~ , . r ~

E L S E V I E R

I0 January 1997

Chemical Physics Letters 264 (1997) 441-448

CHEMICAL PHYSICS LE'r'rERS

Molecular structures, vibrational spectra and rotational barriers of C2H 6, Si2H 6, SiGeH 6 and Ge2H 6 - experiment and theory in

harmony

Jan Urban a,b, Peter R. Schreiner c,l, George Vacek d, Paul von Ragu6 Schleyer c, Joan Q. Huang a, Jerzy Leszczynski a

a Jackson State University, Department of Chemistry, Lynch Street, Jackson, MS 39217, USA b Comenius University, Department of Biophysics and Chemical Physics, Bratislava, Mlynskdolina F1, Slovakia

c Computer Chemistry Center, lnstitutfiir Organische Chemie der Universitat Erlangen-Nr, rnberg, Henkestr. 42, D-91054 Erlangen, Germany

a Swiss Center for Scientific Supercomputing (SCSC), Swiss Federal Institute of Technology (ETH-Zentrum), CH-8092 Zurich, Switzerland

Received 26 September 1996; in final form 5 November 1996

Abstract

The staggered and eclipsed conformers of the title compounds were optimized at the HF, MP2, B3LYP, and CISD levels of theory utilizing polarized triple-~" basis sets; CCSD(T) single points were computed for the CISD structures. All experimental geometrical parameters are reproduced well at the correlated levels. The rotational barriers are better described with larger basis sets, and require sophisticated electron correlation treatments (CISD or CCSD) for quantitative agreement with experiment. B3LYP rotational constants are generally somewhat too small due to the incomplete inclusion of higher-order perturbations. The vibrational frequencies computed using MP2 and B3LYP, agree well with experiment after the application of scaling factors of 0.945 and 0.98, respectively.

I. Introduct ion

Disilane, silylgermane, and digermane are the simplest saturated compounds containing Si-Si, Si - Ge, and G e - G e bonds. Like ethane for hydrocar- bons, they are the basis for understanding the struc- tures and bonding in the higher group XIV element homologues. The experimental structures (bond lengths, bond angles) as well as the infrared spectra

Current address: lnstitut fiir Organische Chemie, Universifftt GiSttingen, Tammannstr. 2, D-37077 GSttingen, Germany.

of these species are available [ 1-9]. A few theoreti- cal papers have dealt with the geometries and the origin of the rotational barriers in XYH 6 molecules (X, Y = Si, Ge) [10-12], but no high level investiga- tion of the rotational barriers, including comparisons between conventional ab initio theory and density functional theory (DFT), is available.

Our previous study [12] showed that high levels of theory reproduce some of the experimentally de- termined features of these species accurately. The good agreement between theory and experiment for Si2H 6 and SiGeH 6 (bond lengths are within 0.01 ~,, angles within 0.1 o of the experimental values) [9] led

0009-2614/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S0009-261 4(96)01341-3

442 J. Urban et aL / Chemical Physics Letters 264 (1997) 441-448

us to suggest that the experimental G e - G e - H angle of 106.4 ° in Ge2H 6 may be in error by 2 ° (the computed angle is 108.5°)[12].

In a comprehensive investigation of the entire set of group XIV hydrides (HaXYH3), Schleyer et al. [11] explained the origin of the rotational barriers, and demonstrated that relativistic effects only are highly important for the heaviest element (Pb). Ge- ometry optimizations were carried out at the Hartree-Fock level using only moderate basis sets in conjunction with relativistic effective core potentials for the heavier elements. These methods give M - M bond lengths which are somewhat too long, leading to an underestimation of the rotational barriers. Elec- tron correlation effects may be important, in particu- lar for the rotational constants. Thus, a re-examina- tion of the structural features and rotational barriers at the currently highest possible ab initio levels is desirable and serves as partial motivation for the present study.

While the IR and Raman spectra for the title compounds are known experimentally, no computed vibrational spectra are available. These are useful, however, for evaluating the quality of the theoretical methods, and for predicting their performance in the application to larger systems.

We now report the structures and rotational barri- ers of XYH 6 (X, Y = Si, Ge) species as well as a full set of vibrational and rotational frequencies for comparison with experiment.

2. Methods

Our previous investigation showed that all the correlated ab initio levels [(MP2, CISD, CCSD, and CCSD(T)] as well as the B3LYP functional in con- junction with triple-~ basis sets yield structures which are in excellent agreement with experiment. Most important was the inclusion of f polarization functions on the heavy atom; including d polariza- tion functions on the hydrogens had little effect, but these may be important in refining the rotational barriers.

