Theoretical calculation of the height of the barrier for OH rotation in phenol

11 February 1994

ELSEVIER

CHEMICAL PHYSICS LETTERS Chemical Physics Letters 218 (1994) 261-269

Theoretical calculation of the height of the barrier for OH rotation in phenol Kyungsun Kim, K.D. Jordan Department of Chemistry and Materials Research Center, University of Pittsburgh, Pittsburgh, PA 15260, USA Received 26 October 1993; in final form 29 November 1993

AbStTWt Many-body perturbation and quadratic configuration interaction calculations with several basis sets are used to estimate the height of the barrier for OH rotation in phenol. Our best estimate of the barrier height is 1076 cm-‘, about 130 cm-’ smaller than the most recent experimental estimates. Density functional calculations are found to give much too large a value of the barrier height.

1. Introduction

Recent studies using high-resolution supersonic jet spectroscopy have provided a wealth of spectroscopic data on l- and 2-hydroxynaphthalene and hydroquinone [ 1,2]. However, accurate values of the heights of the OH rotational barriers in these compounds are unknown. High quality electronic structure calculations could provide this information, but it would be highly desirable to have a calibration of the theoretical methods employed. Phenol would appear to be the ideal system for use in such a calibration since estimates of its barrier height have been deduced from spectroscopic studies, with values of the barrier height ranging from 1150 to 1213 cm-’ [ 3-5 ]. The most recent estimates of the barrier height are 1207 cm-’ [3] and 1213 cm-’ [5]. In this work we use the Hartree-Fock (HF ) , manybody perturbation theory (MBPT) [ 6 1, quadratic CI with single, double, and perturbative tripole excitations (QCISD (T) ) [ 7 1, and density functional [ 8 ] methods to calculate the height of the OH rotational barrier in phenol. Our best theoretical estimate of the

barrier is about 130 cm- ’ lower than the most recent values deduced from spectroscopic studies.

2. Methodology The HF, MBPT, and QCISD (T) calculations were carried out with the GAUSSIAN 92 program [ 9 1, and the density functional theoretical (DFT) calculations were carried out with the deMon program [ 10 1. The geometries of the minimum energy planar structure and the perpendicular transition state structure #I were optimized by means of second-order MBPT (MP2) (MP2) as well as by means of DFT, in both the local spin density (LSD) and non-local spin density (NLSD) approximations. The MP2 op“’ The harmonic frequencies were calculated in the HF/6-3 1G* approximation for both the planar and perpendicular structures. In the former case, all frequencies were real, and in the latter, there was one imaginary frequency, indicating that the transition state indeed has a perpendicular structure.

0009-2614/94/%07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI0009-2614(93)El482-V

262

K. Kim, K.D. Jordan /Chemical Physics Letters 218 (1994) 261-269

timizations u were carried out using both the 6-3 1G* and 6-3 1G” basis sets [ 12 1, and the DFT optimizations were carried out using the [3s2pld/2slp] DZVPP basis set of Godbout et al. [ 13 1. In both the minimum energy and transition state structures one plane of symmetry was retained; no other constraints were imposed. The LSD calculations were carried out using the Dirac [ 141 exchange and the Vosko, Wilk, and Nusair (VNW) correlation functional [ 15 1, whereas the NLSD calculations were carried out using the nonlocal exchange and correlation functionals of Becke [ 161 and Perdew [ 171, respectively, and referred to collectively as the BP potential. The auxiliary basis sets of Godbout et al. [ 131 were used to fit the electron densities and exchange-correlation potential and energy. (3slpld) auxiliary basis sets were used for the H atoms and either (7s3p3d) or (8s4p4d) auxiliary basis sets were used for the C and 0 atoms. The fine grid option of the deMon program was used in order to minimize the errors due to grid choices. The MP2/6-3 lG* optimized geometries were used for MP2 calculations with several larger basis sets, including the 6-3 1 + + G (2df, p) basis set of Pople and co-workers [ 10,181, the [3s2pld/2slp] cc-pVDZ, [4s3pld/3slp] cc-pVTZ1, and [4s3p2d/3slp] ccpVTZ2 correlation-consistent basis sets of Dunning [ 191 #3, and the [ 4s3p2d/3slp] aug-cc-pVDZ* basis set, formed from the cc-pVDZ basis set by adding diffuse s, p, and d functions to the C and 0 atoms and diffuse s functions to the H atoms #4. The exponents of these diffuse functions are from Kendall and Dunning [ 201. Fourth-order MBPT (MP4SDTQ) calculations were carried out with the 6-31G*, 63 1 + G**, and modified 6-3 1 + G (2df, p) basis sets, and QCISD (T) calculations were carried out with the 6-3 lG* basis set, again using the MP2/6-3 1G* optimized geometries. x2 The MP2/6-31G*

