- Email: [email protected]
Linear versus cyclic sixteen electron triatomics: P2S and SiS2
20 January 1995
CHEMICAL
PHYmCS LETTERS ELS EV I ER
Chemical PhysicsLetters 232 (1995) 313-318
Linear versus cyclic sixteen electron triatomics: P2S and SiS2 Randall D. Davy, Samuel Holiday Department of Chemistry, Liberty University, Lynchburg, VA 24502, USA
Received 4 November 1994
Abstract
Ab initio theoretical methods have been used to determine the geometries, energies and vibrational frequencies of linear, cyclic singlet and cyclic triplet isomers of P2S and SIS2.Although it has not been observed, the cyclic singlet structure for P2S has been previously predicted theoretically to be the ground state. In the present study both the cyclic singlet and the cyclic triplet isomers of P2S are found to lie below the experimentally observed linear isomer. The linear SiS2 isomer, however, is the lowest energy isomer, and the cyclic triplet is quite high lying. The reason for this reversal and why the cyclic P2S isomers have not been observed are discussed.
1. Introduction
The chemistry of second row main group elements differs from the first row in several important ways. One way is their tendency to either polymerize or form rings, rather than forming small open chain molecules. Sixteen electron triatomics such as N20 and CO2 are linear and have been predicted to have very high-lying ring states [ 1 ], but those triatomics that contain second row atoms such as P~- [ 2,3 ], N2S [4,5 ], P2F ÷ [ 6 ], and P20 [ 7 ] are more likely to have either ground or low-lying ring states. These second row triatomics tend to be very reactive and experimental data for them are rare. Experimental work on P2S by Mielke, Brabson and Andrews [ 8 ], and on SiS2 by SchniSckel and K r p p e [9] find only linear isomers. In this Letter, we examine the structures, energetics and theoretical vibrational frequencies of P2S and SiS2 isomers in order to both more thoroughly establish the relative energies of the linear and ring isomers, and determine whether the ring form might have been produced experimentally, but not detected. P2S was initially examined by M N D O methods as
a possible fragmentation product of P453 [ 10 ]. The M N D O method found the linear isomer PPS to be at lower energy than the ring. Theoretical studies by Busch and Schoeller found cyclic P2S lower energy by 7.3 kcal/mol for CISD + Davidson's correction energies at S C F / D Z P optimized geometries [ 11 ]. Chaban, Klimenko and Charkin found the cyclic form to be lower than the linear, but only by 5 kcal/mol for M P 3 / D Z P energies at SCF 3-21G ° geometries [ 12]. The experimental results of Mielke et al. conclusively showed the production of the linear PPS isomer but found no experimental evidence for the ring. They also carried out theoretical studies at the S C F / D Z P level and found the cyclic isomer lower energy by 12 kcal/mol. They found theoretical harmonic vibrational frequencies that, when scaled by 0.9, fell into a region masked in their spectra. Keck, Kuchen, Tommes, Terlouw, and Wong conducted a mass spectrometry study in which they produce the P2S radical cation [ 13 ]. They also find the cyclic structure for the cation to be 100 kcal/mol lower energy than the open chain ion at the HF 6-31G ° level of theory. Based on neutralization-reionization experi-
0009-2614/95/$09.50 © 1995 ElsevierScience B.V. All rights reserved SSD10009-2614 (94)01366-7
314
R.D. Davy, S. Holiday / Chemical Physics Letters 232 (1995) 313-318
merits they conclude that the neutral P2S ring is also formed. Experiments on SiS2 have been fewer than those of P2S. Schn6ckel and K~ippe have studied O=Si=O, O=Si=S and S=Si=S and compared the results to the analogous carbon containing molecules, including experimental IR spectra and theoretical analysis of the bonding and vibrational spectra of the linear molecules only [ 9 ].
"'S"
:p
P: 2.015
1.920
2. Theoretical methods
The Hartree-Fock (HF) method was used with a double zeta plus polarization function (DZP) basis set and a triple zeta (valence) plus two polarization functions basis set (TZ2P). The DZP basis consists of the Huzinaga-Dunning DZ basis contracted as: (1 ls7p/6s4p) [14,15] plus a single d function with exponent of 0.50 for Si, P and S. The TZ2P basis is a more flexible (12s9p/6s5p) contraction of the Huzinaga primitives due to McClean and Chandler [ 16 ] plus two d functions with exponents of (1.0, 0.25) for Si, ( 1.2, 0.30) for P and ( 1.4, 0.35) for S. At the HF level all optimized structures were found by analytic gradient methods, and vibrational frequencies were obtained by analytic second derivatives. The effects of electron correlation were included by the method of configuration interaction including all single and double excitations (CISD) and the coupled cluster method including all single and double excitations (CCSD). The 1s orbitals of all atoms and their virtual counterparts were excluded from the CI and CC procedures. In the present study geometries were reoptimized at the correlated levels via analytic gradient techniques, to fully account for changes due to electron correlation, except for the CCSD method for open shell molecules. The CCSD energies of these states were evaluated at the CISD optimized geometries. Vibrational frequencies for correlated methods were evaluated via finite difference of first derivatives. The PSI suite of programs was used throughout [171. 3. Results and discussion
The best estimate geometries for the various isomers and states of P2S are given in Fig. 1. The cyclic
:P
P
S
1.906 3B 2
"'S'"
:P
2.209
P:
Fig. 1. Geometries for various P2S isomers. For the linear and cyclic singlet these are CCSD/TZ2P results. For the cyclic triplet they are CISD/TZ2P results.
