Ab initio calculation of vibrational circular dichroism spectra using large basis set MP2 force fields

29 July 1994

ELSEVIER

Chemical Physics Letters 225 (1994) 247-257

Ab initio calculation of vibrational circular dichroism spectra using large basis set MP2 force fields P.J. Stephens ‘, CF. Chabalowski b, F.J. Devlin a, K.J. Jakanen ’ ’ Department of Chemistry University of Southern California, Los Angeles, C4 90089-0482. USA b United States Army Research Laboratory, AMSRL-WT-PC, Aberdeen Proving Ground, MD 21005-5066, US4 ’ Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, IL 61801, USA Received 22 March 1994; in final form 23 May 1994

Ah!?trrct Ab initio calculations of the vibrational circular dichroism (VCD) spectra of 2,3-trans-d+xirane (1 ), 1,2-trans-da-cyclopropane (2), l-‘3C-1,2,3-anti-d3-cyclopropane (3), and propylene oxide (4) based on [ %4p2d/3s2p] MP2 harmonic force fields are reported. The results are in perfect qualitative and good quantitative agreement with existing experimental VCD spectra except in the C-H stretching region of 4 where Fermi resonance occurs. Calculations for l-3 using a larger [ 8s6p3d/6s3p] basis set exhibit insensitivity to a substantial increase in basis set size.

1. Im.roductlon

The prediction of the circular dichroism of the fundamental vibrational transitions of a chiral molecule at the harmonic level of approximation requires the implementation of [ 1,2 ]

~i=~~~~~lr~~ll>i~~ll~maelo>il 3

(la) (lb)

= ‘( 2A3COi)"2&M~~S~,i e

(lc)

Riis the rotational strength of the fundamental excitation of the ith normal mode of energy fzwi-The corresponding normal coordinates, Qi, are related to Cartesian nuclear displacement coordinates X, (&nucleus; a!=~, y, z) via xti = C sh,iQi *

i

(2)

The electric and magnetic dipole transition moments, whose scalar products determine rotational strenghts, are in turn a function, respectively, of the tensors, P$ and A4&. The tensors Pip,which determine electric dipole transition moments, are the wellknown atomic polar tensors ( APTs) [ 31. The tensors M&, which determine magnetic dipole transition moments, are the atomic axial tensors (AATs), more recently introduced into the literature [ l-3 1. Since the development of Eq. ( 1c ) for vibrational magnetic dipole transition moments, a substantial number of predictions of vibrational circular dichroism (VCD) spectra utilizing Eq. ( 1) and ab initio SCF or post-SCF calculations of APTs and AATs have been published. For some molecules, predictions have been compared to experimental data (see, for example, Refs. [ 4- 16 ] ) . Unfortunately, these predictions have used vibrational force fields of widely differing provenance, reliability and accuracy. The accuracy of predicted VCD intensities has therefore been limited

0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDIOOO9-2614(94)00605-P

248

R.J. Stephens et al, /Chemical Physics Letters 225 (1994) 247-257

not only by errors in the APTs and AATs but also by errors in vibrational frequencies and normal coordinates. Unambiguous attribution of the origins of differences between predicted and observed VCD spectra has thus been impossible. Accurate harmonic vibrational force fields, frequencies and normal coordinates require ab initio calculations at the post-SCF level. Of the various approaches to the inclusion of correlation in the calculation of harmonic force fields Moller-Plesset second-order perturbation theory (MP2) has been the most widely used. When large basis sets are used, MP2 force fields typically yield harmonic frequencies in error by only 1%-3% [ 171. Anharmonicity corrections to vibrational frequencies are then comparable to or larger than errors in harmonic frequencies. Calculations of vibrational spectra using such force fields should not be significantly limited in accuracy by residual errors in the harmonic force fields. Of course, large basis set MP2 calculations of harmonic force fields are computationally demanding. However, recent advances in the computation of MP2 second derivatives via analytical derivative methods [ 18,191, [ 201 * have greatly enlarged the range of molecules for which such calculations are feasible. As a result, large basis set MP2 calculations for chiral molecules whose VCD spectra have been measured experimentally are now practicable. We here report calculations of VCD spectra which take advantage of this development. The following molecules have been studied:

D

1

2

b

D (1’

3

D

4

‘3C)

MP2 force fields have been calculated using a [5s4p2d/3s2p] (TZ/2P [3]) basis set. APTs and AATs have also been calculated using this basis set. The results are compared to existing VCD spectra and to rotational strengths obtained thence. For l-3 the sensitivity of the results to further enlargement of the basis set to the [8s6p3d/6s3p] (VD/3P [3]) level has also been examined. The VD/3P calculations for 1 were reported in a prior communication [ 2 I]. ’ SeeGAUSSIAN 92 users manual.