optimized geometry for the planar minimum energy structure of phenol is taken from ref. [ 111. s3 The full cc-pVTZ basis set contains two polarization functions on each atom. The single hydrogen p polarization functions in the cc-pVTZ1 and copVTZ2 basis sets and the single carbon d polarization function in the cc-pVTZ1 basis set are taken from the cc-pVDZ basis set. M The aug-cc-pVDZ basis set of Kendall and Dunning also includes diffuse p functions on the H atoms. These are omitted in the aug-cc-pVDZ* basis set and in the aug-cc-pVTZl* basis set, used for HF and DFT calculations.

The MP2/6-3 1G* optimized geometries were also used for LSD and NLSD calculations using the ccpVTZ1, aug-cc-pVTZl*, DZVPP, and TZVP basis sets. The latter two basis sets are from Godbout et al., and provide, respectively, double-zeta-plus polarization and triple-zeta-plus polarization function descriptions of the valence electrons [ 131. The DFT calculations were carried out using six-component d functions, while, with one exception, the HartreeFock (HF), MBPT, and QCISD(T) calculations were carried out using five-component d functions. In the MBPT and QCISD(T) calculations only the valence electrons were correlated, whereas in the DFT calculations, correlation effects are included for all electrons. Single-point NLSD calculations were carried out perturbatively using the LSD densities, whereas in the geometry optimizations at the NLSD level of theory, the NLSD energies were calculated self-consistently, i.e. by solution of the appropriate Kohn-Sham equations.

3. Results The geometrical parameters for both the minimum energy and transition state structures obtained from the MP2/6-31G*, MP2/6-31G*+, LSD/DZVPP, and NLSD/DZVP> optimizations are summarized in Table 1, along with the experimental parameters reported by Larsen [ 2 1] for the planar equilibrium structure. The atom numbering scheme is shown in Fig. 1. The results for the minimum energy structure are considered first. 3.1. Geometry and dipole moment of the minimum energy structure The geometrical parameters obtained from the two MP2 optimizations are in fairly good agreement with the experimentally determined parameters, with the greatest discrepancy between theory and experiment being for the OH bond length, which is 0.016 and 0.007 8, longer than the experimental value at the MP2/6-3 1G* and MP2/6-3 lG** levels of theory, respectively. As expected, the errors in the calculated CH bond lengths are reduced upon inclusion of the p polarization functions on the H atoms. The average

263

K. Kim, K.D. Jordan /Chemical Physics Letters 218 (1994) 261-269 Table 1 Equilibrium Property

geometries

‘, dipole moments

Expt. b

MP2/0” 6-31Goc

1.3912 1.3944 1.3954 1.3954 1.3922 1.3912 1.3745 1.0835 1.0856 1.0802 1.0836 1.0813 0.9574

LC6C,0,C2

LHOC,Cr

119.22 120.85 119.43 120.48 119.24 120.79 119.48 120.0 1 117.01 121.55 119.78 120.25 108.77 0.00 0.00 180.00 180.00 180.00 180.00 0.00

(D), and rotational

1.3969 1.3965 1.3947 1.3978 1.3930 1.3975 1.3749 1.0873 1.0894 1.0865 1.0873 1.0863 0.9738 119.57 120.28 119.65 120.45 119.44 120.61 119.33 120.16 116.87 121.64 120.06 120.25 108.39 0.00 0.00 180.00 180.00 180.00 180.00 0.00

constants

(GHz)