The ab initio programs Gaussian 94 [13] (for D F r and MP2) and PSI 2.0.8 [14] [for CISD, CCSD, and CCSD(T)] were utilized. Five ab initio and the B3LYP density functional [15,16] levels were em- ployed for geometry optimizations and single energy points. For the HF, MP2, and D F r calculations the basis set utilized was constructed as follows: McLean's valence triple-~" basis set [17] was aug-

Table 1

Computed molecular parameters of C2H 6. Bond lengths in ,~, angles in degrees, rotational constants in cm -~ , and energy in E h

Level Conformation R(C - C) R(C - H) L H - C - C L H - C - H Energy Rotational constants

HF eclipsed 1.539 1.082 I 11.6 107.3 - 79.25205 (A) 2.7536 (B) 0.6604 TZ(2d,2p) staggered 1.525 1.083 111.2 107.7 - 79.25692 2.7326 0.6720

l-IF eclipsed 1.539 1.083 111.6 107.3 - 79.25344 (A) 2.7522 (B) 0.6601 TZ(2df,2pd) staggered 1.524 1.084 I 11.2 107.7 - 79.25830 2.7315 0.6722

MP2 ecl ipsed 1.540 1.086 111.7 107.2 - 79.58995 (A) 2.7391 (B) 0.6583 TZ(2d,2p) staggered 1.527 1.087 111.2 107.7 - 79.59462 2.7161 0.6700

MP2 eclipsed 1.536 1.087 111.7 107.1 - 79.62270 (A) 2.7331 (B) 0.6606 TZ(2df,2pd) staggered 1.522 1.088 I 11.3 107.6 - 79.62740 2.7105 0.6719

DFT ecl ipsed 1.543 1.090 111.8 107.1 - 79.85654 (A) 2.7226 (B) 0.6553

TZ(2d,2p) staggered 1.529 1.091 111.4 107.5 - 79.86072 2.7015 0.6663 DFT ecl ipsed 1.541 1.090 111.8 107.1 - 7 9 . 8 5 8 3 0 (A) 2.7217 (B) 0.6559 TZ(2df,2pd) staggered 1.527 1.091 111.4 107.5 - 79.86248 2.7010 0.6671 CISD ecl ipsed 1.534 1.088 I 11.7 107.2 - 79.59654 (A) 2.7291 (B) 0.6622

- 79.63043 a T-Z(df, p) staggered 1.520 1.089 111.2 107.7 - 79.60146 2.7065 0.6735

- 79.63534 a exptl, b staggered 1.531 1.096 - 107.8 - -

a Davidson ' s correction applied, CISD + Q. b Ref. [31].

J. Urban et al. / Chemical Physics Letters 264 (1997) 441--448 443

mented with two sets of p-polarization functions on hydrogen and two sets of five d-polarization func- tions on silicon (denoted 2p,2d), while Huzinaga ' s partially uncontracted [433111/431 1 1 / 4 " ] basis set [18] with two sets of five d-polarization functions (adl = 0.108, Otd2 = 0 . 3 8 2 ) was used for Ge. This basis is referred to as TZ(2d,2p). Adding a set of f-polarization functions on the heavy atoms (af<o~) =

0.45, af~si ) = 0.3, af~c)= 0.8) and a set of d-func- t ions on the hyd rogens (rid(H) = 1.0) gave TZ(2df,2pd). For disilane, s i lylgermane and diger- mane only the 3s,3p electrons of Si and the 4s,4p electrons of Ge were correlated at the MP2 level; at all other levels the Ge 3d electrons were correlated as well. A basis set of triple-~" plus polarization quality was used for the CISD [19], CCSD [20], and CCSD(T) [21] calculations. A primit ive basis set for Ge(15s l2p7d) [22] was contracted to Ge(10s8p3d) and augmented with polarization functions: af~ce ) = 0.45, CrOCCe ) = 0.19 [23]. McLean ' s valence triple-~" basis set [17] was augmented with a set of five d- and seven f-polarization functions for silicon; ad<S~ ) = 0.50, af<S~ ) = 0.32. For carbon and hydrogen, a standard H u z i n a g a - D u n n i n g - H a y triple-st basis set

[23,24] was augmented with a set of five d- and seven f-polarization functions Crd<C)= 0.75, af<C)= 0.80 and a set of p-polarization functions ap<H)= 0.75, respectively. This basis can be referred to as TZ(df, p).

