I6 Although the detailed nature of the bonding in Cuz, Ag2, and Au2 may be quite different, it is possible that size-consistency effects in correlated calculations including f-type basis functions could have an important effect on Re in Ag, and Auz. Good agreement for Re of AgH and AuH was obtained between the present calculations and nonrelativistic and relativistic allelectron calculations by McLean2' and by Lee and M ~ L e a n . ~ , The calculated values shown in Table V all agree to within 0.01 A with the exception of the relativistic S C F calculation on AuH, where the present value is shorter by 0.05 A. The close agreement demonstrates the ability of the REP'S and NEP's to reproduce the effects of the core electrons in the hydride calculations. An A R E P SCF calculation on AuH was also performed including the 5s and 5p shells in the valence space. As shown in Table VI, R, was calculated to be 0.02 A longer than that due to the 11electron AREP. This indicates that the effect of adding the next inner shell for the hydride calculations is negligible. McLean also performed nonrelativistic all-electron S C F calculations on Ag,.,l The present l l-electron N E P S C F value for Re is 2.91 A compared to his value of 2.79 A. The same difference is seen in comparing an 11-electron N E P S C F calculation on Au, by Christiansen and Ermler19 with an all-electron calculation by Lee et aLZ0 To investigate the effect of the next inner shell s and
(24) (a) Muller, W.; Flesch, J.; Meyer, W. J . Chem. Phys. 1984,80, 3297. (b) . , Muller. W.: Mever. W. J . Chem. Phvs. 1984. 80. 3311. (25) Partridge, H.; Bauschlicher, C. W.; Walch, S. P.; Liu, B. J . Chem. Phys. 1983, 79, 1866. (26) Christiansen, P. A. Chem. Phys. Lett. 1984, 109, 145. (27) Wang, S.W.; Pitzer, K. S . J . Chem. Phvs. 1983. 79. 3851. (28) Shim, I.; Gingerich, K. A. J . Chem. Phis. 1983, 79, 2903. (29) Sunil, K. K.; Jordan, K. D.; Raghavachari, K. J . Phys. Chem. 1985, 89, 457. (30) Werner, H.; Martin, R. L. Chem. Phys. Lett. 1985, 113, 451. (31) Scharf, P.; Brode, S.;Ahlrichs, R. Chem. Phys. Lett. 1985, 113,447. (32) Lee, Y. S.;McLean, A. D. J . Chem. Phys. 1982, 76, 735.
The Journal of Physical Chemistry, Vol. 89, No. 24, 1985 5205 p electrons, a 19-electron N E P S C F calculation was performed on Ag,. Table VI shows that Re is calculated to be 0.03 A shorter than in the 11-electron N E P S C F calculation. The remaining 0.09-A difference may be due to the use of a basis set that is too small to describe the core orbitals in the all-electron calculations resulting in superposition errors or to deficiencies in the NEP's. With respect to the magnitudes of the relativistic contraction in Ag and Au molecules, Lee and McLean, in the relativistic all-electron SCF calculations on AgH and AuH referred to above, ~ ~it is report contractions of 0.08 and 0.25 A, r e s p e c t i ~ e l y .If assumed that the relativistic contractions will approximately double in the homonuclear dimer, subtraction from the nonrelativistic all-electron value of Re (2.79 A) for Ag, gives an Re that is 0.14 A too long compared to experiment. However, for Au,, doubling the AuH contraction and subtracting it from the nonrelativistic all-electron Re (2.84 A) yields a bond length that is 0.13 A too short compared to experiment. The ratios of the various contractions may yield some information. The ratio of bond length contractions (Au:Ag) in the hydrides is 3.2. The ratio of contractions obtained when the calculated relativistic expectation values ( r ) for the valence s orbital of each atomic species are compared to nonrelativistic values is 2.7. If it is assumed that the relativistic contraction in Au2 is 3 times as great as that in Ag,, a range of contraction of 0.30-0.48 8, is predicted for Au2 based on relativistic contractions for Ag2 of 0.10-0.16 A.22,28(The validity of comparing atomic orbital relativistic contractions to relativistic bond contractions is not clear since the latter is obtained to a large extent in a perturbation theory approach using the relativistic Hamiltonian and a nonrelativistic wave f ~ n c t i o n . ' ~ J ~ ) When subtracted from the nonrelativistic all-electron result for Au2,15this yields a range of 2.39-2.54 A for Re. Considering that the experimental bond length of Au2 (2.47 A) lies in the upper end of this range and that the predicted range may be shifted to even shorter bond lengths if CI calculations are considered, it is suggested