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The [HCS]+ and [H2CS]2+ potential energy surfaces: Predictions of bridged equilibrium structures
Journal of Molecular Structure (Theochem), 163 (1988) 151-161 Elsevier Science Publishers, B.V., Amsterdam - Printed in The Netherlands
THE [HCS] + AND [H,CS] ‘+ POTENTIAL ENERGY SURFACES: PREDICTIONS OF BRIDGED EQUILIBRIUM STRUCTURES*
MING WAH WONG, ROSS H. NOBES and LEO RADOM Research School of Chemistry, Australian National University, Canberra A.C.T. 2601 (Australia) (Received 26 May 1987)
ABSTRACT Ab initio molecular orbital calculations with moderately large basis sets and incorporating electron correlation are carried out for carbon monosulfide (CS) and its mono- and di-protonated forms. The global minimum on the [HCS]+ potential energy surface is the linear thioformyl cation (HCS+). The isomeric CSR cation has an unusual bridged structure. It lies in a potential well, 298 kJ mol-’ above HCS+, but is separated from HCS+ by only a very small barrier (10 kJ mol-I). The remarkable feature about the [H,CS]*+ potential surface is that in this case a bridged structure (HCSH”) represents the lowestenergy isomer. The thioformaldehyde dication (H,CS’+) is predicted to have little or no barrier towards rearrangement to HCSH”. INTRODUCTION
Carbon monoxide (CO) and carbon monosulfide (CS) and their monoprotonated forms have attracted considerable recent interest as possible interstellar species. Indeed, CO [l], HCO’ [2, 31, COH’ [ 41, CS [5] and HCS’ [6] have all been observed in interstellar space, leaving only CSH’ of this set still to be observed. Ab initio molecular orbital studies proved helpful for the interstellar identification of several of these species, namely HCO’ [7, 81, COH’ [g--11] and HCS’ [ 121, with the theoretical predictions in each of these cases preceding laboratory characterization [ 13-151. For CSH’, however, the calculations performed to date [16-221 suggest that there is little or no barrier to rearrangement to HCS’, so that CSH’ is unlikely to be observable in the interstellar medium. The calculations revealed, however, an interesting bent structure for CSH+ which we felt warranted further investigation. Our initial calculations on CSW, reported in a preliminary manner elsewhere [22], revealed that the degree of bending increased markedly with inclusion of electron correlation in the theoretical treatment. Since the previous theoretical studies of the structure of this system [16-211 had been restricted to optimizations at the Hartree-Fock level, it was desirable to extend such studies by carrying out systematic optimizations at cor*Dedicated to Prof. M. J. S. Dewar on the occasion of his 70th birthday. 0166-1280/88/$03.50
o 1988 Elsevier Science Publishers B.V.
152
related levels of theory. The results of such calculations are described in this paper. In addition, as part of a continuing interest in the structures and stabilities of multiply-charged ions, the diprotonated system [H&S] ‘+ was investigated. We are unaware of any previous calculations in the literature on this system other than the preliminary report [ 221 of our present investigation in which it was noted that HCSH’+ has a quite remarkable bridged equilibrium structure. In this paper it is shown that the bridged HCSH*+ structure in fact represents the lowest-energy isomer on the [ H,CS] *+potential energy surface. Finally, results for CS itself are reported in this paper, partly to provide a basis on which to judge the performance of the various theoretical levels, and partly to enable the proton affinity of carbon monosulfide to be calculated. The latter has attracted some controversy in the literature [ 23-251. METHOD AND RESULTS
Standard ab initio molecular orbital calculations [26] were carried out with a modified version [27, 281 of Gaussian 82 [29] and with the Gamess [30, 311 and Berkeley [32] programs. Geometry optimizations were performed with the split-valence plus polarization 6-31G(d, p) basis set [ 33,341, with a triple-zeta-valence plus polarization basis set (denoted TZV(d, p) [35-371 and, in some cases, with supplemented versions of these sets: 6-31G(2d, 2p), 6-31G(df, p) and TZP(2d, 2~) [38]. Electron correlation was incorporated in these optimizations via M#ller-Plesset perturbation theory terminated at second- (MP2), third- (MP3) or fourth- (MP4) order [ 39-411 or via configuration interaction calculations with single and double substitutions (CISD). Improved relative energies were obtained by carrying out CISD/TZV(d, p) calculations at the CISD/TZV(d, p) or CISD/G-31G(d, p) optimized structures. The Davidson correction for quadruple excitations [42] has been applied, leading to CISD(Q)/TZV(Bd, 2p) relative energies. Corrections for zero-point vibrational energies were obtained through MP2/6-31G(d ) calculations of harmonic vibrational frequencies, scaled by 0.93 [43, 441. The calculated vibrational frequencies also served to characterize stationary points on the surfaces as equilibrium structures (all real frequencies), transition structures (one imaginary frequency) or higher-order saddle points (two or more TABLE 1 Calculated total energies (hartree) for carbon monosulfide (CS, l)*”
6-31G(d, p) TZV(d, P)
HF
MP2
MP3
MP4
CISD
-435.30432 -435.33925
-435.54266 -435.59368
-435.55193 -435.60196
-435.57964 -435.63114
-435.54010 -435.58787
aGeometries fully optimized at the levels specified. bCalculated zero-point vibrational energy is 7.8 kJ mall’ (MP2/6-31G(d)//MP2/6_31G(d)). CCalculated total energies at higher levels for the CISD/TZV(d, p) structure are -435.60655 (CISD/TZV( 2d, 2~)) and -435.63692 (CISD(Q)/TZV( 26, 2~)) hartree.