2. Methods Ab initio calculations have been carried out using CRAY-YMP versions of CADPAC 4.0 and 5.0 and CRAY-YMP and CRAY-2 versions of GAUSSIAN 92. MP2 Hessians and APTs were calculated at the TZ/2P basis set level for oxirane (5) and cyclopropane (6) using ‘conventional’ methods and CADPAC 4.0 and for propylene oxide (4) using semi-direct methods and GAUSSIAN 92; the latter were also used for calculations on 5 and 6 at the VD/3P basis set level. SCF APTs were calculated for each molecule at all basis set levels using CADPAC 4.0 or 5.0. AATs were calculated about an origin 0 using the distributed origin (DO) gauge [ 2,3 ] when

where RI: is the equilibrium position of nucleus 1, and (Z&)” is the electronic AAT of nucleus A obtained with the coordinate origin at R,O.The ‘local’ AATs, (Z$#, were calculated at the SCF level using CADPAC 4.0 or 5.0 via the relation [ 31

where (I$> ’ is the electronic AAT obtained with the origin at 0 and E&( n;) is the electronic APT calculated using the momentum representation [ 3 1. SCF and ‘semi-MP2’ DO gauge AATs were then obtained by combining SCF local AATs and either SCF or MP2 APTs respectively using Eq. (3 ). Vibrational frequencies and normal coordinates were obtained from the appropriately mass-weighted Hessian. Rotational strengths were obtained from Eq. ( 1). Note that the use of the DO gauge in the calculation of AATs guarantees origin-independent rotational strengths (as long as the same APTs are used in Eq. (3) as in Eq. ( 1b ) ) . Dipole strengths, defined by Di=I(“lPe,l11>i12~

(5)

were simultaneously calculated via Eq. ( 1b ) . Calculated frequencies, dipole strengths and rotational strengths have been used to synthesize unpolarized absorption and VCD spectra using Lorentzian band shapes [ 7 1.

R. J. Stephenr et al. / Chemical Physics Letters 225 (1994) 24 7-25 7

3. Results and discussion Experimental solution unpolarized absorption and VCD spectra of l-4 [ 11,22-241 in C-H stretching, C-D stretching and mid-IR spectral regions are reproduced in Figs. l-4. Mid-IR spectra have not yet been reported for 3. Frequencies, dipole strengths and rotational strengths calculated using TZ/2P MP2 force fields and APTs and TZ/2P semi-MP2 AATs for l-4 are 3300 I 12

3200 ’

2400 -

2300

1300

1200

1100

1000

900

’

24

JG

m

0 .-I

6

*

2

60

E

1300

1200

1100

1000

900

wavenumbers Fig. 1. Predicted and experimental unpolarized absorption and VCD spectra of 1. Upper and middle spectra are predicted using TZ/ZP and VD/3P basis sets respectively; half widths and half height of the Lorentzian bands ( y) are 6.0 cm-’ (mid-IR region) and 10.0 cm-’ (C-H/C-D stretching regions). Lower spectra are the experimentalspectraof Freedman et al. [ 22 ] in Cs, (midIR region) and C,Cl. (C-H/C-D stretching regions); note that absorption at 1034 and 1117 cm-’ is attributed to impurities. VCD spectra are for (2S, 3S)-1. Upper and lower frequencyscales apply to calculated and experimental spectra respectively. Left and right vertical scales apply to C-H/C-D stretching and midIR spectra respectively.