singlet, a cyclic triplet (a 3B2 state made up of singly occupied a2 and bl ) and the linear ringlet P=P=S were evaluated. The theoretical geometries of these isomers at all levels of theory and their harmonic vibrational frequencies are given in Table 1. The best estimate geometries for linear S=Si=S, the ringlet ring and the cyclic triplet ring (also 3B2) are given in Fig. 2. The theoretical geometries of these isomers at all levels of theory, and their harmonic vibrational frequencies are given in Table 2. Absolute energies at all levels of theory are given in Table 3 for all molecules, and relative energies are given in Table 4. Our results for geometries of linear P=P=S and cyclic singlet P2S are in agreement with the earlier studies of Busch and Schoeller and Chaban et al. The HF method underestimates the P-P and P-S bond lengths for both of these species by 0.03 to 0.05 compared to the CISD and CCSD methods. The cyclic triplet is unusual in that there is almost no change in bond lengths upon correlation. The energy difference between the ringlet ring and the linear form is very stable across theoretical methods. Our best estimate of the energy difference is 7.9 kcal/mol at the CCSD/TZ2P level plus zero-point vibrational en-
R.D. Davy, S. Holiday / Chemical PhysicsLetters 232 (1995) 313-318
Table 1 Theoretical geometries in A and deg, and harmonic vibrational frequencies for P2S isomers a
sin~et P=P=S P-P P-S asymm, str symm. str. bend sin~et ring P-P P-S A~ringstr. AI ringer. B2 ring Mr.
SCF
CISD
CCSD
1.856/1.856 1.898/1.893 972/967 565/564 152/193
1.879/1.882 1.905/1.904 953 555 141
1.902/1.906 1.918/1.920 914 529 123
1.958/1.959 2.175/2.178 776/772 526/512 321/304
tfipletring P-P P-S A~ fingstr. A~ ringstr. B2ringstr.
1.980/1.985 2.180/2.191 737 516 301
2.196/2.203 2.090/2.091 651/637 487/480 477/463
2,009/2.015 2,193/2.208 684 492 283
2.195/2.209 2.094/2.101 647 483 466
315
Table 2 Theoretical geometries in ,/k and deg, and harmonic vibrational frequencies for SiSzisomers" SCF
CISD
CCSD
S-~Si=Ssinglet Si-S asym. str sym. str. bend
1.904/1.906 1.913/1.916 972/967 966 558/553 547 170/216 150
1.925/1.931 942 530 129
SiS2sin~et dng Si-S S-S A~ ringer. Alringstr. B2fingstr.
2.116/2.121 2.157/2.153 657/649 42/469 404/390
2.116/2.125 2.172/2.172 651 455 410
2.123/2.139 2.195/2.198 632 429 407
SiS2triplet ring Si-S S-S A1 ring s t r . AI ring s t r . B2ring s t r .
2.328/2.325 1.982/1.976 682/677 412/419 218/232
2.314/2.320 1.998/1.995 657 424 340
"Notation is DZP/TZ2P. If only one number is given it is DZP.
"Notation is DZP/TZ2P. If only one number is given it is DZP.
S
S i - -
•
S
•
Si
"S • "
2.198
"S • •
1.995
S"
S" °•
Fig. 2. Geometries for various SiS2 isomers. For the linear and cyclicsinglet these are CCSD/TZ2P results. For the cyclictriplet they are CISD/TZ2P results.
ergy (ZPVE) corrections. The agreement between the C C S D / D Z P vibrational frequencies and the experimental values of Mielke et al. [ 8 ] is within 3%, and gives confidence that the predicted frequencies for cyclic P2S are also reliable. Our results, however, put the one ring frequency with some intensity at 492 cm -~ (roughly a P - P stretch), and if we make a 3% correction as mentioned above, the frequency of the ring stretch is 477 c m - i, which is just on the edge o f the 460-480 cm-~ range masked by P4 absorptions in the matrix experiment. As Mielke et al. pointed out, the calculated intensities for the cyclic singlet are quite small; the largest intensity is 24 k m / m o l for the 477 cm-1 band. This intensity is only about an eighth o f the intensity of the linear asymmetric stretch, and this lack o f intensity will make cyclic molecule difficult to observe in a matrix study. The published spectra do not show this region, and thus direct spectroscopic observation o f the cyclic molecule is lacking. In P~-, which is isoelectronic to P2S, the linear closed shell singlet and ring 3A~ state are nearly degenerate [ 2 ]. Based on this result one would expect a low-lying triplet ring for PzS. In fact, at the SCF level, the 3B2 state of the ring is predicted to be the ground state, lying below the singlet ring by 7.3 kcal/
316
R.D. Davy, S. Holiday / Chemical Physics Letters 232 (I 995) 313-318
Table 3 Absolute energies in hartree for P2S a n d SiS2 isomers SCF
CISD
CCSD
P2S PffiPffiS ( D Z P ) (TZ2P) singlet ring ( D Z P ) (TZ2P) triplet ring ( D Z P ) (TZ2P)
-
1078.90842 1078.99877 1078.92285 1079.01118 1078.93479 1079.01957
-
1079.38663 1079.46144 1079.40008 1079.47365 1079.39762 1079.46958
-
1079.46218 1079.54048 1079.47628 1079.55334
SiS2 S-Si~S (DZP) (TZ2P) singlet ring ( D Z P ) (TZ2P) triplet ring ( D Z P ) (TZ2P)
-
1083.97407 1084.06666 1083.94116 1084.03049 1083.88741 1083.97517
-
1084.43282 1084.58000 1084.40164 1084.54736 1084.34301 1084.48917
-
1084.49583 1084.65999 1084.46871 1084.63103
Table 4 R e l a t i v e energies o f P2S a n d SiS2 i s o m e r s in k c a l / m o l SCF
CISD
CCSD
P2S P-P=S (DZP) (TZ2P) singlet ring ( D Z P ) (TZ2P) triplet ring ( D Z P ) (TZ2P)
9.0 7.8 0.0 0.0 - 7.5 -5.3
8.4 7.7 0.0 0.0 1.5 2.6
8.9 8.1 0.0 0.0
SiS2 S~Si-S (DZP) (TZ2P) singlet ring ( D Z P ) (TZ2P) triplet ring ( D Z P ) (TZ2P)
0.0 0.0 20.7 22.6 54.4 57.4
0.0 0.0 19.6 20.5 58.9 57.0
0.0 0.0 17.0 18.2
mol (as also found by Busch and Schoeller) [ 11 ] at the SCF/DZP level, and by 5.3 kcal/mol at the SCF/ TZ2P level. Busch and Schoeller found that electron correlation (via the average coupled pair functional method) at the optimized SCF structures put the triplet ring 9.2 kcal/mol above the singlet ring, thus, at this level it is also above the linear structure. Optimization at correlated levels (CISD/TZ2P) puts the triplet ring above the singlet ring, but only by 2.3 kcal/ mol. Inclusion of Davidson's correction to the CISD energies increases the gap to 5.5 kcal/mol; however, the triplet ring is still lower energy than the observed