MP2/90” 6-31G” 1.3966 1.3959 1.3943 1.3973 1.3926 1.3972 1.3735 1.0824 1.0844 1.0816 1.0824 1.0814 0.9651 119.59 120.25 119.67 120.44 119.44 120.60 119.34 120.04 116.91 121.66 120.06 120.25 108.44 0.00 0.00 180.00 180.00 180.00 180.00 0.00

6-31G’ 1.3959 1.3959 1.3967 1.3967 1.3959 1.3959 1.3943 1.0873 1.0868 1.0869 1.0873 1.0868 0.9724 119.59 120.51 119.59 120.25 119.80 120.25 119.65 119.02 119.71 121.38 120.09 120.10 108.33 0.55 0.14 179.36 179.82 179.56 176.84 91.58

of the ground LSD/O” DZVPP

state of phenol and its transition NLSD/O” DZVPP

LSD/90” DZVPP

6-31G1.3956 1.3953 1.3963 1.3963 1.3953 1.3956 1.3933 1.0824 1.0819 1.0820 1.0824 1.0819 0.9643 119.60 120.50 119.60 120.25 119.80 120.25 119.67 118.98 119.71 121.42 120.08 120.10 108.07 0.52 0.14 172.40 179.82 179.61 176.90 91.55

1.3976 1.3948 1.3943 1.3969 1.3921 1.3973 1.3590 1.0979 1.1011 1.0969 1.0980 1.0976 0.9775 119.58 120.02 119.86 120.49 119.21 120.84 119.41 119.72 117.63 121.76 119.91 120.35 108.71 0.00 0.00 180.00 180.00 180.00 180.00 0.00

1.4072 1.4072 1.4054 1.4086 1.4040 1.4087 1.3814 1.0957 1.0975 1.0939 1.0951 1.0954 0.9753 119.60 120.11 119.74 120.60 119.16 120.79 119.30 119.96 117.28 121.37 120.09 120.36 108.36 0.00 0.00 180.00 180.00 180.00 180.00 0.00

1.3955 1.3950 1.3954 1.3954 1.3950 1.3955 1.3776 1.0982 1.0985 1.0976 1.0982 1.0985 0.9755 119.80 120.13 119.80 120.33 119.61 120.33 119.64 118.67 119.90 121.53 120.02 120.20 109.53 0.62 0.16 179.26 179.69 179.52 176.95 91.52

state

NLSD/ 90” DZVPP 1.4053 1.4076 1.4065 1.4065 1.4076 1.4053 1.4010 1.0957 1.0956 1.0946 1.0957 1.0956 0.9749 119.75 120.20 119.75 120.42 119.45 120.42 119.53 119.07 119.86 121.18 120.05 120.27 108.57 0.61 0.17 179.44 179.76 179.63 176.71 91.64

fi

1.224

1.426

1.378

1.700

1.637

1.400

1.366

1.590

1.574

A B C

5.6505 2.6192 1.7899

5.6444 2.6118 1.7856

5.6534 2.6147 1.7878

5.6369 2.5849 1.7820

5.6449 2.5885 1.7844

5.6486 2.6231 1.7913

5.5694 2.5721 1.7595

5.6481 2.5950 1.7879

5.5744 2.5433 1.7560

’ Bond lengths are in A and angles in deg. b The experimental geometrical parameters ’ The MP2/6-3 lG* geometrical parameters

are from ref. [ 2 11. for the minimum energy structure

error in the calculated rotational constants is reduced from 5.9 to 3.2 MHz in going from the MP2/6-31G* to the MP2/6-3 1GW optimized geometries. In the determination of the geometrical parameters from the microwave data, it was assumed that the following pairs of bonds had equal lengths: C4CS

of phenol are from ref.