153 TABLE 2 Calculated total energies (hartree) and zero-point vibrational energies (ZPVE, kJ mol-*) for [ HCS]’ structures*
_
HF/6-31G(d, p) MP2/6-31G(d, p) MP3/6-31G(d, p) MP4/6-31G(d, p) CISDIG-31G(d, p) HFITZV(d, P) MPP/TZV(d, p) MP3ITZV(d, P) MP4/TZV(d, p) CISD/TZV(d, p) CISD/TZV( 2d, 2~)~ CISD(Q)/TZV( 2d, 2~)~ ZPVEC Nid
HCS+( 2) c -v
CSH+( 3) Cs
TS: 3 + 2(4) Cs
CSH’ (5) c f-V
-435.61254 -435.86788 -435.87510 -435.90056 -435.86103 -435.64705 -435.91390 -435.92070 -435.94151 -435.90514 -435.92192 -435.95195 37.6 0
-435.50036 -435.72602 -435.74641 -435.77009 -435.73713 -435.53650 -435.77836 -435.79789 -435.82078 -435.78433 -435.80294 -435.83362 23.6 0
-435.48253 -435.72736 -435.74369 -435.76687 -435.73050 -435.52140 -435.17814 -435.19430 -435.81868 -435.77915 -435.79695 -435.82854 19.6 1
-435.43736 -435.69553 -435.70433 -435.74537 -435.69209 -435.47286 -435.74584 -435.75413 -435.79561 -435.73925 -435.75382 -435.19052 21.2 2
*Geometries fully optimized at the level specified, unless otherwise noted. bCISD/TZV(d, p) optimized structures. ‘MP2/6-31G(d)//MP2/6-3lG(d) level. dNumber of imaginary frequencies. frequencies). Unless otherwise noted, calculated relative energies refer to CISD(Q)/TZV(2d, 2p) values with zero-point vibrational correction. Calculated total energies are shown in Tables 1-3, structures for CS in Table 4, structures and relative energies for the various [HCS]+ species are shown in Tables 5 and 6, respectively, and for the [H&S] 2+species in Tables 7 and 8, respectively. The CS, [HCS]+ and [H,CS] 2+ structures, calculated
imaginary
TABLE 3 Calculated total energies (hsrtree) and zero-point vibrational energies (ZPVE, kJ mol-‘) for [ H,CS] ‘+ structures*
HF/6-31G(d, p) MP2/6-31G(d, p) MP3/6-31G(d,p) MP4/6-31G(d, p) CISDIG-31G(d, p) MP3/TZV(d, p) CISD/TZV( 2d, 2~)~ CISD(Q)/TZV( 2d, 2~)~ ZPVEC Nld
HCSH*+ (6) Cs
H,W+(7) C Z”
TS: 7 -+ 6(8) Cs
HCSH”(9) C -”
-435.52307 -435.76691 -435.78203 -435.80347 -435.76723 -435.83091 -435.83262 -435.86158 50.6 0
-435.52628 -435.75003 -435.77358 -435.79234 -435.76472 -435.81825 -435.82333 -435.85336 48.7 0
-435.51555 -435.75002 -435.77269 -435.79198 -435.76207 -435.81823 -435.82571 -435.85579 47.9 1
-435.47150 -435.72946 -435.73789 -435.76641 -435.72360 -435.78636 -435.78329 -435.81431 46.2 2
*Geometries fully optimized at the level specified, unless otherwise noted. bCISD/6-31G(d,p) optimized structures. CMP2/6-31G(d)//MP2/6-31G(d) level. dNumber of imaginary frequencies.
154 TABLE 4 Optimized geometries for CS
6-31G(d, p) TZV(d, P)
HF
MP2
MP3
MP4
CISD
1.520 1.518
1.546 1.546
1.532 1.531
1.572 1.572
1.536 1.535
at the CISD/TZV(d, p) (CS and [HCS] ‘) or CISD/G-31G(d, p) ([H,CS] 2+) levels are displayed in Fig. 1. Finally, schematic energy profiles representing rearrangements on the [HCS] + and [H,CS] 2+ potential energy surfaces are shown in Figs. 2 and 3, respectively. Throughout this paper, bond lengths are given in A and bond angles in degrees. DISCUSSION
Carbon monosulfide (CS) Carbon monosulfide (1) has been examined in the present study largely to provide a benchmark assessment of the various levels of theory for structural predictions. The results in Table 4 show that, while the MP3 and CISD bond 1'
x I.
(1.899) /
c-s
1.535
1.076
1.477
H-C-S
/ / C
1 G-v)
2
1.614
3
I.571
G)
-f+
‘\
,’
(1.439))/\\ 1.516 “,
1.373
S
nb
1+ C-S-H
1.382
78.2
L”)
1'
H
1'
Ii
~6).,
“m& 179.7
4
G,)
5
-i2+
H
H
c-s
/d 7
,,*,
cc,,
G,)
-12*
12'
L- s 91.9
1551
123.8
6
Hb I.192
1.126 \
(CA
1.525
8 G)
,105
H-C-S-H
1 477
9
Fig. 1. Optimized structures used in higher-level energy calculations: for CS and [HCS]+( l-5) and CISD/G-31G(d, p) for [H,CS]*+(6-9).
1.438
LJ
CISD/TZV(d,
p)
r( C-S) r( S-H)
r(C-S) r( S-H) r( C-H)b
r( C-H)b < CSH
r( C-S) r( S-H)
MP4
CISD
1.568 1.532 1.330 50.8 1.592 1.376
1.552 1.361
1.593 1.426 1.529 60.6
1.607 1.355 2.044 86.9
1.531 1.638 1.263 46.8
1.081 1.495
1.075 1.454
1.568 1.367
1.555 1.567 1.300 49.2
1.609 1.372 1.877 77.6
1.077 1.475
1.573 1.367
1.675 1.376
1.551 1.372
1.534 1.648 1.276 47.1
1.606 1.369 2.018 85.0
1.073 1.455
1.560 1.574 1.324 50.0 1.567 1.372
1.591 1.383
1.608 1.392 1.821 74.4
1.076 1.477
MP3
1.576 1.530 1.366 52.2
1.593 1.453 1.512 59.3
1.079 1.497
MP2
parameter, included for completeness.