249

given in Tables l-4. Unpolarized absorption and VCD spectra derived thence are plotted in Figs. l-4. Comparison of calculated and experimental unpolarized absorption and VCD spectra leads to unambiguous assignments of the fun&mental bands of 1, 2 and 4 in the mid-IR region and of l-3 in the C-H and C-D stretching regions. The frequencies, dipole strengths and rotational strengths reported [ 11,2224] for these bands are listed in Tables l-4. Assignment of the C-H stretching spectra of 4 is less straightforward. Only one of the fundamentals can be confidently assigned, its experimental frequency, dipole strength and rotational strength are given in Table 4. Analogous calculations have also been carried out for l-3 using the VD/3P basis set. The results are given in Tables l-3 and plotted in Figs. l-3. All VD/ 3P results are qualitatively identical to those obtained at the TZ/2P basis set level. They require no changes in the assignments of the spectra of l-3. Calculated TZ/2P vibrational frequencies are in excellent qualitative agreement with experiment for all assigned fundamentals of l-4. Calculated frequencies are greater than experimental frequencies, with the exception of two low frequency modes of 4. The ranges/averages of the (absolute) differences are: 1, 1S”~6.8%/4.1W; 2 and 3, 3.1%-7.2°/b/5.00~ 4, OS%-7.0%/3.6%. For the mid-IR modes alone the ranges/averages are: 1, lS%-3.4%/2.6Ob, 2 and 3, 3.1%-5.0%/3.9%; 4, 0.5%-5.0%/3.2%. For the C-H and C-D stretching modes alone, the rangesjaverages are: 1, 5.3°&6.80Yo/6.10/6, 2 and 3, 5.5O/b-7.2W/ 6.3%; 4, 7.0%/7.0%. Calculated VD/3P MP2 frequencies for l-3 are very close to the TZ/2P MP2 frequencies. The maximum/average differences are: 1, 1.2%/0.3%; 2 and 3, 2.2%/0.7W. The differences between calculated and experimental frequencies are very little altered. For l-3, a very large ( x 5OW) increase in the basis set size above the TZ/2P level thus yields insignificant improvement. The differences between experimental and calculated frequencies can be attributed to residual errors in the calculated harmonic frequencies and to the contributions of anharmonicity and solvent effects to the experimental frequencies. A comparison of calculated TZ/ZP MP2 and experimentally derived harmonic frequencies for several small molecules found differences averaging 2.2% [ 17 1. Gas phase and so-

250

R.J. Stephens et al. /Chemical 3300

3200

24002300

7’

2300

2200

Physics Letters 225 (1994) 247-257 1400

1300

1200

1100

I

I

I

I

I

I

1400

1300

1200

1100

1000

906

1000

900

wavenumbers Fig 2. Predicted and experimental unpolarixed absorption and VCD spectra of 2. Upper and middle spectra are predicted using TZ/2P and VD/3P basis sets respectively; y is 6.0 cm-’ and 10.0 cm-’ in the mid-IR and C-H/C-D stretching regions respectively. Lower spectra are the experimental spectra of Freedman et al. [23] in CS, (mid-IR region) and C,Cl, (C-H/C-D stretching regions). VCD spectra are for (lS, 2S)-2. Upper and lower frequency scales apply to calculated and experimental spectra respectively. Left and right vertical scales apply to C-H/C-D stretching and mid-IR spectra respectively.

lution frequencies reported for 1 [ 22 ] and 2 [ 23 ] differ on average by 0.4% and 0.6% respectively. We therefore conclude that anharmonicity is overall the dominant contributor to the differences in calculated and experimental frequencies for 1-4. This conclusion is consistent with known anharmonicity contributions to experimental frequencies for other small molecules [ 25 1. Dipole strengths calculated at the TZ/2P basis set level are in excellent qualitative agreement with ex-

perimental dipole strengths for all assigned fundamentals of l-4,demonstrating the substantial accuracy of both the harmonic normal coordinates and the ATPs. In l-3, dipole strengths are very little changed on expansion of the basis set to the VD/3P level, indicating substantial basis set saturation in the TZ/ZP APTs. Quantitative comparison of calculated and experimental dipole strenghts is complicated by the absence of well-defined error bars on experimental di-

R.J. Stephens et al. /Chemical Physics Letters 225 (1994) 247-257 3300 3200 2400 2300 -1

6

4

T If

% 4 + 2

t 0

lr

-9

--

-2

60

E

T

2

n

A

40

20

0

3100 3000 2300 2200

wavenumbers Fig. 3. Predicted and experimental unpolarized absorption and VCD spectra of 3. Upper and middle spectra are predicted using TZ/ZP and VD/3P basis sets respectively; y= 10.0 cm-‘. Lower spectra are the experimental spectra of Freedman et al. [ 241 in C&l,. VCD spectra are for (2S, 3S)3. Upper and lower frequency scales apply to calculated and experimental spectra respectively.

pole strengths, which were obtained by fitting of absorption spectra using analytical band shape functions. The dipole strengths of weak bands and of poorly resolved bands are particularly uncertain. Undoubtedly, a significant fraction of the difference between calculated and experimental dipole strengths is attributable to experimental error. On the other hand, errors in calculated dipole strengths arising from residual errors in normal coordinates and APTs and from the absence of anharmonicity and condensed phase effects can all be expected to contribute