that the relativistic contraction in Ag2 should be about 0.1 A or less. The ratio of the contractions in Ag, to Au,, comparing the present calculations with the N E P calculations, is 2.4. This is in qualitative agreement with the arguments given above. In the case of Ag,', the results of Table I1 show that Re and we are of expected magnitudes compared to those of Ag,. Re is longer for the ionized species and we is smaller. In contrast to Ag2, a contraction of 0.07 A is observed in proceeding from AREP S C F to CI( 1) calculations. The vertical ionization potential is 5.59 eV based on the REP S C F calculations, compared to the Koopmans' theorem value of 5.94 eV. The results of Au,', shown in Table 111, are consistent with those obtained for Ag,'. Re is longer than in Auz, we is smaller, and a shortening of 0.06 8, in Re is observed in proceeding from AREP SCF to CI(1) calculations. The vertical ionization potential is 7.06 eV and the Koopmans' theorem value is 7.46 eV. For the heteronuclear diatomic molecule AgAu, R, is calculated to be 2.69, 2.73, and 2.63 A at the SCF, MCSCF, and CI(1) levels, respectively, as shown in Table IV. Basch has calculated Re to be 2.65 %I through an AREP MCSCF calculation.22 The discrepancy with the present value is consistent with the differences observed in calculations on Ag, and Au2 and may, again, be attributed to the use of an REP based on Phillips-Kleinmann psuedoorbitals. In comparison with the Ag2 and Au2 results, the AgAu calculations differ in that they show a shortening in Re in proceeding from SCF to CI(1). In addition, a substantial incremental increase in energy upon correlation is observed in AgAu above that in both A u and ~ Ag,. For example, at R = 5.0 A, the energy lowering in Ag2 and Au, is 0.030 and 0.034 au whereas in AgAu it is 0.042 au. It is not surprising that different behavior is observed in AgAu. In the homonuclear dimers, d and s shells that have the same principal quantum numbers in the respective atoms are correlated. In AgAu, the principal quantum number differs by one between gold and silver. (33) Ziegler, T.;Snijders, J. G.; Baerends, E. J. Chem. Phys. Len. 1981, 74, 1271.
J. Pkys. Ckem. 1985,89, 5206-5212
5206
The Ag, and Au2 calculations exhibit consistent behavior with respect to the various basis sets and the levels of calculations (SCF, MCSCF, and CI). For Re, neither molecule shows a significant decrease in proceeding from S C F to CI( 1 ) nor upon the addition of the Langhoff-Davidson correction to the CI(2) calculations. In the CI(2) calculations Ag, shows a slightly greater shortening than Au, (0.03 A). Computed bond lengths are dependent on the size of the basis set, the presence of f-type basis functions, the extent of CI performed, and the form of the EP. Differences between the present calculated values and experiment are consistent with other recent molecular calculations involving heavy atoms. This is interpreted as being due more to basis set and electron correlation factors and less to the quality of the REP'S. In particular, for group 11 systems, it may also be necessary to include triple and higher excitations involving the d-shell electrons. However, the inclusion of core polarization and core-valence correlation effects into the REP'S should be examined. Alternatively, fewer electrons may be included in the core, thus permitting the explicit treatment of intershell correlation p h e r ~ o m e n a .This ~ ~ ~results, ~~ however, in considerably more complex calculations due to the increase in the number of electrons that must be treated explicitly.
Deviations between calculated and experimental values of Re are 0.29 8, for Ag, and 0.18 8, for Au2, based on the 1 1-electron CI( 1) results. The additional 0.1 1-8, deviation in Ag, may be due to an uncertainty in the reported experimental value, since it was not obtained by direct measurement. The possibility of uncertainty is further supported by comparing the bond lengths of AgH, AuH, AgAI, and A u A I . ~ The ~ experimental values in the silver compounds are 0.1 1 h 0.03 8, longer than those in the respective gold compounds. The experimental Re values for Ag, and Au2 are the same, 2.47 8,. In addition, it is not unreasonable to expect Re of Au, to experience greater relativistic shortening than Ag2 since such effects are substantially greater in gold. If the actual bond length in Ag, is 0.1 A longer than reported,I7 R , for AgAu is predicted to be 2.5 8,.