1.558 1.560 1.305 49.5
1.616 1.365 1.948 81.1
1.077 1.476
1.583 1.560 1.317 49.5
1.628 1.388 1.775 71.6
1.083 1.508
HF
MP3
HF
MP2
TEV(& P)
6-31G(d, p)
structures
aBond lengths in Angstroms; angles in degrees. b Non-independent
CSH+( 5)
TS: 3 + 2(4)
CSH+( 3)
r(H-C)
HCS’(2)
r(C-S)
Parametera
Species
Optimized geometries for [HCS]’
TABLE 5
1.669 1.385
1.590 1.566 1.342 50.3
1.628 1.415 1.712 68.1
1.082 1.510
MP4
1.571 1.373
1.563 1.568 1.327 50.2
1.614 1.382 1.899 78.2
1.076 1.477
CISD
156 TABLE 6 Calculated relative energies (kJ mol-‘) for [HCS]’
HF/6-3.1G(d, p) MP2/6-31G(d, p) MP3/6-31G(d, p) MP4/6-31G(d, p) CISD/GdlG(d, p) HF/TWd, P) MWTZVd, P) MPS/TZV( d, p) MP4/TZV(d, p) CISD/TZV(d, p) CISD/TZV( 2d, 2~)s CISD( Q)/TZV( 2d, 2~)~ CISD( Q)/TZV( 26, 2~)’ b aCISD/TZV(d,
structures
HCS+(2)
CSH+( 3)
TS: 3 -+ 2(4)
CSH+( 6)
-295 -367 -333 -343 -325 -290 -356 -322 -333 -317 -312 -311 -298
0 0
47 2 12 9 17 40 1 9 6 14 16 13 10
165 85 116 65 118 167 85 115 66 118 129 113 111
0 0 0
0 0 0 0 0 0
0 0
p) optimized structures. bIncluding zero-point vibrational correction.
lengths for CS are close to the experimental value of 1.535 A [45], the HF, MP2 and (particularly) MP4 values agree less well. We will comment elsewhere [46] on the generality of this unusual behavior. For the present, it is sufficient to say that, on the basis of the results for CS, we have chosen to use CISD optimized structures for our highest-level energy comparisons in the remainder of this paper. MP3 structures would also have been acceptable. The dependence of the CS bond length on basis set is rather less important. Thus, CISD calculations with 6-31G(d, p), TZV(d, p) and TZV(2d, 2~) basis
-100 -150 -200 -250 -300
Fig. 2. Schematic energy profile showing rearrangement processes on the [ HCS]+ potential energy surface.
157
Fig. 3. Schematic energy profile showing rearrangement potential energy surface.
processes on the [H2CS12+
sets yield bond lengths of 1.536, 1.535 and 1.533 A respectively. We have chosen to use the 6-31G(d, p) and TZV(d, p) basis sets for geometry optimization for the remaining systems in this paper. Thus, our highest-level energy comparisons are based on CISD/TZV(d, p) (for CS and [HCS]+) or CISD/ 6-31G(d, p) (for [H&S] *+) optimized structures. The [HCS]’
system
The thioformyl cation (HCS’, 2) represents the global minimum on the [HCS] + potential energy surface and has been examined theoretically by a number of previous workers [12, 16-22, 241. It has been observed in interstellar space [ 61 and in the laboratory [ 151. The best calculated structure (Table 5, Fig. 1) has r(H-C) = 1.076 a and r(C-S) = 1.477 A, reasonably close to the best values (1.080 and 1.475 A, respectively) estimated by Botschwina and Sebald [24]. Note that, as for CS (see above), the MP2 and MP4 structures for HCS’ are quite poor, the C-S bonds being considerably overestimated. For the CSH’ cation (3), our Hartree-Fock calculations (Table 5) confirm previous predictions [17-221 of a strongly bent structure with a CSH bond angle of 85-87”. The calculations at correlated levels, the first to be reported at such levels for this species, indicate significantly increased bending. The degree of bending (as measured by the CSH angle) is very sensitive to the level of theory used, the values in Table 5 ranging from 59.3” at MPB/TZV(d, p) to 86.9” at HF/6-31G(d, p). Additional calculations yield 77.0” at MP3/6-31G(2d, 2~) and 75.5” at MP3/6-31G(df, p), The best structure (CISD/TZV(d, p)) predicts a bending angle of 78.2”. The calculated S-H length (1.382 A) is only marginally longer than that in H2S (1.336 A, exptl.) but the C-S bond (1.614 A) is quite elongated. In the light of the large varia-
158 TABLE 7 Optimized geometries for [H,CS ] ‘+ structures Species
Parametera
6-31G(d, P)
TZVW
P)
HF
MP2
MP3
MP4
CISD
MP3
r(C-Hbjb rCS-Hb,
1.107 1.538 1.396 2.051 177.5 88.6
1.113 1.533 1.525 1.444 179.3 56.4
1.110 1.519 1.522 1.433 179.6 56.2
1.115 1.548 1.509 1.494 180.6 58.5
1.109 1.519 1.516 1.439 179.7 56.6
1.109 1.524 1.545 1.467 179.8 57.1
HzCS"(7)
r(C-H) NC-S)
1.119 1.581 121.4
1.154 1.526 125.7
1.142 1.538 124.4
1.151 1.541 125.5
1.136 1.551 123.8
1.142 1.541 124.3
TS:7'6(8)
r(H,-C) NC-S)
1.106 1.504 1.764 1.236 161.9 43.5 79.5
1.144 1.525 2.319 1.165 132.7 26.2 118.5
1.120 1.524 2.100 1.186 146.2 33.7 100.9
1.129 1.535 2.179 1.187 143.6 31.6 105.6
1.113 1.525 1.970 1.198 152.7 37.4 91.9
1.131 1.539 2.292 1.155 132.6 27.0 115.9
1.101 1.455 1.446
1.110 1.495 1.447
1.105 1.476 1.439
1.112 1.515 1.441
1.105 1.477 1.438
1.105 1.478 1.450
HCSH"(6)
r(Ha-C) tic-w
r@---H&’ r(C-Hb)
r(H-C) tic-S) r(S-H)
*Bond lengths in Angstroms; included for completeness.