All geometries were optimized by analytical gra- dient methods [25]. The M P 2 / / T Z ( 2 d f , 2 p d ) opti- mized structures were used for MP4(SDTQ) single energy points. CISD opt imized geometries were taken for the coupled cluster calculations which were car- ried out with PSI 2.0.8.[14]. The Davidson ' s correc- tion [26] was applied to CISD energies and is de- noted as CISD + Q.

3. R e s u l t s a n d d i s c u s s i o n

All optimization levels (MP2, B3LYP, and CISD) produce comparable geometries (Tables 1-7). Al- though the inclusion of electron correlation tends to reduce the central XY bond distances, this effect is somewhat unsystematic for Ge2H 6. While a larger basis set emphasizes the bond length reduction due to correlation for all other species, the G e - G e bond

Table 2 Molecular parameters of Si 2 H 6. Bond

Basis

HF (2d,2p) eclipsed 2.379 1.483 staggered 2.368 1.483

TZ (2df,2pd) eclipsed 2.379 1.478 staggered 2.367 1.478

MP2 (2d,2p) eclipsed 2.366 1.483 staggered 2.353 1.483

TZ (2df,2pd) eclipsed 2.363 1.477 staggered 2.349 1.478

DFT (2d,2p) eclipsed 2.365 1.487 staggered 2.357 1.483

TZ (2df,2pd) eclipsed 2.363 1.483 staggered 2.351 1.484

CISD (df, pd) eclipsed 2.345 1.477

TZ staggered 2.333 1.477

exptl, b staggered 2.331 1.492(3)

lengths in ,~,, angles in degrees, rotational constants in cm- ~, and energy in E h

Conformation R(Si-Si) R(Si-H) Z.H-Si-Si /_H-Si-H Energy Rotational

10.5 10.3 10.5 10.3 10.3 10.1 10.3 10.1 10.5 10.3

110.5 110.3 110.5

110.4

110.3(4)

constants

108.5 - 580.70659 (A) 1 .AA.A.A. (B) 0.1643 108.6 - 580.70823 1.4398 0.1656 108.5 --581.36494 (A) 1.4538 (B) 0.1644 108.6 - 581.36657 1.4494 0.1682 108.6 - 580.94080 (A) 1.4408 (B) 0.1660 108.7 - 580.94267 1.4354 0.1676 108 .6 -581.62760 (A) 1.4525 (B) 0.1664 108.8 - 581.62939 1.4477 0.1682 108.5 -581.99173 (A) 1.4354 (B) 0.1659 108.6 - 581.99331 1.4406 0.1670 108.4 - 582.64434 (A) 1.4440 (B) 0.1661 108.7 - 582.64597 1.4386 0.1677 108 .4 -581.613873 (A) 1.4563 (B) 0.1686

- 581.642237 a 108.6 -581.615973 1.4531 0.1703

- 581.644437 ~ 108.6 - -

a Davidson's correction applied, CISD + Q. b Ref. [9].

Tab

le 3

M

olec

ular

par

amet

ers

of G

eSiH

6. B

ond

leng

ths

in/~

, an

gles

Bas

is

Con

form

atio

n R

(Si-

Ge)

R

(Ge-

H)

HF

(2d,

2p)

eclip

sed

2.41

9 1.

531

stag

gere

d 2.

408

1.53

1 T

Z

(2df

,2pd

) ec

lipse

d 2.

406

1.52

8 st

agge

red

2.39

7 1.

529

MP2

(2

d,2p

) ec

lipse

d 2.

407

1.53

3 st

agge

red

2.39

7 1.

533

TZ

(2

df,2

pd)

eclip

sed

2.38

9 1.

529

stag

gere

d 2.

380

1.52

9 D

FT

(2d,

2p)

eclip

sed

2.40

1 1.

532

stag

gere

d 2.

397

1.48

3 T

Z

(2df

,2pd

) ec

lipse

d 2.

386

1.52

9 st

agge

red

2.37

9 1.

482

C1S

D

(df,

pd)

eclip

sed

2.38

2 1.

527

TZ

st

agge

red

2.37

3 1.

528

expt

l, b

stag

gere

d 2.

358(

3)

1.53

8(3)

a D

avid

son'

s co

rrec

tion

app

lied,

CIS

D +

Q.

b R

ef.

[9].

c R

ef.