linear singlet. Unfortunately the same difficulties that impede observation of the singlet ring are present with the triplet ring: the only theoretically predicted vibrational frequency with any intensity is the band at 483 cm- ~, which will be obscured by P4. In contrast to P2S, the linear isomer of SiS2 is lower energy than the singlet ring, which is in turn lower than the triplet ring at all levels of theory. The energy difference between linear and cyclic singlet SiS2is 17.8 kcal/mol at the CCSD/TZ2P level, including ZPVE corrections, and our best estimate for the cyclic singlet-cyclic 3B2 energy difference is 56.9 kcal/mol based on the CISD/TZ2P optimizations plus ZPVE corrections. Although the singlet ring lies quite high compared to S=Si=S, if Si and $2 react in the gas phase the ring might be kinetically stable enough to be trapped in a matrix. Our theoretical harmonic vibrational frequency for the asymmetric stretch of the linear molecule is in good agreement with the experimental resuits of Schn~kel and K6ppe. The CCSD/DZP value is 942.1, only 2.6% higher than their value of 918 cm- ~. Based on this agreement we would predict that if the singlet ring were isolated, its strongest intensity mode (roughly a ring breathing mode) would appear at about 613 cm-~. The predicted intensity of this line is only about one quarter of the strongest mode of linear SiS2 (63 km/mol versus 240 km/mol), so the line might be quite weak. The paper of SchnSckel and K6ppe did not discuss the spectrum below 720
R.D. Davy, S. Holiday / Chemical PhysicsLetters 232 (1995) 313- 318
cm-] but it is unlikely that they could have formed the higher energy ring structure because their starting materials were SiS and COS. These two formulas, PzS and SIS2, present a puzzle that is completely absent from their first row analogues N20 and COz. They have the same electron count, but very different ground state structures. The inert s pair effect has long been recognized as a reason for second row elements adopting geometries quite different from those of the first row [ 18,19 ]. Busch and Schoeller use this explanation for the ring ground state of P2S [ 11 ] as follows: Triatomics with second row atoms tend to have those atoms in terminal positions so that their 3s electrons can remain lone pairs; thus, for triatomics made up of all second row atoms, rings are preferred because there is then no 'central' atom that is forced to use its 3s electrons to bond. However, it seems that this explanation should hold for SiS2 as well - if inert pairs of 3s electrons make P2S a ring, why do they not make SiS2 a ring? It is clear that systems such as Walsh's rules [20 ] are difficult to extend to the second row, as Burdett and Marsden have also pointed out [ 21 ]. The simplest explanation for the case at hand is the difference in the occupations of the ~ orbitals of the two systems. Fig. 3 shows the three ring ~ orbitals (labelled Ibm, 2b,, and la2) for three cases: P~-, for which the linear and ring isomers are degenerate, SIS2, which is linear and P2S, which is cyclic. (The P~- is D3h symmetry, but the orbitals are written in C2v symmetry for simplicity.) Between P2S and SiS2 the energies of the a2 and bl orbitals reverse. Because the p orbitals on the S are so much lower energy than those of Si, in the SiS2 case the four n electrons end up concentrated in what are essentially S-S ;r bonding and antibonding orbitals. For P2S, however, since the p orbitals of phosphorus and sulfur are closer in energy, the b~ orbital is lower energy and spreads the four ~ electrons around the ring. Clearly opening the ring will cause the SiS2 a 2 orbital to drop in energy as the antibonding interaction decreases. The HOMO of the PzS ring does not drop in energy upon ring opening because changes in the antibonding interactions cancel: as the ring opens, and the sulfur swings away from the terminal phosphorus (decreasing an antibonding interaction), the other sulfur to phosphorus bond shortens (increasing an antibonding interaction). In other words for SiS2, the gain in stabil-
317
2bl a2
e"
a2"
SiS 2
P2S
Fig. 3. Qualitativeenergyorderingof the r orbitalsfor cyclicSIS2, P~-, and P2S.Note that connectinglines indicatesymmetryrelation only, not relativeenergiesof orbitalsfor differentmolecules. ity from allowing the Si 3s electrons to be a lone pair is canceled by creating a four-electron repulsive interaction between the two sulfur atoms. The changes in geometry between the singlet and triplet rings also illustrate the nature of the ring orbitals. The 3B2 P2S ring is formed by excitation of an electron from the 2bl orbital which is P - P bonding and P-S antibonding to the a2 orbital, which is P - P antibonding and P-S nonbonding. The triplet ring thus has a longer P - P bond than the singlet ring (2.209 A for the triplet, 1.985 A for the singlet at the CISD/TZ2P level), and the triplet has shorter P-S bonds than the ringlet (2.101 - triplet, 2.191 - singlet at the CISD/TZ2P level). For SiS2 the triplet is formed by the opposite excitation: f r o m the a2 to the 2b]. Thus the S-S bond shortens from 2.172 to 1.995 A upon forming the triplet ring, and the Si-S bonds lengthen from 2.125 to 2.320 A. The much larger singlet-triplet energy difference for SiS2 indicates that the 2b~ orbital is much higher energy than the a2 in this case, which again reflects the energy difference between the sulfur 3p and silicon 3p orbitals.