hond angles in degrees. bNon-independent
parameter,
tion in geometrical parameters calculated at the various levels of theory for CSH+(3), the possible residual errors are larger than would normally be associated with, for example, CISD/TZV(d, p) calculations. The CSH’+ cation (3) lies 298 kJ mol-’ higher in energy than HCS’ (2). Rearrangement of 3 to 2 can take place via transition structure 4 and requires just 10 kJ mol-l (Fig. 2). Perhaps surprisingly, the calculated structure for 4 is much less sensitive to level of theory than that for 3 (Table 5). The small TABLE 8 Calculated relative energies (kJ mol-I) for [H,CS] *+ structures HCSH*+( 6) HF/6-31G(d, p) MP2/6-31G(d, P) MP3/6-31G(d, p) MP4/6-3lG(d, p) CISD/G-BlG(d, p) MPS/TZV(d, p) CISD/TZV( 2d, 2~)~ CISD(Q)/TZV( 2d, 2p)a CISD( Q)/TZV( 2d, 2p)4 u %ISD/G-31G(d,
-44 -22 -29 -7 -33 -24 -22 -20
8
H,CS*+( 7)
TS: 7 + 6(8)
HCSH’+( 9)
0 0 0 0 0 0 0 0 0
28 0 2 1 7 0 -6 -6 -7
144 54 94 68 108 a4 105 103 100
p) optimized structures. bIncluding zero-point vibrational correction.
barrier separating 3 from 2 supports previous indirect conclusions on this point [16, 201 and suggests that CSH’ (3) will not be observable in interstellar space. A linear CSH’ structure (5) lies substantially higher in energy (111 kJ mol-‘) than the bent equilibrium structure (3). Interestingly, however, both the C-S and S-H bond lengths are shorter in 5 than in 3. There has been some controversy in the literature concerning the proton affinity 0’ carbon monosulfide [23-251. Our best value (799 kJ mol-‘) is close to other recent theoretical estimates [20, 21, 241, and supports the more recent experimental value of Smith and Adams (788 kJ mol-‘) [25] over the older experimental value (730 kJ mol-‘) [23]. The [H2CS] ” system Other than a preliminary discussion based on the present results [22], there have been no previous reports in the literature on the [H,CS] ‘+ system. It is found, quite remarkably, that the lowest-energy isomer on the [H&S] ‘+ potential energy surface corresponds to a bridged HCSH*+ structure (6). It is essential to take account of electron correlation in order to obtain a satisfactory description of the degree of bridging in 6. Thus, the (bridging) CSH,, bond angle decreases from 88.6” at HF/6-31G(d, p) to 56-59” at correlated levels (Table 7). In contrast to the situation for CSH’ (5), there is not a large difference between the bridging angles predicted at the various correlated levels. The CISD/G-31G(d, p) structure (6, Fig. 1) has a CSHb angle of 56.6”, associated with elongated C-H and S-H bonds to the bridging hydrogen and a quite short C-S bond. The thioformaldehyde dication (7) lies 20 kJ mol-’ higher in energy than 6. The calculated height of the barrier for rearrangement of 7 to 6 (via transition structure 8) is very sensitive to the level of theory used. The best calculations (Table 8, Fig. 3) suggest that the barrier is close to zero. In this sense, the thioformaldehyde dication (7) roughly represents the transition structure for scrambling of the two hydrogen atoms in HCSH*+ (see Fig. 3, 6 + 6’). As with CSW (5), the linear structure of HCSH2+ (9) is found to have a high energy, in this case 120 kJ mol-’ above 6. CONCLUDING
REMARKS
Several important points emerge from this study: (i) CISD and MP3 are much more satisfactory than MP2 or MP4 in describing the structures of CS (1) and HCS’ (2) and probably of the other systems examined in this paper. (ii) Electron correlation is essential for a satisfactory description of the bridged equilibrium structures of CSH+ (3) and HCSH’+ (6).
160
(iii) The global minimum on the [HCS]’ potential energy surface corresponds to the linear HCS’ structure (2). The CSH+ isomer (3) lies in a shallow potential well with only a small barrier for rearrangement to 2. (iv) The lowest-energy isomer on the [H&S] *+ potential energy surface corresponds to a bridged HCSH*+ structure (6). There is little or no barrier for rearrangement of H2CS2+ (7) to 6. ACKNOWLEDGEMENTS
We are indebted to Dr. M. F. Guest and Professor H. F. Schaefer for the Gamess and Berkeley programs and to Dr. B. F. Yates for valuable discussions. REFERENCES 1 2 3 4
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161 30 M. F. Guest, J. Kendrick and S. A. Pope, GAMESS Documentation, SERC Daresbury Laboratory, Warrington, WA4 4AD, Gt. Britain, 1983. 31 M. Dupuis, D. Spangler and J. J. Wendoloski, NRCC Software Catalog, Vol. 1, Program No. QGOl, 1980. 32 P. Saxe, D. J. Fox, H. F. Schaefer and N. C. Handy, J. Chem. Phys., 77 (1982) 5584. 33 P. C. Hariharan and J. A. Pople. Theor. Chim. Acta, 28 (1973) 213. 34 M. M. Francl, W. J. Pietro, W. J. Hehre, J. S. Binkley, M. S. Gordon, D. J. DeFrees and J. A. Pople, J. Chem. Phys., 77 (1982) 3654. 35 T. H. Dunning, J. Chem. Phys., 55 (1971) 716. 36 A. D. McLean and G. S. Chandler, J. Chem. Phys., 72 (1980) 5639. 37 R. Ahlrichs and P. R. Taylor, J. Chem. Phys., 78 (1981) 315. 38M. J. Frisch, J. A. Pople and J. S. Binkley, J. Chem. Phys., 80 (1984) 3265. 39 J. A. Pople, J. S. Binkley and R. Seeger, Int. J. Quantum Chem. Symp., 10 (1976) 1. 40 R. Krishnan and J. A. Pople, Int. J. Quantum Chem., 14 (1978) 91. 41 R. Krishnan, M. J. Frisch and J. A. Pople, J. Chem. Phys., 72 (1980) 4244. 42 E. R. Davidson, in R. Daudel (Ed.), The World of Quantum Chemistry, Reidel, Dordrecht, 1974, pp. 17-30. 43 R. F. Hout, B. A. Levi and W. J. Hehre, J. Comput. Chem., 3 (1982) 234. 44 D. J. DeFrees and A. D. McLean, J. Chem. Phys., 82 (1985) 333. 45 R. Kewley, K. V. L. N. Sastry, M. Winnewisser and W. Gordy, J. Chem. Phys., 39 (1963) 2860. 46 M. W. Wong, R. H. Nobes and L. Radom, to be published.