[3].

in d

egre

es,

rota

tiona

l co

nsta

nts

in c

m-

~,

R(S

i-H

) L

H-S

i-G

e L

Si-

Ge-

H

1.48

2 11

0.3

110.

6 1.

482

110.

1 11

0.5

1.47

7 11

0.3

110.

8 1.

477

110.

1 11

0.6

1.48

2 11

0.2

110.

5 1.

483

110.

0 11

0.2

1.47

6 11

0.2

110.

7 1.

477

110.

0 11

0.5

1.48

7 11

0.3

110.

8 1.

483

110.

1 11

0.6

1.48

2 11

0.3

110.

9 1.

482

110.

1 11

0.8

1.47

5 11

0.2

110.

8

1.47

5 11

0.0

110.

7

1.49

4(6)

-

and

ener

gy i

n E

h

LH

-Si-

H

LH

-Ge-

H

108.

7 10

8.4

108.

8 10

8.5

108.

7 10

8.2

108.

8 10

8.3

108.

8 10

8.5

109.

0 10

8.7

108.

8 10

8.3

108.

9 10

8.5

108.

6 10

8.1

108.

8 10

8.3

109.

0 10

8.7

108.

8 10

8.2

108.

8 10

8.1

108.

9 10

8.2

108.

8 10

8.3

Ene

rgy

-236

5.56

404

-236

5.56

545

-236

5.90

214

-236

5.90

351

-236

5.79

395

-236

5.79

554

-236

6.16

050

-236

6.16

189

-236

7.96

304

-236

8.29

240

-236

8.29

769

-236

8.29

900

-236

8.22

707

-236

8.27

507

-236

8.22

838

-236

8.27

635

Rot

atio

nal c

onst

ants

(A)

1.39

85

(B)

0.11

66

1.39

49

0.11

75

(A)

1.40

79

(B)

0.11

78

1.40

36

0.11

85

(A)

1.39

40

(B)

0.11

77

1.38

88

0.11

86

(A)

1.40

53

(B)

0.11

93

1.40

09

0.12

02

(A)

1.39

55

(B)

0.11

81

1.39

15

0.11

90

(A)

1.40

34

(B)0

.119

5 1.

3985

0.

1201

(A

) 1.

4102

(B

)0.1

200

1.40

72

0.12

09

(B)

0.12

19

¢

t~ E

t~

4~

0o

J. Urban et al. / Chemical Physics Leuers 264 (1997) 441-448 445

lengthens marginally with MP2//TZ(2df,2pd). The B3LYP method, however, behaves 'regularly' for Ge2 H,6. As expected, the XY bond lengths are around 0.01 A longer in the eclipsed conformers, while the XH and YH bond lengths remain nearly constant (AR = 0.001 ,~); the HXY angles also are largely unaffected (within 0.1 °) according to the CISD re- sults. Our previous study [12] revealed that all stag- gered conformations have XY bond lengths which are consistently longer than experiment; CISD has the smallest deviation from experimental values (0.000 ~, for Si2H6, 0.013 A for Ge2H6, and 0.008

,~, for SiGeH6). One may assume that the accuracy is comparable for the experimentally unknown geome- tries of the eclipsed conformers [31].

The rotational barriers for ethane, disilane, silyl- germane, and digermane at different levels of theory are given in Table 5. Schleyer et al. [11 ] as well as Bader et al. [27] have analyzed the origin of the rotational barriers in XYH 6 compounds in detail. In summary, the stabilizing vicinal t r (XH)~ tr * (YH) delocalization is mainly responsible for a more stable staggered versus eclipsed conformation. Decreased overlap due to a longer XY bond is the origin of

Table 4

Molecular parameters of Ge 2 H 6. Bond lengths in ,~, angles in degrees, rotational constants in cm -~ , and energy in E h

Basis Conformation R(Ge-Ge) R(Ge-H) Z.H-Ge-Ge Z.H-Ge-H Energy Rotational constants

HF (2d,2p) eclipsed 2.460 1.530 110.4 108.6 -4150.42183 (A) 1.3541 (B) 0.0678 staggered 2.449 1.530 110.3 108.7 - 4150.42304 1.3519 0.0683

TZ (2df,2pd) eclipsed 2.447 1.527 110.5 108.4 - 4150.43742 (A) 1.3629 (B) 0.0685 staggered 2.438 1.527 110.4 108.5 - 4150.43857 1.3601 0.0689