318
R.D. Davy, S. Holiday / Chemical Physics Letters 232 (1995) 313-318
4. Concluding remarks It is clear from these results that the p r e d i c t i o n o f the geometries o f second row c o m p o u n d s cannot be accomplished b y electron counting alone. However, the second row t r i a t o m i c s do t e n d much m o r e strongly t o w a r d ring structures than first row triatomics. This is so much the case that even in a 'Hiickel a n t i a r o m t i c ' four x electron system the cyclic structure is lowest energy.
Acknowledgement F u n d i n g for this research was p r o v i d e d by the Jeffress Trust o f Virginia grant J-242, a n d is gratefully acknowledged. A d d i t i o n a l funding for the purchase o f an IBM RS6000 workstation was p r o v i d e d by Research C o r p o r a t i o n a n d Liberty University. G r e a t appreciation is also expressed to H.F. Schaefer III and the Center for C o m p u t a t i o n a l Q u a n t u m Chemistry for support while this work was being put on paper.
References [ 1] W.A. Latham, L. Radom, P.C. Hariharan, W.J. Hehre and J.A. Pople, Topics Current Chem. 40 ( 1973 ) 1. [2] T.P. Hamilton and H.F. Schaefer III, Chem. Phys. Letters 166 (1990) 303. [3] G.M. Chaban, N.M. Klimenko and O.P. Charkin, Bull. Acad. Sci. USSR Chem. Sci. 7 (1990) 590.
[4] R.D. Davy and H.F. Schaefer III, J. Am. Chem. Soc. 113 (1991) 1917. [5] G.M. Chaban, N.M. Klimenko and O.P. Charkin, Russian J. Inor. Chem. 37 (1992) 97. [ 6] V.V. Yakobsen, T.S. Zyubina and O.P. Charkin, Russian J. Inor. Chem. 33 (1988) 1727. [7] R.D. Davy and H.F. Schaefer III, J. Am. Chem. Soc. 113 ( 1991 ) 3697. [8] Z. Mielke, G.D. Brabson and L. Andrews, J. Phys. Chem. 95 (1991) 75. [ 9 ] H. Schn6ckel and R. K6ppe, J. Am. Chem. Soc. 111 (1989) 4583. [ 10] J.R. Bews and C. Glidewell, J. Mol. Struct. 86 (1982) 217. [ 11 ] T. Busch and W.W. Schoeller, Atoms Molec. Clusters 13 (1989) 289. [ 12 ] G.M. Chaban, N.N. Klimenko and O.P. Charldn, Bull. Acad. Sci. USSR Chem. Sci. 4 (1990) 307. [13] H. Keck, W. Kucben, P. Tommes, J.K. Terlouw and T. Wong, Phos. Sulfur Silicon 63 ( 1991 ) 307. [ 14 ] S.J. Huzinaga, J. Chem. Phys. 42 (1965) 1293; Approximate atomic wavefunctions II, Department of Chemistry Report, University of Alberta, Edmonton ( 1971 ). [ 15 ] T.H. Dunning, J. Chem. Phys. 53 (1970) 2823; 55 ( 1971 ) 716. [ 16 ] A.D. McCiean and G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [ 17 ] C.L. Janssen, E.T. Seidl, G.E. Scuseria, T.P. Hamilton, Y. Yamaguchi, R.B. Remington, Y. Xie, G. Vacek,C.D. Sherili, T.D. Crawford, J.T. Fermann, W.D. Allen, B.R. Brooks, G.B. Fitzgerald, D.J. Fox, J.F. Gaw, N.C. Handy, W.D. Laidig, T.J. Lee, R.M. Pitzer, J.E. Rice, P. Saxe, A. Scbeiner, H.F. Schaefer III, Psi 2.0.8 (PSITECH, Watldnsville, 1992). [ 18 ] H.A. Bent, J. Chem. Educ. 37 (1960). [ 19] W. Kutzelnigg, Angew. Chem. Intern. Ed. Engl. 23 (1984) 272. [20] A.D. Walsh, J. Chem. Soc. (1953) 2260. [21 ] J.K. Burdett and C.J. Marsden, Nouv. J. Chem. 12 (1988) 797.