THE [HCS] + AND [H,CS] ‘+ POTENTIAL ENERGY SURFACES: PREDICTIONS OF BRIDGED EQUILIBRIUM STRUCTURES*
MING WAH WONG, ROSS H. NOBES and LEO RADOM Research School of Chemistry, Australian National University, Canberra A.C.T. 2601 (Australia) (Received 26 May 1987)
ABSTRACT Ab initio molecular orbital calculations with moderately large basis sets and incorporating electron correlation are carried out for carbon monosulfide (CS) and its mono- and di-protonated forms. The global minimum on the [HCS]+ potential energy surface is the linear thioformyl cation (HCS+). The isomeric CSR cation has an unusual bridged structure. It lies in a potential well, 298 kJ mol-’ above HCS+, but is separated from HCS+ by only a very small barrier (10 kJ mol-I). The remarkable feature about the [H,CS]*+ potential surface is that in this case a bridged structure (HCSH”) represents the lowestenergy isomer. The thioformaldehyde dication (H,CS’+) is predicted to have little or no barrier towards rearrangement to HCSH”. INTRODUCTION
Carbon monoxide (CO) and carbon monosulfide (CS) and their monoprotonated forms have attracted considerable recent interest as possible interstellar species. Indeed, CO [l], HCO’ [2, 31, COH’ [ 41, CS [5] and HCS’ [6] have all been observed in interstellar space, leaving only CSH’ of this set still to be observed. Ab initio molecular orbital studies proved helpful for the interstellar identification of several of these species, namely HCO’ [7, 81, COH’ [g--11] and HCS’ [ 121, with the theoretical predictions in each of these cases preceding laboratory characterization [ 13-151. For CSH’, however, the calculations performed to date [16-221 suggest that there is little or no barrier to rearrangement to HCS’, so that CSH’ is unlikely to be observable in the interstellar medium. The calculations revealed, however, an interesting bent structure for CSH+ which we felt warranted further investigation. Our initial calculations on CSW, reported in a preliminary manner elsewhere [22], revealed that the degree of bending increased markedly with inclusion of electron correlation in the theoretical treatment. Since the previous theoretical studies of the structure of this system [16-211 had been restricted to optimizations at the Hartree-Fock level, it was desirable to extend such studies by carrying out systematic optimizations at cor*Dedicated to Prof. M. J. S. Dewar on the occasion of his 70th birthday. 0166-1280/88/$03.50
o 1988 Elsevier Science Publishers B.V.
152
related levels of theory. The results of such calculations are described in this paper. In addition, as part of a continuing interest in the structures and stabilities of multiply-charged ions, the diprotonated system [H&S] ‘+ was investigated. We are unaware of any previous calculations in the literature on this system other than the preliminary report [ 221 of our present investigation in which it was noted that HCSH’+ has a quite remarkable bridged equilibrium structure. In this paper it is shown that the bridged HCSH*+ structure in fact represents the lowest-energy isomer on the [ H,CS] *+potential energy surface. Finally, results for CS itself are reported in this paper, partly to provide a basis on which to judge the performance of the various theoretical levels, and partly to enable the proton affinity of carbon monosulfide to be calculated. The latter has attracted some controversy in the literature [ 23-251. METHOD AND RESULTS
Standard ab initio molecular orbital calculations [26] were carried out with a modified version [27, 281 of Gaussian 82 [29] and with the Gamess [30, 311 and Berkeley [32] programs. Geometry optimizations were performed with the split-valence plus polarization 6-31G(d, p) basis set [ 33,341, with a triple-zeta-valence plus polarization basis set (denoted TZV(d, p) [35-371 and, in some cases, with supplemented versions of these sets: 6-31G(2d, 2p), 6-31G(df, p) and TZP(2d, 2~) [38]. Electron correlation was incorporated in these optimizations via M#ller-Plesset perturbation theory terminated at second- (MP2), third- (MP3) or fourth- (MP4) order [ 39-411 or via configuration interaction calculations with single and double substitutions (CISD). Improved relative energies were obtained by carrying out CISD/TZV(d, p) calculations at the CISD/TZV(d, p) or CISD/G-31G(d, p) optimized structures. The Davidson correction for quadruple excitations [42] has been applied, leading to CISD(Q)/TZV(Bd, 2p) relative energies. Corrections for zero-point vibrational energies were obtained through MP2/6-31G(d ) calculations of harmonic vibrational frequencies, scaled by 0.93 [43, 441. The calculated vibrational frequencies also served to characterize stationary points on the surfaces as equilibrium structures (all real frequencies), transition structures (one imaginary frequency) or higher-order saddle points (two or more TABLE 1 Calculated total energies (hartree) for carbon monosulfide (CS, l)*”
6-31G(d, p) TZV(d, P)
HF
MP2
MP3
MP4
CISD
-435.30432 -435.33925
-435.54266 -435.59368
-435.55193 -435.60196
-435.57964 -435.63114
-435.54010 -435.58787
aGeometries fully optimized at the levels specified. bCalculated zero-point vibrational energy is 7.8 kJ mall’ (MP2/6-31G(d)//MP2/6_31G(d)). CCalculated total energies at higher levels for the CISD/TZV(d, p) structure are -435.60655 (CISD/TZV( 2d, 2~)) and -435.63692 (CISD(Q)/TZV( 26, 2~)) hartree.