251

significantly. Comparison of the dipole strengths of the u& and d,-isotopomers of 1, calculated at the VD/ 3P MP2 level, to accurate gas phase experimental values demonstrated [ 2 1 ] that ( 1) with the exception of C-H and C-D stretching modes, calculated dipole strengths agreed with experimental values within experimental error while, (2) in the case of C-H and C-D stretching modes, agreement was significantly worse. Errors arising from errors in the harmonic force field and APTs and from the absence of anharmonicity thus appear to be small except in hydrogenic stretching modes, where anharmonicity is more significant. Given the small differences in dipole strengths of l-3 at the TZ/2P and VD/3P levels, it can then be inferred that, for l-4 at both TZ/ 2P and VD/3P levels: ( 1) in the mid-IR region the dominant contributions to the differences in calculated and experimental dipole strengths are condensed phase effects and experimental errors and ( 2 ) anharmonicity is also likely to contribute significantly in the C-H and C-D stretching regions. Rotational strengths calculated at the TZ/2P basis set level are in excellent qualitative agreement with experimental rotational strengths for all assigned fundamentals of l-4. In particular, all signs are correctly predicted. The substantial accuracy of the MP2 force field and APTs is further confirmed. In addition, the substantial accuracy of the semi-MP2 AATs is demonstrated. In l-3, rotational strengths are very little changed on expansion of the basis set to the VD/ 3P level, with the exception of the C-H and C-D stretching modes. For the mid-IR modes, basis set saturation appears to be comparable to that of the dipole strengths; for the C-H and C-D stretching modes it is somewhat less. The difference must be attributed to a lesser degree of basis set saturation of the AATs than of the APTs. This conclusion is confirmed by calculations of dipole and rotational strengths using VD/3P force fields and TZ/ZP APTs and AATs (Tables l-3). As are dipole strengths, experimental rotational strengths are obtained by fitting of VCD spectra using analytical band shape functions. Rowever, the quantitative accuracy of experimental rotational strengths is substantially less well-defined than that of dipole strengths since experimental VCD spectra are less accurate than unpolarized absorption spectra [ 26,27 1. Resolution is lower. Signal-to-noise ratio are

252

R.J. Stephens et al. /Chemical Physics Letters 225 (1994) 247-257 3300 3200 3100

1600 1500 1400 1300 1200 1100 1000

900

000

700

30

6

20

“70 4 *

10

2i 0

-10 250

200

150

E 60 100

30

0

50

3100

3000

2900

1600

1500

1400

1300

1200

1100

1000

900

800

7

P

wavenumbers Fii 4. Predicted and experimental unpolarized absorption and VCD spectra of 4. Upper spectra are predicted using the TZ/ZP basis set; y is 6.0 and 10.0 cm-’ in the mid-IR and C-H stretching regions respectively. Lower spectra are the experimental spectra of Kawiecki et al. [ 111 in Cs, and Ccl,. VCD spectra are for (S)-4. Upper and lower frequency scales apply to calculated and experimental spectra respectively.

much worse. Absolute calibration is less straightforward and reliable. Artefactual signals are difficult to eliminate. It is consequently very difficult to quantify the contributions of experimental error to the differences between calculated and experimental rotational strengths. Theoretical errors are also hard to quantitate. Errors in the harmonic force field and APTs are undoubtedly insignificant relative to errors in the AATs. The predominant deficiency in the AATs is the incomplete inclusion of correlation as a result of the

calculation of the local AATs at only the SCF level. In the case of the TZ/2P calculations, as discussed above, some basis set error is also present. An estimate of the overall sensitivity of rotational strengths to the inclusion of correlation in the AATs can be obtained by eliminating correlation contributions to the APT& Rotational strengths obtained using SCF APTs and AATs are given in Tables l-4. The (absolute) changes in rotational strengths for those bands of l4 for which experimental rotational strengths are available average 2.9 x 1O-U esu2 cm2 at the TZ/2P

253

R.J. Stephens et al. / Chemical Physics Letters 225 (1994) 24 7-25 7 Table 1 Frequencies, dipole strengths and rotational strengths of 1’

3223 3219 2371 2358 1443 1381 1260 1147 1132 974 928 898 830 770 672

exp. b

exp. b talc.