[ 111.

and C&, CIC2 and C1C6, and H4H5 and HSH4 [ 18 1. In fact the MP2 calculations predict the C3C4 distance to be about 0.003 A shorter than the C4C5 distance, and the CLC2 and C1C6 bonds to be the second and third longest CC bonds, whereas in Larsen’s analysis they were the shortest. This leads us to ques-

264

K. Kim, K.D. Jordan /Chemical Physics Letters 218 (1994) 261-269

Fig. 1. Atom number scheme for the C and 0 atoms of phenol. The hydrogen atom designated Hi is bonded to carbon atom Ci.

tion whether the constraints imposed in the determination of the geometry from the spectroscopic data may have led to CICz and C1C6bond lengths that are too small. In order to test this possibility, the geometry of phenol was optimized at the MP2/6-3 1G* level of theory subject to the same constraints as were imposed in the determination of the experimental structure. The trends in the resulting CC bond lengths are nearly the same as those obtained from the unconstrained calculations, indicating that the imposition of these constraints is not responsible for the different trends in the CC bond lengths obtained from theory and experiment. With the exception of the CH, CO, and OH bond lengths, the geometrical parameters determined from the LSD/DZVPP calculations are quite close to those from the MP2/6-31G* calculations. The CH bond lengths and the OH bond length are 0.012-0.017 8, longer and the CO bond length is 0.014 8, shorter in the LSD/DZVPP than in the MP2/6-3 1G” calculations. In these cases, the MP2 values of the geometrical parameters are closer to experiment than are the LSD values. Although the inclusion of non-local corrections by means of the BP potential leads to slightly shorter CH and OH bonds, thereby improving agreement with experiment, it also leads to CC and CO bond lengths appreciably longer than the MP2 or experimental values. The inadequacy of the NLSD (BP) procedure for calculating the geometry of phenol is also apparent from the fact that the errors in the rotational constants associated with the NLSD/ DZVPP geometry are over an order of magnitude larger than the rotational constants associated with the MP2/6-3 lGf+ or LSD/DZVPP geometries. Both the LSD and NLSD calculations give Cl& and CICs bond lengths longer than the average CC bond length, in agreement with the MP2 calculations. This lends further support to the interpretation that the analysis

of the experimental data gave CICz and CC6 bond lengths which are too short. Table 1 also reports the calculated and experimental dipole moments. With the most flexible basis sets considered, the dipole moment is found to be around 1.40 D in the HF approximation and to range from 1.31 and 1.36 D in the MP2 approximation. For comparison, the experimental value of the dipole moment is 1.22 D [ 3 1. A dipole moment of 1.40 D is obtained in the LSD/DZVPP approximation, and a slightly smaller value ( 1.36 D) is calculated in the NLSD/DZVPP approximation. 3.2. Transition state structure and barrier height We turn now to the barrier height, considering first the results of the HF and MP2 calculations using the MP2/6-3 1G* optimized geometries. The total energies and barrier heights obtained at the HF, MP2, LSD, and NLSD levels of theory are summarized in Table 2. The HF/6-3 1G* calculations give a barrier height of 93 1 cm-‘, which is appreciably lower than values of the barrier height deduced from experiments. The two most recent experimental values of the barrier height are nearly the same, being 1207 and 12 13 cm- ’ [ 3,5 1, and, in the remainder of this work, the former value is used. The calculated barrier height increases to 1280 cm-’ in the MP2 approximation. MP2 calculations with more flexible basis sets reveal that the barrier height undergoes a small reduction upon inclusion of p polarization functions on the hydrogen atoms and a much larger reduction upon inclusion of diffuse s and p functions on the C and 0 atoms. The MP2/6-31 +G*+ barrier height is 1041 cm-‘, 239 cm-’ smaller than the MP2/6-3 lG* value. The MP2 barrier height changes relatively little upon further expansion of the s and p basis sets of the C, 0 and H atoms. For example, MP2 calculations with the 6-3 11 + G” basis sets give a barrier height nearly identical to the MP2/6-31 +G” value. The MP2 barrier height is somewhat higher ( 1098 cm-’ ) with the aug-cc-pVDZ* basis set than with the 6-31 lG** value, but with more flexible augmented correlationconsistent basis sets (with only a single polarization function on each atom), MP2 barrier heights close to that obtained with the 6-3 1+ G** basis set are expected. In fact, in the HF approximation, the barrier height obtained with the aug-cc-pVTZl* basis set is