153 TABLE 2 Calculated total energies (hartree) and zero-point vibrational energies (ZPVE, kJ mol-*) for [ HCS]’ structures*
_
HF/6-31G(d, p) MP2/6-31G(d, p) MP3/6-31G(d, p) MP4/6-31G(d, p) CISDIG-31G(d, p) HFITZV(d, P) MPP/TZV(d, p) MP3ITZV(d, P) MP4/TZV(d, p) CISD/TZV(d, p) CISD/TZV( 2d, 2~)~ CISD(Q)/TZV( 2d, 2~)~ ZPVEC Nid
HCS+( 2) c -v
CSH+( 3) Cs
TS: 3 + 2(4) Cs
CSH’ (5) c f-V
-435.61254 -435.86788 -435.87510 -435.90056 -435.86103 -435.64705 -435.91390 -435.92070 -435.94151 -435.90514 -435.92192 -435.95195 37.6 0
-435.50036 -435.72602 -435.74641 -435.77009 -435.73713 -435.53650 -435.77836 -435.79789 -435.82078 -435.78433 -435.80294 -435.83362 23.6 0
-435.48253 -435.72736 -435.74369 -435.76687 -435.73050 -435.52140 -435.17814 -435.19430 -435.81868 -435.77915 -435.79695 -435.82854 19.6 1
-435.43736 -435.69553 -435.70433 -435.74537 -435.69209 -435.47286 -435.74584 -435.75413 -435.79561 -435.73925 -435.75382 -435.19052 21.2 2
*Geometries fully optimized at the level specified, unless otherwise noted. bCISD/TZV(d, p) optimized structures. ‘MP2/6-31G(d)//MP2/6-3lG(d) level. dNumber of imaginary frequencies. frequencies). Unless otherwise noted, calculated relative energies refer to CISD(Q)/TZV(2d, 2p) values with zero-point vibrational correction. Calculated total energies are shown in Tables 1-3, structures for CS in Table 4, structures and relative energies for the various [HCS]+ species are shown in Tables 5 and 6, respectively, and for the [H&S] 2+species in Tables 7 and 8, respectively. The CS, [HCS]+ and [H,CS] 2+ structures, calculated
imaginary
TABLE 3 Calculated total energies (hsrtree) and zero-point vibrational energies (ZPVE, kJ mol-‘) for [ H,CS] ‘+ structures*
HF/6-31G(d, p) MP2/6-31G(d, p) MP3/6-31G(d,p) MP4/6-31G(d, p) CISDIG-31G(d, p) MP3/TZV(d, p) CISD/TZV( 2d, 2~)~ CISD(Q)/TZV( 2d, 2~)~ ZPVEC Nld
HCSH*+ (6) Cs
H,W+(7) C Z”
TS: 7 -+ 6(8) Cs
HCSH”(9) C -”
-435.52307 -435.76691 -435.78203 -435.80347 -435.76723 -435.83091 -435.83262 -435.86158 50.6 0
-435.52628 -435.75003 -435.77358 -435.79234 -435.76472 -435.81825 -435.82333 -435.85336 48.7 0
-435.51555 -435.75002 -435.77269 -435.79198 -435.76207 -435.81823 -435.82571 -435.85579 47.9 1
-435.47150 -435.72946 -435.73789 -435.76641 -435.72360 -435.78636 -435.78329 -435.81431 46.2 2
*Geometries fully optimized at the level specified, unless otherwise noted. bCISD/6-31G(d,p) optimized structures. CMP2/6-31G(d)//MP2/6-31G(d) level. dNumber of imaginary frequencies.
154 TABLE 4 Optimized geometries for CS
6-31G(d, p) TZV(d, P)
HF
MP2
MP3
MP4
CISD
1.520 1.518
1.546 1.546
1.532 1.531
1.572 1.572
1.536 1.535
at the CISD/TZV(d, p) (CS and [HCS] ‘) or CISD/G-31G(d, p) ([H,CS] 2+) levels are displayed in Fig. 1. Finally, schematic energy profiles representing rearrangements on the [HCS] + and [H,CS] 2+ potential energy surfaces are shown in Figs. 2 and 3, respectively. Throughout this paper, bond lengths are given in A and bond angles in degrees. DISCUSSION
Carbon monosulfide (CS) Carbon monosulfide (1) has been examined in the present study largely to provide a benchmark assessment of the various levels of theory for structural predictions. The results in Table 4 show that, while the MP3 and CISD bond 1'
x I.
(1.899) /
c-s
1.535
1.076
1.477
H-C-S
/ / C
1 G-v)
2
1.614
3
I.571
G)
-f+
‘\
,’
(1.439))/\\ 1.516 “,
1.373
S
nb
1+ C-S-H
1.382
78.2
L”)
1'
H
1'
Ii
~6).,
“m& 179.7
4
G,)
5
-i2+
H
H
c-s
/d 7
,,*,
cc,,
G,)
-12*
12'
L- s 91.9
1551
123.8
6
Hb I.192
1.126 \
(CA
1.525
8 G)
,105
H-C-S-H
1 477
9
Fig. 1. Optimized structures used in higher-level energy calculations: for CS and [HCS]+( l-5) and CISD/G-31G(d, p) for [H,CS]*+(6-9).