MP2 (2d,2p) eclipsed 2.426 1.529 110.5 108.4 - 4150.69039 (A) 1.3601 (B) 0.0700 staggered 2.439 1.533 110.1 108.8 - 4150.64869 1.3449 0.0689

TZ (2df,2pd) eclipsed 2.449 1.532 110.3 108.7 - 4150.64733 (A) 1.3490 (B) 0.0684 staggered 2.418 1.529 110.4 1 0 8 . 5 -4150.69158 1.3567 0.0700

DFT (2d,2p) eclipsed 2.442 1.534 110.4 1 0 8 . 5 -4150.93379 (A) 1.3575 (B) 0.0691 staggered 2.433 1.534 110.3 108.6 - 4153.93482 1.3457 0.0692

TZ (2df,2pd) eclipsed 2.428 1.529 110.6 108.3 - 4150.94927 (A) 1.3700 (B) 0.6990 staggered 2.418 1.529 110.5 108.4 - 4153.95023 1.3585 0.0700

CISD (f, pd) eclipsed 2.424 1.525 110.5 108.4 -4154.834497 (A) 1.3661 (B) 0.0697

- 4154.902663 a TZ staggered 2.416 1.526 110.4 108.5 - 4154.835663 1.3634 0.0702

-4154.903808 a exptl, b staggered 2.403(3) 1.541(6) 112.5(8) 106.4(8) c _ _

a Davidson's correction applied, specified as CISD + Q. b Ref. [9].

c Probably incorrect, see Ref. [12].

Table 5 Rotational barriers a of the XYH 6 (X, Y = C, Si, and Ge) species

HF(1) I'-IF(2) MP2(I) MP2(2) DFT(I) DFI"(2) AZPE CISD C I S D + Q b CCSD

C 2 H6 3.06 3.05 2.94 2.95 2.62 2.63 - 0.30 3.09 3.08 3.08 Si2 H6 1.03 1.02 1.17 1.12 0.99 0.99 - 0.07 1.38 1.38 1.38 SiGeH 6 0.88 0.86 1.00 0.88 0.65 0.83 -0 .06 0.79 0.81 0.79 Ge2H 6 0.76 0.52 0.75 0.86 0.65 0.61 -0.11 0.70 0.72 0.70

CCSD(T) Exptl. Ref. [5]

3.11 2.90 c 2.75 1.42 1.22 d 0.95 0.79 n.a. 0.61 0.70 n.a. 0.66

a All values are in kcal mol- i, the numbers in parentheses refer to basis set 1 - TZ(2d,2p); 2 - TZ(2df,2pd). b Davidson's correction applied. c Ref. [31]. d Ref. [6].

446 J. Urban et aL / Chemical Physics Letters 264 (1997) 441-448

sma l l e r ro ta t iona l ba r r i e r s for the h e a v i e r species .

W e a lso f ind the e x p e c t e d inve r se ly p ropor t iona l

r e l a t i onsh ip b e t w e e n the s ign and s ize of the differ-

e n c e s in b o n d l eng th s ( m o s t l y c o m p u t e d s o m e w h a t

too long) and ro ta t iona l ba r r i e r s ( c o m p u t e d too smal l )

at H F and M P 2 ( T a b l e 5). T h e B 3 L Y P ro ta t iona l

ba r r ie r s are gene ra l ly 10% too smal l , e v e n w h e n the

g e o m e t r i e s are c lose to e x p e r i m e n t . Th i s is l ike ly due

to the i n c o m p l e t e i nc lu s ion o f h i g h e r - o r d e r per turba-

t ions in such h y b r i d H a r t r e e - F o c k dens i ty func t iona l

s c h e m e s [33].

T h e h i g h l y co r re l a t ed c o n f i g u r a t i o n in te rac t ion and

coup l ed c lus te r m e t h o d s o v e r e s t i m a t e the bar r ie r s to

ro ta t ion o f the t i t le mo lecu l e s , a l t hough the overa l l

Table 6 Computed (harmonic, sealed: MP2: 0.945; DFT: 0.98, see text) and observed (fundamental) vibrational frequencies of ethane (in cm- ~ )

Assignment Staggered Eclipsed

MP2 a DFT a Exptl. b Exptl. ¢ MP2 DFT

C-C torsional 320 302 303 278 300 292i CH 3 rocking 828 809 822 822 858 895 C-C stretching 1030 976 1016 945 977 991 CH 3 rocking 1231 1195 1246 1190 1120 1172 CH 3 deform. 1412 1382 1438 1379 1337 1410 CH 3 deform. 1431 1397 1 449 1388 1479 1440 CH 3 deform. 1414 1397 1526 1469 1482 1505 CH 3 deform. 1524 1478 1552 1472 1455 1515 C-H stretching sym. 3086 2970 3043 2896 2939 3040 C-H stretching anti-sym. 3088 2971 3061 2950 2946 3046 C-H stretching sym. 3160 3014 31 40 2954 3009 3086 C-H stretching anti-sym. 3182 3039 3175 2996 3029 3109

a IlTZ(2df,2pd). b Ref. [31]. ¢ Ref. [32].