CdC.

TZf2P

R

D

I

MP2 c

VDf3P

3218 3213 2367 2353 1440 1380 1266 1147 1128 973 923 900 820 775 675

3021 3014 2252 2232

1226 1109 1102 948 914

SCF ’

TZ/ZP

VD/3P’

TZf2P

VD/3P

21.2 5.9 6.9 24.6 8.0 0.4 19.1 1.5 6.6 54.7 12.3 123.6 32.1 110.4 1.1

31.0 (26.9) 7.4 (6.0) 8.6 (7.0) 27.7 (24.4) 8.4 (8.0) 0.6 (0.4) 19.7 (18.7) 1.9 (2.0) 6.3 (6.7) 57.1 (55.7) 11.9 (11.7) 122.8 (121.0) 38.7 (33.4) 113.9 (112.5) 0.8 (1.1)

48.4 6.2 7.7 43.7 12.1 1.0 25.6 0.6 9.9 108.1 20.2 195.9 51.8 142.8 1.5

50.9 7.4 9.0 45.9 12.6 1.1 26.6 0.1 11.1 108.2 20.1 192.0 59.3 148.2 1.5

53 5.7 27 (12) (2.3) 29.6 8.6 54 6.3

exp. b

talc. MP2 =

SCF f

TZJZP VD/3P’

TZ/2P

15.7 22.8 (15.7) -18.1 -24.4 (-18.2) 9.1 12.7 (9.2) -7.5 -11.2 (-7.4) -7.7 -8.3 (-7.4) -1.2 -1.3 (-1.2) 10.2 10.9 (10.2) -5.0 -6.3 (-5.9) 8.8 10.1 (9.0) -26.7 -28.2 (-26.5) -2.6 -3.6 (-3.0) 8.3 8.0 (8.5) 0.4 1.7 (0.7) 10.2 11.8 (10.5) 0.3 0.0 (0.1)

21.0 29.1 11.4 -19.5 -25.0 -8.9 10.4 13.7 12.1 -9.9 -14.1 - 10.4 -9.0 -9.9 (-15) -2.0 -1.9 (-2.5) 10.9 11.9 24.1 3.1 -4.9 7.8 ;:: 11.1 -35.1 -36.9 -29.0 0.1 -1.7 -6.2 7.6 7.1 (-+5) -0.1 1.5 (+) 12.2 14.4 0.8 0.6

VDJ3P

a Frequencies, F, in cm - ‘; dipole strengths D in 10m40esu’ cm*; rotational strengths R in lo-” em’ cm2. Rotational strengths are for the (2S, 3s) enantiomer. b From Freedman et al. [22]; in C&l., solution for C-H and C-D stretching modes and in CSs solution otherwise; values in parentheses estimated from gas phase data. Rotational strengths were not normalized to 100% enantiomeric excess (ee); ee for (2S, 3S)-1 and (2R, 3R)-1 were estimated to be 94%. =Calculated using MP2 APTs. d Calculated using SCF APTs. c Calculated using MP2 APTs and semi-MP2 AATs. f Calculated using SCF APTs and AATs. *Numbers in parentheses are obtained using TZ/ZP APTs and AATs.

basis set level. The differences between rotational strengths calculated using TZ/ZP MP2 APTs and semi-MP2 AATs and experimental rotational strengths average 6.4~ 1O-44esu2 cm2. It is therefore reasonable to conclude that a significant fraction of residual differences between calculated and experimental rotational strengths can be attributed to the incomplete inclusion of correlation in the calculation of AATs. Our calculations do not successfully reproduce the C-H stretching VCD of 4. This could be attributed to residual errors in our harmonic calculations or to anharmonic&y (Fermi resonance). In view of the obvious complexity of the C-H stretching absorption spectrum, the latter is almost certainly the principal contributor.