1.438
LJ
CISD/TZV(d,
p)
r( C-S) r( S-H)
r(C-S) r( S-H) r( C-H)b
r( C-H)b < CSH
r( C-S) r( S-H)
MP4
CISD
1.568 1.532 1.330 50.8 1.592 1.376
1.552 1.361
1.593 1.426 1.529 60.6
1.607 1.355 2.044 86.9
1.531 1.638 1.263 46.8
1.081 1.495
1.075 1.454
1.568 1.367
1.555 1.567 1.300 49.2
1.609 1.372 1.877 77.6
1.077 1.475
1.573 1.367
1.675 1.376
1.551 1.372
1.534 1.648 1.276 47.1
1.606 1.369 2.018 85.0
1.073 1.455
1.560 1.574 1.324 50.0 1.567 1.372
1.591 1.383
1.608 1.392 1.821 74.4
1.076 1.477
MP3
1.576 1.530 1.366 52.2
1.593 1.453 1.512 59.3
1.079 1.497
MP2
parameter, included for completeness.
1.558 1.560 1.305 49.5
1.616 1.365 1.948 81.1
1.077 1.476
1.583 1.560 1.317 49.5
1.628 1.388 1.775 71.6
1.083 1.508
HF
MP3
HF
MP2
TEV(& P)
6-31G(d, p)
structures
aBond lengths in Angstroms; angles in degrees. b Non-independent
CSH+( 5)
TS: 3 + 2(4)
CSH+( 3)
r(H-C)
HCS’(2)
r(C-S)
Parametera
Species
Optimized geometries for [HCS]’
TABLE 5
1.669 1.385
1.590 1.566 1.342 50.3
1.628 1.415 1.712 68.1
1.082 1.510
MP4
1.571 1.373
1.563 1.568 1.327 50.2
1.614 1.382 1.899 78.2
1.076 1.477
CISD
156 TABLE 6 Calculated relative energies (kJ mol-‘) for [HCS]’
HF/6-3.1G(d, p) MP2/6-31G(d, p) MP3/6-31G(d, p) MP4/6-31G(d, p) CISD/GdlG(d, p) HF/TWd, P) MWTZVd, P) MPS/TZV( d, p) MP4/TZV(d, p) CISD/TZV(d, p) CISD/TZV( 2d, 2~)s CISD( Q)/TZV( 2d, 2~)~ CISD( Q)/TZV( 26, 2~)’ b aCISD/TZV(d,
structures
HCS+(2)
CSH+( 3)
TS: 3 -+ 2(4)
CSH+( 6)
-295 -367 -333 -343 -325 -290 -356 -322 -333 -317 -312 -311 -298
0 0
47 2 12 9 17 40 1 9 6 14 16 13 10
165 85 116 65 118 167 85 115 66 118 129 113 111
0 0 0
0 0 0 0 0 0
0 0
p) optimized structures. bIncluding zero-point vibrational correction.
lengths for CS are close to the experimental value of 1.535 A [45], the HF, MP2 and (particularly) MP4 values agree less well. We will comment elsewhere [46] on the generality of this unusual behavior. For the present, it is sufficient to say that, on the basis of the results for CS, we have chosen to use CISD optimized structures for our highest-level energy comparisons in the remainder of this paper. MP3 structures would also have been acceptable. The dependence of the CS bond length on basis set is rather less important. Thus, CISD calculations with 6-31G(d, p), TZV(d, p) and TZV(2d, 2~) basis
-100 -150 -200 -250 -300
Fig. 2. Schematic energy profile showing rearrangement processes on the [ HCS]+ potential energy surface.
157
Fig. 3. Schematic energy profile showing rearrangement potential energy surface.
processes on the [H2CS12+
sets yield bond lengths of 1.536, 1.535 and 1.533 A respectively. We have chosen to use the 6-31G(d, p) and TZV(d, p) basis sets for geometry optimization for the remaining systems in this paper. Thus, our highest-level energy comparisons are based on CISD/TZV(d, p) (for CS and [HCS]+) or CISD/ 6-31G(d, p) (for [H&S] *+) optimized structures. The [HCS]’
system
The thioformyl cation (HCS’, 2) represents the global minimum on the [HCS] + potential energy surface and has been examined theoretically by a number of previous workers [12, 16-22, 241. It has been observed in interstellar space [ 61 and in the laboratory [ 151. The best calculated structure (Table 5, Fig. 1) has r(H-C) = 1.076 a and r(C-S) = 1.477 A, reasonably close to the best values (1.080 and 1.475 A, respectively) estimated by Botschwina and Sebald [24]. Note that, as for CS (see above), the MP2 and MP4 structures for HCS’ are quite poor, the C-S bonds being considerably overestimated. For the CSH’ cation (3), our Hartree-Fock calculations (Table 5) confirm previous predictions [17-221 of a strongly bent structure with a CSH bond angle of 85-87”. The calculations at correlated levels, the first to be reported at such levels for this species, indicate significantly increased bending. The degree of bending (as measured by the CSH angle) is very sensitive to the level of theory used, the values in Table 5 ranging from 59.3” at MPB/TZV(d, p) to 86.9” at HF/6-31G(d, p). Additional calculations yield 77.0” at MP3/6-31G(2d, 2~) and 75.5” at MP3/6-31G(df, p), The best structure (CISD/TZV(d, p)) predicts a bending angle of 78.2”. The calculated S-H length (1.382 A) is only marginally longer than that in H2S (1.336 A, exptl.) but the C-S bond (1.614 A) is quite elongated. In the light of the large varia-
158 TABLE 7 Optimized geometries for [H,CS ] ‘+ structures Species
Parametera
6-31G(d, P)
TZVW
P)
HF
MP2
MP3
MP4
CISD
MP3
r(C-Hbjb rCS-Hb,
1.107 1.538 1.396 2.051 177.5 88.6
1.113 1.533 1.525 1.444 179.3 56.4
1.110 1.519 1.522 1.433 179.6 56.2
1.115 1.548 1.509 1.494 180.6 58.5
1.109 1.519 1.516 1.439 179.7 56.6
1.109 1.524 1.545 1.467 179.8 57.1
HzCS"(7)
r(C-H) NC-S)
1.119 1.581 121.4
1.154 1.526 125.7
1.142 1.538 124.4
1.151 1.541 125.5
1.136 1.551 123.8
1.142 1.541 124.3
TS:7'6(8)
r(H,-C) NC-S)
1.106 1.504 1.764 1.236 161.9 43.5 79.5
1.144 1.525 2.319 1.165 132.7 26.2 118.5
1.120 1.524 2.100 1.186 146.2 33.7 100.9
1.129 1.535 2.179 1.187 143.6 31.6 105.6
1.113 1.525 1.970 1.198 152.7 37.4 91.9
1.131 1.539 2.292 1.155 132.6 27.0 115.9
1.101 1.455 1.446
1.110 1.495 1.447
1.105 1.476 1.439
1.112 1.515 1.441
1.105 1.477 1.438
1.105 1.478 1.450
HCSH"(6)
r(Ha-C) tic-w
r@---H&’ r(C-Hb)
r(H-C) tic-S) r(S-H)
*Bond lengths in Angstroms; included for completeness.