CHEMICAL
PHYmCS LETTERS ELS EV I ER
Chemical PhysicsLetters 232 (1995) 313-318
Linear versus cyclic sixteen electron triatomics: P2S and SiS2 Randall D. Davy, Samuel Holiday Department of Chemistry, Liberty University, Lynchburg, VA 24502, USA
Received 4 November 1994
Abstract
Ab initio theoretical methods have been used to determine the geometries, energies and vibrational frequencies of linear, cyclic singlet and cyclic triplet isomers of P2S and SIS2.Although it has not been observed, the cyclic singlet structure for P2S has been previously predicted theoretically to be the ground state. In the present study both the cyclic singlet and the cyclic triplet isomers of P2S are found to lie below the experimentally observed linear isomer. The linear SiS2 isomer, however, is the lowest energy isomer, and the cyclic triplet is quite high lying. The reason for this reversal and why the cyclic P2S isomers have not been observed are discussed.
1. Introduction
The chemistry of second row main group elements differs from the first row in several important ways. One way is their tendency to either polymerize or form rings, rather than forming small open chain molecules. Sixteen electron triatomics such as N20 and CO2 are linear and have been predicted to have very high-lying ring states [ 1 ], but those triatomics that contain second row atoms such as P~- [ 2,3 ], N2S [4,5 ], P2F ÷ [ 6 ], and P20 [ 7 ] are more likely to have either ground or low-lying ring states. These second row triatomics tend to be very reactive and experimental data for them are rare. Experimental work on P2S by Mielke, Brabson and Andrews [ 8 ], and on SiS2 by SchniSckel and K r p p e [9] find only linear isomers. In this Letter, we examine the structures, energetics and theoretical vibrational frequencies of P2S and SiS2 isomers in order to both more thoroughly establish the relative energies of the linear and ring isomers, and determine whether the ring form might have been produced experimentally, but not detected. P2S was initially examined by M N D O methods as
a possible fragmentation product of P453 [ 10 ]. The M N D O method found the linear isomer PPS to be at lower energy than the ring. Theoretical studies by Busch and Schoeller found cyclic P2S lower energy by 7.3 kcal/mol for CISD + Davidson's correction energies at S C F / D Z P optimized geometries [ 11 ]. Chaban, Klimenko and Charkin found the cyclic form to be lower than the linear, but only by 5 kcal/mol for M P 3 / D Z P energies at SCF 3-21G ° geometries [ 12]. The experimental results of Mielke et al. conclusively showed the production of the linear PPS isomer but found no experimental evidence for the ring. They also carried out theoretical studies at the S C F / D Z P level and found the cyclic isomer lower energy by 12 kcal/mol. They found theoretical harmonic vibrational frequencies that, when scaled by 0.9, fell into a region masked in their spectra. Keck, Kuchen, Tommes, Terlouw, and Wong conducted a mass spectrometry study in which they produce the P2S radical cation [ 13 ]. They also find the cyclic structure for the cation to be 100 kcal/mol lower energy than the open chain ion at the HF 6-31G ° level of theory. Based on neutralization-reionization experi-
0009-2614/95/$09.50 © 1995 ElsevierScience B.V. All rights reserved SSD10009-2614 (94)01366-7
314
R.D. Davy, S. Holiday / Chemical Physics Letters 232 (1995) 313-318
merits they conclude that the neutral P2S ring is also formed. Experiments on SiS2 have been fewer than those of P2S. Schn6ckel and K~ippe have studied O=Si=O, O=Si=S and S=Si=S and compared the results to the analogous carbon containing molecules, including experimental IR spectra and theoretical analysis of the bonding and vibrational spectra of the linear molecules only [ 9 ].
"'S"
:p
P: 2.015
1.920
2. Theoretical methods
The Hartree-Fock (HF) method was used with a double zeta plus polarization function (DZP) basis set and a triple zeta (valence) plus two polarization functions basis set (TZ2P). The DZP basis consists of the Huzinaga-Dunning DZ basis contracted as: (1 ls7p/6s4p) [14,15] plus a single d function with exponent of 0.50 for Si, P and S. The TZ2P basis is a more flexible (12s9p/6s5p) contraction of the Huzinaga primitives due to McClean and Chandler [ 16 ] plus two d functions with exponents of (1.0, 0.25) for Si, ( 1.2, 0.30) for P and ( 1.4, 0.35) for S. At the HF level all optimized structures were found by analytic gradient methods, and vibrational frequencies were obtained by analytic second derivatives. The effects of electron correlation were included by the method of configuration interaction including all single and double excitations (CISD) and the coupled cluster method including all single and double excitations (CCSD). The 1s orbitals of all atoms and their virtual counterparts were excluded from the CI and CC procedures. In the present study geometries were reoptimized at the correlated levels via analytic gradient techniques, to fully account for changes due to electron correlation, except for the CCSD method for open shell molecules. The CCSD energies of these states were evaluated at the CISD optimized geometries. Vibrational frequencies for correlated methods were evaluated via finite difference of first derivatives. The PSI suite of programs was used throughout [171. 3. Results and discussion
The best estimate geometries for the various isomers and states of P2S are given in Fig. 1. The cyclic
:P
P
S
1.906 3B 2
"'S'"
:P
2.209
P:
Fig. 1. Geometries for various P2S isomers. For the linear and cyclic singlet these are CCSD/TZ2P results. For the cyclic triplet they are CISD/TZ2P results.