A number of calculations of rotational strengths for have previously been reported [4,69,11,12,16,24,28-341. These calculations have used a variety of harmonic force fields: ab initio SCF [ 16,29-33 1, empirically scaled ab initio SCF (‘scaled quantum mechanical, SQM’) [4,6-8,11,12,28,34] and empirical general valence [9,28,33]. These diverse force fields vary substantially in reliability and their deficiencies are reflected in rotational strengths calculated thence. The harmonic force fields utilized in the present calculations are substantially more reliable than any used previously and reduce to insignificance the error in rotational strengths originating from errors in harmonic force fields. Previous calculations have also adopted a considerable diversity of approaches to the calculation of l-4

254

R. J. Stephens et al. / Chemical Physics Letters 225 (I 994) 24 7-25 7

Table 2 Frequencies, dipole strengths and rotational strengths of 2 ’ D

B

talc. TZf2P

3298 3253 3250 3200 2394 2383 1517 1396 1344 1221 1169 1136 1093 1078 977 932 882 806 746 640 628

exe. b VD/3P

3290 3245 3242 3192 2388 2371 1510 1392 1342 1222 1160 1130 1087 1054 956 916 877 802 740 638

R

talc.

exp. b

MP2

3076 3041 3035 3012 2270 2257 1338 1290 1180 1134 1087 1052 1037 942

SCF

talc.

exp. b

MP2

TZ/ZP

VD/3P

TZ/ZP

VD/3P

5.8 10.1 1.7 10.1 1.4 6.7 1.7 2.0 4.7 0.1 5.4 10.5 12.8 25.5 2.0 12.1 85.7 18.3 8.6 4.2 1.3

9.2 (6.0) 13.0 (9.8) 2.0 (1.6) 12.5 (10.2) 1.8 (1.4) 9.4 (6.7) 1.0 (1.9) 1.2 (2.0) 3.2 (5.1) 0.1 (0.1) 5.3 (6.0) 9.6 (9.7) 13.6 (14.7) 27.0 (27.9) 2.9 (3.0) 13.3 (13.4) 80.8 (82.6) 75.6 (77.1) 7.6 (8.4) 4.1 (4.4) 1.2 (1.4)

20.9 30.1 4.5 26.6 4.2 22.0 0.8 1.2 3.0 0.1 4.0 6.7 9.2 15.4 0.0 29.4 107.0 80.1 8.7 3.3 0.9

25.7 32.9 4.7 29.2 4.7 25.2 0.5 0.8 2.3 0.1 4.2 6.9 10.7 18.4 0.3 28.6 101.7 77.2 8.3 3.4 0.8

19 25 21 15 8.4 6.8 13 21 23 38 15

SCF

TZ/ZP

VD/3P

TZ/SP

VD/3P

3.2 - 16.6 12.0 1.6 -4.4 4.1 0.9 -6.4 8.3 2.5 -25.0 -4.8 25.8 -4.1 4.0 3.4 6.3 - 12.2 1.8 0.0 0.2

4.7 (3.7) -21.8 (-17.2) 14.8 (11.7) 2.5 (2.0) -6.1 (-4.4) 5.8 (4.2) 0.6 (0.8) -4.9 (-6.3) 6.8 (8.4) 1.9 (1.8) -25.4 (-26.3) -6.1 (-5.7) 28.6 (28.3) -3.5 (-3.6) 3.8 (4.3) 2.5 (2.7) 5.2 (6.0) -11.1 (-12.1) 2.1 (1.7) -0.8 (-0.1) 0.6 (0.2)

5.6 -29.6 21.3 2.8 -8.7 8.3 0.6 -4.7 6.3 2.0 -20.2 -3.7 21.0 -3.6 0.5 5.0 6.6 -11.8 2.0 -0.1 0.1

7.6 - 35.8 24.3 4.1 - 10.8 10.3 0.4 -3.9 5.5 1.6 -21.8 -5.1 24.6 -2.8 1.3 3.5 5.5 -10.8 2.3 -0.7 0.5

4.8 -9.9 4.4 1.4 -3.7 3.3 -7.7 10.2 3.0 -42.6 -13.3 28.2 -15.9 5.5

’ Definitions and units as in Table 1. Rotational strengths are for the ( lS, 2S)-enantiomer. b From Freedman et al. [23]; in C,Cq solution for C-H and C-D stretching modes and in CSz solution otherwise. Rotational strengths were not normalized to 100% ee; ee for ( lR, 2R)-2 and ( lS, 2S)-2 were > 98%.

APTs and AATs. APTs have been calculated ab initio at the SCF level using both derivative methods (numerical [4,12] and analytical [ 6,7,9,11,28,29-331) and sum-over-states methods [ 8,16 1. APTs have also been calculated less accurately via fmed partial charge (FPC) [ 11,28 1, and ‘floating basis set vibronic coupling’ approaches [ 34 ]. AATs have been calculated ab initio at the SCF level using both derivative methods (numerical [4,12] and analytical [ 6,7,9,11,28] ) and sum-over-states methods [ 8,161, and using both common origin [ 4,9,11,12,16] and distributed origin gauges [ 6-9,11,28 1. In addition, AATs have been calculated less accurately via fued partial charge (FPC) [11,28],atomicpolartensor (APT) [11,28], ‘floating basis set vibronic coupling’ [ 341, localized molecular orbital (LMO) [ 32,33 ] and sub-SCF sumover-states approaches [ 29-3 11. The MP2 APTs and

semi-MP2 distributed origin gauge AATs utilized in the present calculations are substantially more accurate than any used previously and considerably reduce the errors in rotational strengths originating in errors in APTs and AATs.