hond angles in degrees. bNon-independent
parameter,
tion in geometrical parameters calculated at the various levels of theory for CSH+(3), the possible residual errors are larger than would normally be associated with, for example, CISD/TZV(d, p) calculations. The CSH’+ cation (3) lies 298 kJ mol-’ higher in energy than HCS’ (2). Rearrangement of 3 to 2 can take place via transition structure 4 and requires just 10 kJ mol-l (Fig. 2). Perhaps surprisingly, the calculated structure for 4 is much less sensitive to level of theory than that for 3 (Table 5). The small TABLE 8 Calculated relative energies (kJ mol-I) for [H,CS] *+ structures HCSH*+( 6) HF/6-31G(d, p) MP2/6-31G(d, P) MP3/6-31G(d, p) MP4/6-3lG(d, p) CISD/G-BlG(d, p) MPS/TZV(d, p) CISD/TZV( 2d, 2~)~ CISD(Q)/TZV( 2d, 2p)a CISD( Q)/TZV( 2d, 2p)4 u %ISD/G-31G(d,
-44 -22 -29 -7 -33 -24 -22 -20
8
H,CS*+( 7)
TS: 7 + 6(8)
HCSH’+( 9)
0 0 0 0 0 0 0 0 0
28 0 2 1 7 0 -6 -6 -7
144 54 94 68 108 a4 105 103 100
p) optimized structures. bIncluding zero-point vibrational correction.
barrier separating 3 from 2 supports previous indirect conclusions on this point [16, 201 and suggests that CSH’ (3) will not be observable in interstellar space. A linear CSH’ structure (5) lies substantially higher in energy (111 kJ mol-‘) than the bent equilibrium structure (3). Interestingly, however, both the C-S and S-H bond lengths are shorter in 5 than in 3. There has been some controversy in the literature concerning the proton affinity 0’ carbon monosulfide [23-251. Our best value (799 kJ mol-‘) is close to other recent theoretical estimates [20, 21, 241, and supports the more recent experimental value of Smith and Adams (788 kJ mol-‘) [25] over the older experimental value (730 kJ mol-‘) [23]. The [H2CS] ” system Other than a preliminary discussion based on the present results [22], there have been no previous reports in the literature on the [H,CS] ‘+ system. It is found, quite remarkably, that the lowest-energy isomer on the [H&S] ‘+ potential energy surface corresponds to a bridged HCSH*+ structure (6). It is essential to take account of electron correlation in order to obtain a satisfactory description of the degree of bridging in 6. Thus, the (bridging) CSH,, bond angle decreases from 88.6” at HF/6-31G(d, p) to 56-59” at correlated levels (Table 7). In contrast to the situation for CSH’ (5), there is not a large difference between the bridging angles predicted at the various correlated levels. The CISD/G-31G(d, p) structure (6, Fig. 1) has a CSHb angle of 56.6”, associated with elongated C-H and S-H bonds to the bridging hydrogen and a quite short C-S bond. The thioformaldehyde dication (7) lies 20 kJ mol-’ higher in energy than 6. The calculated height of the barrier for rearrangement of 7 to 6 (via transition structure 8) is very sensitive to the level of theory used. The best calculations (Table 8, Fig. 3) suggest that the barrier is close to zero. In this sense, the thioformaldehyde dication (7) roughly represents the transition structure for scrambling of the two hydrogen atoms in HCSH*+ (see Fig. 3, 6 + 6’). As with CSW (5), the linear structure of HCSH2+ (9) is found to have a high energy, in this case 120 kJ mol-’ above 6. CONCLUDING
REMARKS
Several important points emerge from this study: (i) CISD and MP3 are much more satisfactory than MP2 or MP4 in describing the structures of CS (1) and HCS’ (2) and probably of the other systems examined in this paper. (ii) Electron correlation is essential for a satisfactory description of the bridged equilibrium structures of CSH+ (3) and HCSH’+ (6).
160
(iii) The global minimum on the [HCS]’ potential energy surface corresponds to the linear HCS’ structure (2). The CSH+ isomer (3) lies in a shallow potential well with only a small barrier for rearrangement to 2. (iv) The lowest-energy isomer on the [H&S] *+ potential energy surface corresponds to a bridged HCSH*+ structure (6). There is little or no barrier for rearrangement of H2CS2+ (7) to 6. ACKNOWLEDGEMENTS
We are indebted to Dr. M. F. Guest and Professor H. F. Schaefer for the Gamess and Berkeley programs and to Dr. B. F. Yates for valuable discussions. REFERENCES 1 2 3 4
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