singlet, a cyclic triplet (a 3B2 state made up of singly occupied a2 and bl ) and the linear ringlet P=P=S were evaluated. The theoretical geometries of these isomers at all levels of theory and their harmonic vibrational frequencies are given in Table 1. The best estimate geometries for linear S=Si=S, the ringlet ring and the cyclic triplet ring (also 3B2) are given in Fig. 2. The theoretical geometries of these isomers at all levels of theory, and their harmonic vibrational frequencies are given in Table 2. Absolute energies at all levels of theory are given in Table 3 for all molecules, and relative energies are given in Table 4. Our results for geometries of linear P=P=S and cyclic singlet P2S are in agreement with the earlier studies of Busch and Schoeller and Chaban et al. The HF method underestimates the P-P and P-S bond lengths for both of these species by 0.03 to 0.05 compared to the CISD and CCSD methods. The cyclic triplet is unusual in that there is almost no change in bond lengths upon correlation. The energy difference between the ringlet ring and the linear form is very stable across theoretical methods. Our best estimate of the energy difference is 7.9 kcal/mol at the CCSD/TZ2P level plus zero-point vibrational en-
R.D. Davy, S. Holiday / Chemical PhysicsLetters 232 (1995) 313-318
Table 1 Theoretical geometries in A and deg, and harmonic vibrational frequencies for P2S isomers a
sin~et P=P=S P-P P-S asymm, str symm. str. bend sin~et ring P-P P-S A~ringstr. AI ringer. B2 ring Mr.
SCF
CISD
CCSD
1.856/1.856 1.898/1.893 972/967 565/564 152/193
1.879/1.882 1.905/1.904 953 555 141
1.902/1.906 1.918/1.920 914 529 123
1.958/1.959 2.175/2.178 776/772 526/512 321/304
tfipletring P-P P-S A~ fingstr. A~ ringstr. B2ringstr.
1.980/1.985 2.180/2.191 737 516 301
2.196/2.203 2.090/2.091 651/637 487/480 477/463
2,009/2.015 2,193/2.208 684 492 283
2.195/2.209 2.094/2.101 647 483 466
315
Table 2 Theoretical geometries in ,/k and deg, and harmonic vibrational frequencies for SiSzisomers" SCF
CISD
CCSD
S-~Si=Ssinglet Si-S asym. str sym. str. bend
1.904/1.906 1.913/1.916 972/967 966 558/553 547 170/216 150
1.925/1.931 942 530 129
SiS2sin~et dng Si-S S-S A~ ringer. Alringstr. B2fingstr.
2.116/2.121 2.157/2.153 657/649 42/469 404/390
2.116/2.125 2.172/2.172 651 455 410
2.123/2.139 2.195/2.198 632 429 407
SiS2triplet ring Si-S S-S A1 ring s t r . AI ring s t r . B2ring s t r .
2.328/2.325 1.982/1.976 682/677 412/419 218/232
2.314/2.320 1.998/1.995 657 424 340
"Notation is DZP/TZ2P. If only one number is given it is DZP.
"Notation is DZP/TZ2P. If only one number is given it is DZP.
S
S i - -
•
S
•
Si
"S • "
2.198
"S • •
1.995
S"
S" °•
Fig. 2. Geometries for various SiS2 isomers. For the linear and cyclicsinglet these are CCSD/TZ2P results. For the cyclictriplet they are CISD/TZ2P results.
ergy (ZPVE) corrections. The agreement between the C C S D / D Z P vibrational frequencies and the experimental values of Mielke et al. [ 8 ] is within 3%, and gives confidence that the predicted frequencies for cyclic P2S are also reliable. Our results, however, put the one ring frequency with some intensity at 492 cm -~ (roughly a P - P stretch), and if we make a 3% correction as mentioned above, the frequency of the ring stretch is 477 c m - i, which is just on the edge o f the 460-480 cm-~ range masked by P4 absorptions in the matrix experiment. As Mielke et al. pointed out, the calculated intensities for the cyclic singlet are quite small; the largest intensity is 24 k m / m o l for the 477 cm-1 band. This intensity is only about an eighth o f the intensity of the linear asymmetric stretch, and this lack o f intensity will make cyclic molecule difficult to observe in a matrix study. The published spectra do not show this region, and thus direct spectroscopic observation o f the cyclic molecule is lacking. In P~-, which is isoelectronic to P2S, the linear closed shell singlet and ring 3A~ state are nearly degenerate [ 2 ]. Based on this result one would expect a low-lying triplet ring for PzS. In fact, at the SCF level, the 3B2 state of the ring is predicted to be the ground state, lying below the singlet ring by 7.3 kcal/
316
R.D. Davy, S. Holiday / Chemical Physics Letters 232 (I 995) 313-318
Table 3 Absolute energies in hartree for P2S a n d SiS2 isomers SCF
CISD
CCSD
P2S PffiPffiS ( D Z P ) (TZ2P) singlet ring ( D Z P ) (TZ2P) triplet ring ( D Z P ) (TZ2P)
-
1078.90842 1078.99877 1078.92285 1079.01118 1078.93479 1079.01957
-
1079.38663 1079.46144 1079.40008 1079.47365 1079.39762 1079.46958
-
1079.46218 1079.54048 1079.47628 1079.55334
SiS2 S-Si~S (DZP) (TZ2P) singlet ring ( D Z P ) (TZ2P) triplet ring ( D Z P ) (TZ2P)
-
1083.97407 1084.06666 1083.94116 1084.03049 1083.88741 1083.97517
-
1084.43282 1084.58000 1084.40164 1084.54736 1084.34301 1084.48917
-
1084.49583 1084.65999 1084.46871 1084.63103
Table 4 R e l a t i v e energies o f P2S a n d SiS2 i s o m e r s in k c a l / m o l SCF
CISD
CCSD
P2S P-P=S (DZP) (TZ2P) singlet ring ( D Z P ) (TZ2P) triplet ring ( D Z P ) (TZ2P)
9.0 7.8 0.0 0.0 - 7.5 -5.3
8.4 7.7 0.0 0.0 1.5 2.6
8.9 8.1 0.0 0.0
SiS2 S~Si-S (DZP) (TZ2P) singlet ring ( D Z P ) (TZ2P) triplet ring ( D Z P ) (TZ2P)
0.0 0.0 20.7 22.6 54.4 57.4
0.0 0.0 19.6 20.5 58.9 57.0
0.0 0.0 17.0 18.2
mol (as also found by Busch and Schoeller) [ 11 ] at the SCF/DZP level, and by 5.3 kcal/mol at the SCF/ TZ2P level. Busch and Schoeller found that electron correlation (via the average coupled pair functional method) at the optimized SCF structures put the triplet ring 9.2 kcal/mol above the singlet ring, thus, at this level it is also above the linear structure. Optimization at correlated levels (CISD/TZ2P) puts the triplet ring above the singlet ring, but only by 2.3 kcal/ mol. Inclusion of Davidson's correction to the CISD energies increases the gap to 5.5 kcal/mol; however, the triplet ring is still lower energy than the observed