4. Conclusion With the exception of the C-H stretching region of 4 which is strongly perturbed by Fermi resonance, VCD spectra of l-4 calculated using large basis set MP2 force fields, together with MP2 APTs and semiMP2 AATs, are in excellent agreement with experiment. Residual errors in frequencies are attributable predominantly to anharmonicity. Residual errors in VCD intensities (rotational strengths) are attribut-

R.J. Stephens et al. / Chemical Physics Letters 225 (1994) 247-25 7

255

Table 3 Frequencies, dipole strengths and rotational strengths of 3 ’

talc. TZ/ZP

3255 3250 3240 2396 2383 2312 1416 1349 1339 1201 1121 1112 1077 959 936 895 841 774 694 610 595

R

D, talc.

B

exp. b VD/3P

3248 3242 3231 2390 2377 2366 1409 1347 1337 1201 1112 1099 1069 941 917 881 838 769 688 608 593

MP2 TZ/ZP

3054 3041 3025 2271 2258 2245 1348 1302 1290 1163 1074 1037

12.9 1.6 6.1 0.5 6.9 5.0 0.1 3.8 4.7 3.4 21.1 4.7 14.5 2.5 0.8 14.9 92.5 74.0 3.1 0.2 5.6

SCF VD/3P

17.8 (12.7) 1.9 (1.5) 7.7 (6.2) 0.7 (0.5) 9.8 (6.9) 6.5 (4.9) 0.1 (0.1) 2.5 (4.2) 3.0 (5.0) 2.8 (3.0) 23.6 (24.6) 1.8 (2.2) 14.6 (15.3) 2.1 (2.2) 0.8 (0.8) 16.2 (16.1) 90.7 (92.7) 71.2 (72.8) 2.1 (3.0) 0.2 (0.3) 5.6 (5.8)

TZ/ZP

40.3 4.2 16.6 1.6 22.4 15.6 0.1 2.3 2.9 2.6 13.9 3.6 9.3 6.4 6.8 29.6 103.0 73.6 2.5 0.1 4.8

exp. b

talc. VD/3P

46.4 4.4 18.2 1.8 26.2 16.9 0.1 1.7 2.1 2.3 17.5 1.6 10.7 5.3 6.0 29.8 100.9 70.7 2.2 0.1 4.9

MP2

SCF

TZ/2P

VD/3P

TZ/ZP

VD/3P

6.9 - 10.6 3.7 2.2 -4.1 1.9 1.0 -3.0 2.2 -2.9 -0.3 1.3 1.5 2.3 -1.5 1.4 -2.2 0.1 0.1 0.0 0.0

7.8 (6.1) - 12.6 (-9.9) 4.8 (3.8) 2.8 (2.0) -5.3 (-3.8) 2.4 (1.7) 1.0 (1.1) -2.5 (-3.1) 1.8 (2.3) -2.6 (-2.6) 0.0 (0.0) 0.6 (0.6) 2.0 (1.9) 2.0 (2.0) -1.4 (-1.5) 1.5 (1.6) -2.3 (-2.4) 0.0 (0.1) 0.1 (0.1) 0.0 (0.0) 0.1 (0.0)

12.3 -18.9 6.6 4.3 -8.1 3.8 1.0 -2.4 1.6 -2.8 -0.2 0.8 1.7 3.3 -2.3 1.4 -2.2 0.1 0.1 0.0 0.0

12.8 -20.7 7.9 5.1 -9.4 4.3 1.0 -2.2 1.4 -2.1 0.1 0.3 2.1 2.8 -2.0 1.5 -2.4 0.0 0.1 0.0 0.1

1.54 - 3.23 1.84 1.32 -2.14 0.65

l Definitions and units as in Table 1. Rotational strengths are for the (2S, 3S)enantiomer. b From Freedman et al. [ 241; in C&l, solution for C-H and C-D stretcbin8 modes and in CS2solution otherwise.Rotationalstrengths werenot normalizedto 100%ee.