Table 7 Computed (harmonic, scaled: MP2: 0.945; DFT: 0.98, see text) and observed (fundamental) vibrational frequencies (in cm- t) of the XYH 6 (staggered) species

Assignment Si 2 H 6 SiGeH 6 Ge 2 H 6

level MP2 a DFT a Exptl. b MP2 DFT Exptl. c MP2 DFT Exptl. d

torsional mode 137 85 - 118 68 144 109 58 1 44 YH 3 rocking 362 361 379 353 359 371 346 343 407 X-Y stretching 422 414 434 353 338 309 258 251 229 XH 3 rocking 623 616 625 588 581 580 548 545 417 XH3 bending e 838 838 844 781 776 780 752 749 755 XH 3 bending r 913 909 909 883 874 890 824 826 765 YH 3 deform. 931 921 929 934 919 930 873 871 875 XH 3 deform. 946 935 940 879 872 881 877 876 898 Y-H stretching 2187 2139 2152 2136 2067 2052 2122 2067 2070 Y-H stretching 2195 2157 2154 2137 2077 2069 2124 2097 2078 X-H stretching 2196 2161 2155 2184 2132 2151 2130 2114 2150 X-H stretching 2203 2170 2179 2193 2151 2160 2129 2104 2114

a IITZ(2dL2pd). b Ref. [9]. c Ref. [8]. d Ref. [7]. e Assigned as HXH-HYH bending for SiGeH 6. f Assigned as H-X-Y bending for SiGeH 6.

J. Urban et al. / Chemical Physics Letters 264 (1997) 441~148 447

agreement with experiment is quite good (deviation: 6 - 14%) . A comparison of the two sets of experimen- tal data in Table 5 casts some doubt on their accu- racy - the deviations are as large as 22%. The highest levels of theory seem to favor the larger experimental barriers [28].

Computed vibrational frequencies are usually somewhat larger than experiment due to the use of the harmonic approximation and the incomplete in- clusion of electron correlation. Hence, we used a scaling factor of 0.945 for the MP2 vibrational fre- quencies as suggested by Pople et al. [29]. This gives reasonable results for ethane in Table 6. However, this empirical scaling factor was devised from a series of benchmark calculations on a large number of molecules containing mostly C, H, N, and O. Thus, it is not obvious that they should also work well for molecules containing bonds to other ele- ments. We find that a somewhat smaller scaling factor of 0.955 should be used for S i l l and GeH vibrations for MP2 in conjunction with triple-~" basis sets. At the DFT level, both S i l l and GeH B3LYP vibrational frequencies should be scaled by 0.98 (Table 6), in agreement with a recently published recommendat ion [30]. However , a much larger set of structures is needed to confirm the generality of these factors.

Computat ion of the equil ibrium geometries of H3XYH 3 (X, Y = C, Si, Ge) molecules in eclipsed and staggered conformations have shown that, al- though large basis sets and sophisticated levels of electron correlation are needed for more quantitative agreement with experiment, the current ab initio methods are able to determine the structures and rotational barriers with acceptable accuracy (the overall deviation from experiment is usually less than 10%). Although the MP2 method gives good geometries, the rotational barriers are relatively large. B3LYP geometries and vibrational frequencies (scaled by 0.98) are excellent, but DFT underesti- mates the rotational barriers.

Acknowledgements

The study in Jackson was supported by the Na- tional Science Foundation (Grant EHR-91-08767 and by a contract (DAAL03-89-0038) between the Army

Research Office and the University of Minnesota for the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory cooperative agree- ment number DAAH04-95-2-0003 contract number DAAH04-95-C-008, the policy of the government, and no official endorsement should be inferred. The Mississippi Center for Supercomputing Research and the Competence Center for Computational Chemistry [C 4] (Zi)rich) are acknowledged for a generous allot- ment of computer time. PRS and GV thank Henry F. Schaefer III for supplying the PSI program suite [14].

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