linear singlet. Unfortunately the same difficulties that impede observation of the singlet ring are present with the triplet ring: the only theoretically predicted vibrational frequency with any intensity is the band at 483 cm- ~, which will be obscured by P4. In contrast to P2S, the linear isomer of SiS2 is lower energy than the singlet ring, which is in turn lower than the triplet ring at all levels of theory. The energy difference between linear and cyclic singlet SiS2is 17.8 kcal/mol at the CCSD/TZ2P level, including ZPVE corrections, and our best estimate for the cyclic singlet-cyclic 3B2 energy difference is 56.9 kcal/mol based on the CISD/TZ2P optimizations plus ZPVE corrections. Although the singlet ring lies quite high compared to S=Si=S, if Si and $2 react in the gas phase the ring might be kinetically stable enough to be trapped in a matrix. Our theoretical harmonic vibrational frequency for the asymmetric stretch of the linear molecule is in good agreement with the experimental resuits of Schn~kel and K6ppe. The CCSD/DZP value is 942.1, only 2.6% higher than their value of 918 cm- ~. Based on this agreement we would predict that if the singlet ring were isolated, its strongest intensity mode (roughly a ring breathing mode) would appear at about 613 cm-~. The predicted intensity of this line is only about one quarter of the strongest mode of linear SiS2 (63 km/mol versus 240 km/mol), so the line might be quite weak. The paper of SchnSckel and K6ppe did not discuss the spectrum below 720
R.D. Davy, S. Holiday / Chemical PhysicsLetters 232 (1995) 313- 318
cm-] but it is unlikely that they could have formed the higher energy ring structure because their starting materials were SiS and COS. These two formulas, PzS and SIS2, present a puzzle that is completely absent from their first row analogues N20 and COz. They have the same electron count, but very different ground state structures. The inert s pair effect has long been recognized as a reason for second row elements adopting geometries quite different from those of the first row [ 18,19 ]. Busch and Schoeller use this explanation for the ring ground state of P2S [ 11 ] as follows: Triatomics with second row atoms tend to have those atoms in terminal positions so that their 3s electrons can remain lone pairs; thus, for triatomics made up of all second row atoms, rings are preferred because there is then no 'central' atom that is forced to use its 3s electrons to bond. However, it seems that this explanation should hold for SiS2 as well - if inert pairs of 3s electrons make P2S a ring, why do they not make SiS2 a ring? It is clear that systems such as Walsh's rules [20 ] are difficult to extend to the second row, as Burdett and Marsden have also pointed out [ 21 ]. The simplest explanation for the case at hand is the difference in the occupations of the ~ orbitals of the two systems. Fig. 3 shows the three ring ~ orbitals (labelled Ibm, 2b,, and la2) for three cases: P~-, for which the linear and ring isomers are degenerate, SIS2, which is linear and P2S, which is cyclic. (The P~- is D3h symmetry, but the orbitals are written in C2v symmetry for simplicity.) Between P2S and SiS2 the energies of the a2 and bl orbitals reverse. Because the p orbitals on the S are so much lower energy than those of Si, in the SiS2 case the four n electrons end up concentrated in what are essentially S-S ;r bonding and antibonding orbitals. For P2S, however, since the p orbitals of phosphorus and sulfur are closer in energy, the b~ orbital is lower energy and spreads the four ~ electrons around the ring. Clearly opening the ring will cause the SiS2 a 2 orbital to drop in energy as the antibonding interaction decreases. The HOMO of the PzS ring does not drop in energy upon ring opening because changes in the antibonding interactions cancel: as the ring opens, and the sulfur swings away from the terminal phosphorus (decreasing an antibonding interaction), the other sulfur to phosphorus bond shortens (increasing an antibonding interaction). In other words for SiS2, the gain in stabil-
317
2bl a2
e"
a2"
SiS 2
P2S
Fig. 3. Qualitativeenergyorderingof the r orbitalsfor cyclicSIS2, P~-, and P2S.Note that connectinglines indicatesymmetryrelation only, not relativeenergiesof orbitalsfor differentmolecules. ity from allowing the Si 3s electrons to be a lone pair is canceled by creating a four-electron repulsive interaction between the two sulfur atoms. The changes in geometry between the singlet and triplet rings also illustrate the nature of the ring orbitals. The 3B2 P2S ring is formed by excitation of an electron from the 2bl orbital which is P - P bonding and P-S antibonding to the a2 orbital, which is P - P antibonding and P-S nonbonding. The triplet ring thus has a longer P - P bond than the singlet ring (2.209 A for the triplet, 1.985 A for the singlet at the CISD/TZ2P level), and the triplet has shorter P-S bonds than the ringlet (2.101 - triplet, 2.191 - singlet at the CISD/TZ2P level). For SiS2 the triplet is formed by the opposite excitation: f r o m the a2 to the 2b]. Thus the S-S bond shortens from 2.172 to 1.995 A upon forming the triplet ring, and the Si-S bonds lengthen from 2.125 to 2.320 A. The much larger singlet-triplet energy difference for SiS2 indicates that the 2b~ orbital is much higher energy than the a2 in this case, which again reflects the energy difference between the sulfur 3p and silicon 3p orbitals.