able predominantly to the incomplete inclusion of correlation in the AATs, to anharmonicity and to condensed phase effects. (In the case of calculations at the TZ/2P level, incomplete basis set saturation may also contribute significantly in the C-H and CD stretching region.) Substantially more accurate calculations require: ( 1) more complete inclusion of correlation in the calculation of AATs, (2) the inclusion of anharmonicity, (3) the inclusion of solvent effects. The formalism for the calculation of AATs at the MCSCF level using either conventional or fielddependent (London/gauge invariant) atomic orbitals has recently been developed and implemented [ 35 1. MCSCF calculations of AATs for l-4, l-4 are substantially more accurate than previous work. For

R.J. Stephens et al. / Chemical Physics L.&ten 225 (I 994) 24 7-25 7

256

Table 4 Frequencies, dipole strengthsand rotational strengths of 4 D

I talc. TZ/ZP

3259 3193 3175 3174 3156 3087 1550 1529 1514 1458 1420 1295 1199 1177 1165 1130 1054 977 916 852 771 407 371 219

exp. b

3041

1500 1456 1444 1406 1369 1262 c 1165 1143 1130 1103 1022 951 893 829 c 748 = 414 373 200*

R

talc.

exp. b

MP2 TZ/2P

SCF TZ/ZP

17.3 25.2 15.9 4.8 21.5 14.6 10.0 19.9 14.1 51.4 11.8 11.4 2.3 13.0 2.5 21.6 31.5 41.9 5.8 199.2 28.5 42.7 46.4 8.1

29.8 55.1 30.7 12.3 34.1 26.5 12.0 15.4 10.2 46.1 14.3 14.1 4.0 20.5 3.6 34.7 36.6 66.1 15.0 312.6 46.8 52.3 59.9 10.6

29.9

15.1 16.0 14.0 52.5 14.7 25.7 = 4.2 13.1 13.9 26.5 56.1 65.9 19.4 287.6 c 40.9 c

talc.

Exp. b

MP2 TZ/ZP

SCF TZ/ZP

1.9 -7.1 16.9 - 10.0 -1.0 -0.4 -3.5 1.8 -1.2 -13.4 -3.5 7.6 -0.7 8.5 -5.9 5.4 -7.1 28.1 -17.1 -3.1 -11.7 3.8 11.9 -3.5

2.2 -8.0 29.0 -19.3 -1.4 -0.6 -4.5 1.4 -1.1 -13.2 -4.4 7.5 - 1.8 9.6 -0.8 9.3 -8.3 35.5 -24.7 -2.2 -15.2 4.5 15.4 -3.7

3.5

-4.0

-8.4 -3.3 15.6= -0.4 21.4 -15.9 8.1 -6.7 71.9 -42.8 -21.6 c

’ Definitions and units as in Table 1. Rotational strengths are for the (S) enantiomer. b From Rawiecki et al. I1 11: in CCL solution, except where indicated. Rotational strengths were not normalized to 10096ee. cCS2solutiondata. - _* Gas-phase data.

the first time, the harmonic force fields used yield frequencies whose deviations from experimental frequencies are due principally to anharmonicity. The MP2 APTs are substantially more accurate than the APTs used in all earlier work. The combined use of MP2 APTs and large basis set SCF local AATs yield distributed origin gauge AATs substantially more accurate than the AATs used in all earlier work. Comparison of the present calculations and others (past or future) which use specific approximations for force fields, APTs and/or AATs will greatly assist the objective analysis of the relative accuracies of these approximations. The evaluation of the accuracy of our predicted VCD spectra for 1-4 is substantially limited by the

uncertainty of the experimental VCD intensities. This work makes clear the importance of further developments in VCD instrumentation: reliable rotational strengths of well-defined accuracy require substantial improvements in resolution, sensitivity, absolute ao curacy and artifact control. It is to be hoped that the greatly improved capabilities of theory illustrated here will encourage such improvements.

Acknowledgement

We are grateful to Professor L.A. Nafie and Dr. T.B. Freedman for a copy of Ref. [ 23 ] prior to publication. PJS is grateful to NSF, NIH, NATO and the San

R.J. Stephens et al. /Chemical Physics Letters 225 (1994) 247-257

Diego Supercomputer Center for support of VCD research at USC over the years. CFC is grateful to the US Army Edgewood Research, Development and Engineering Center for partial support.

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