Conclusions The spectroscopic analyses of the calculated potential energy curves show little difference between AREP SCF and REP S C F results. Thus, interatomic spin-orbit coupling effects on the valence electrons in these molecules are negligible for the ground electronic states. In comparing the silver and gold molecular calculations, the magnitudes of the relativistic effects are of reasonable sizes. The contraction in bond length due to relativistic effects is expected to be greater in Au, than in Ag,, and this is the case when the 1 1-electron REP calculations are compared to 11-electron N E P calculations. The contraction in Au, is found to be 0.36 A and that in Ag, is 0.15 8,. The relativistic contraction in Ag, is consistent with that reported by Weltner and Van Zee in their recent review of transition-metal molecules.35
Acknowledgment. This research was partially supported by the National Science Foundation under Grants CHE-8214689 and PRM-8219469. (35) Weltner, W.; Van Zee, R. J. Annu. Rev. Phys. Chem. 1984, 35,291. (36) In this paper the periodic group notation is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA become groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the p-block elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., 111 3 and 13.)
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(34) Huber, K. P.;Herzberg, G. 'Constants of Diatomic Molecules"; Van Nostrand: New York, 1979.
The Chemiluminescent Reaction of N(4S,) Atoms with Azlde Radicals S. J. David and R. D. Coombe* Department of Chemistry, University of Denver, Denver, Colorado 80208 (Received: June 24, 1985)
Discharge-flow methods are used to study chemiluminescence from the reaction of N(4Su)atoms with N3 radicals. The azide radicals are produced by the reaction of HN3 with fluorine atoms. The N + N3 reaction produces intense N2 first positive (B3n, A,&+) emission in the visible and near-IR regions. From the variation of the time profile of this emission with changes in the reagent densities, the rate constant of the F + HN, reaction is determined to be k2 = (1.6 f 0.2) X IO-'o cm3 s-I, and the rate constant of the N + N, reaction is determined to have a lower limit k , 1 6 X lo-" cm3 s-I. For the conditions of these experiments, the yield of B3n, A'&,+ photons relative to the limiting HN3 flow was found to be approximately 20%. The yield of N2(A3Z,+) is such that its presence can be accounted for by radiation from the B3n,state. The high yield of N2(B3n,)can be understood by considering the operation of both spin and orbital angular momentum constraints in the system.
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Introduction A number of experiments performed in recent years have shown that the reactions of gas-phase N, radicals are often strongly constrained to produce electronically excited products by the separate conservation of spin and orbital angular momentum. For example, the reactions of halogen atoms with N 3 produce very high yields of the excited a'A and blZ+ states of the nitrogen halide diatomics.' These reactions are an example of the case where the singlet ground-state potential energy surface of the (,P) + (X2n,)reagents correlates adiabatically to the ground state (X'Z,') of molecular nitrogen and excited singlet states of the (1) A. T. Pritt, Jr., D. Patel, and R. D. Coombe, Int. J . Chem. Kine?., 16, 977 (1984).
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nitrene. The high yields observed are a result of spin conservation in these systems, which is strong because of the small spin-orbit coupling in the lighter halogens. A significant reduction in the yield of excited singlets is observed in the Br + N3 case relative to F + N 3 or C1 + N3, as expected. Although these systems demonstrate the strength of spin conservation, they offer no information about the role of orbital angular momentum correlations. The 211gground state of N3 correlates to N(,D) + N2(X'Z,+). Hence, to the extent that orbital correlations are important, R + N3 reactions should produce states of the nitrene N R which correlate to R N(,D). For the case of reaction with halogen atoms, both the a'A and b'Z+ excited states of the nitrogen halide diatomics correlate to N(,D), but then these are the only singlet states energetically accessible by the reactions in question. In this paper, we discuss
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0 1985 American Chemical Society