318
R.D. Davy, S. Holiday / Chemical Physics Letters 232 (1995) 313-318
4. Concluding remarks It is clear from these results that the p r e d i c t i o n o f the geometries o f second row c o m p o u n d s cannot be accomplished b y electron counting alone. However, the second row t r i a t o m i c s do t e n d much m o r e strongly t o w a r d ring structures than first row triatomics. This is so much the case that even in a 'Hiickel a n t i a r o m t i c ' four x electron system the cyclic structure is lowest energy.
Acknowledgement F u n d i n g for this research was p r o v i d e d by the Jeffress Trust o f Virginia grant J-242, a n d is gratefully acknowledged. A d d i t i o n a l funding for the purchase o f an IBM RS6000 workstation was p r o v i d e d by Research C o r p o r a t i o n a n d Liberty University. G r e a t appreciation is also expressed to H.F. Schaefer III and the Center for C o m p u t a t i o n a l Q u a n t u m Chemistry for support while this work was being put on paper.
References [ 1] W.A. Latham, L. Radom, P.C. Hariharan, W.J. Hehre and J.A. Pople, Topics Current Chem. 40 ( 1973 ) 1. [2] T.P. Hamilton and H.F. Schaefer III, Chem. Phys. Letters 166 (1990) 303. [3] G.M. Chaban, N.M. Klimenko and O.P. Charkin, Bull. Acad. Sci. USSR Chem. Sci. 7 (1990) 590.
[4] R.D. Davy and H.F. Schaefer III, J. Am. Chem. Soc. 113 (1991) 1917. [5] G.M. Chaban, N.M. Klimenko and O.P. Charkin, Russian J. Inor. Chem. 37 (1992) 97. [ 6] V.V. Yakobsen, T.S. Zyubina and O.P. Charkin, Russian J. Inor. Chem. 33 (1988) 1727. [7] R.D. Davy and H.F. Schaefer III, J. Am. Chem. Soc. 113 ( 1991 ) 3697. [8] Z. Mielke, G.D. Brabson and L. Andrews, J. Phys. Chem. 95 (1991) 75. [ 9 ] H. Schn6ckel and R. K6ppe, J. Am. Chem. Soc. 111 (1989) 4583. [ 10] J.R. Bews and C. Glidewell, J. Mol. Struct. 86 (1982) 217. [ 11 ] T. Busch and W.W. Schoeller, Atoms Molec. Clusters 13 (1989) 289. [ 12 ] G.M. Chaban, N.N. Klimenko and O.P. Charldn, Bull. Acad. Sci. USSR Chem. Sci. 4 (1990) 307. [13] H. Keck, W. Kucben, P. Tommes, J.K. Terlouw and T. Wong, Phos. Sulfur Silicon 63 ( 1991 ) 307. [ 14 ] S.J. Huzinaga, J. Chem. Phys. 42 (1965) 1293; Approximate atomic wavefunctions II, Department of Chemistry Report, University of Alberta, Edmonton ( 1971 ). [ 15 ] T.H. Dunning, J. Chem. Phys. 53 (1970) 2823; 55 ( 1971 ) 716. [ 16 ] A.D. McCiean and G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [ 17 ] C.L. Janssen, E.T. Seidl, G.E. Scuseria, T.P. Hamilton, Y. Yamaguchi, R.B. Remington, Y. Xie, G. Vacek,C.D. Sherili, T.D. Crawford, J.T. Fermann, W.D. Allen, B.R. Brooks, G.B. Fitzgerald, D.J. Fox, J.F. Gaw, N.C. Handy, W.D. Laidig, T.J. Lee, R.M. Pitzer, J.E. Rice, P. Saxe, A. Scbeiner, H.F. Schaefer III, Psi 2.0.8 (PSITECH, Watldnsville, 1992). [ 18 ] H.A. Bent, J. Chem. Educ. 37 (1960). [ 19] W. Kutzelnigg, Angew. Chem. Intern. Ed. Engl. 23 (1984) 272. [20] A.D. Walsh, J. Chem. Soc. (1953) 2260. [21 ] J.K. Burdett and C.J. Marsden, Nouv. J. Chem. 12 (1988) 797.