K. Kim, K.D. Jordan /Chemical PhysicsLetters218 (1994) 261-269 Table 2 Total energies (hartree), rotational barriers, NLSD methods and employing the MP2/6-3 Method

AE (cm-‘), and dipole moments lG* optimized geometries

(D) of phenol calculated

AE’

Total energy

265

using the HF, MP2, LSD, and

p (minimum)

minimum

transition

HF/6-3 lG* HF/6-3lG” HF/6-3 1 + GHF/6-31+G(2d,p) HF/6-31 +G(2d, 2p) HF/6-31+G(Zdf, p) HF/6-31+ +G(2df, p) HF/6-31 IGHF/6-311 +G” HF/6-31 lG(2d, p) HF/cc-pVDZ HF/aug-cc-pVDZ* HF/cc-pVTZ1 HF/aug-cc-pVTZ 1l HF/cc-pVTZ2 b

-305.55443 -305.57046 -305.58109 -305.58525 - 305.58624 - 305.59494 -305.59500 -305.63166 -305.63693 -305.64114 -305.58625 -305.59929 - 305.63494 - 305.64070 -305.65125

-305.55019 -305.56640 -305.57743 -305.58161 -305.58258 -305.59090 -305.59104 -305.62773 -305.63325 -305.63718 -305.58197 - 305.59548 -305.63104 - 305.63704 - 305.64734

931 892 803 798 801 885 869 863 808 869 939 838 855 804 858

1.509 1.494 I .527 1.428 1.417 1.427 1.427 1.469 1.511 1.396 1.412 1.396 1.461

MP2/6-31G’ MP2/6-31G” MP2/6-3 I + G” MP2/6-31 +G(2d, p) MP2/6-31 +G(2d, 2p) MP2/6-31+G(Zdf,p) MP2/6-31+ +G(Zdf, p) MP2/6-311G” MP2/6-311 +G” MP2/6-31 lG(2d, p) MPZ/cc-pVDZ MP2/aug-cc-pVDZ* MPZ/cc-pVTZ1 MPZ/cc-pVTZ2 b

- 306.47954 - 306.53050 -306.55131 -306.61858 - 306.62475 -306.71730 -306.71759 -306.65403 -306.66558 -306.71640 -306.55368 -306.60481 - 306.65704 -306.73821

-306.47371 - 306.52488 -306.54656 -306.61373 -306.61989 -306.71198 -306.71238 - 306.64867 - 306.66085 -306.71080 -306.54775 -306.59981 -306.65165 -306.73277

1280 1234 1041 1062 1066 1168 1143 1177 1038 1229 1302 1098 1184 1195

1.427

LSD/DZVPP LSD/TZVP LSD/cc-pVTZ1 LSD/aug-cc-pVTZ

- 304.87254 -304.91498 - 304.90549 -304.91252

-304.86551 - 304.90783 - 304.89793 -304.90523

1544 1569 1661 1599

- 307.53302 -307.57317 - 307.56498 -307.57075

- 307.52691 - 307.56684 -307.55839 -307.56441

1341 1390 1446 1392

NLSD/DZVPP NLSD/TZVP NLSD/cc-pVTZ1 NLSD/aug-cc-pVTZl*

l*

’ The barrier heights were calculated from total energies to ten significant b This set of calculations was done using 6-component d functions.

34 cm-’ lower than that calculated with the aug-ccpVDZ’ basis set and is nearly identical to that obtained with the 6-3 1+ G” basis set. Replacing the single d polarization function by two d functions on the heavy atoms causes the MP2 barrier height to increase by about 20 cm-’ (as evi-

state

1.397 1.406

1.446 1.362 1.351

1.314

figures.

dented by comparison of the 6-31 +G” and 63 1 + G (2d, p) results). The addition of an f polarization function to each heavy atom causes the MP2 barrier height to increase by another 106 cm-’ (as evidenced by comparison of the 6-3 1 + G( 2d, p) and 6-31 +G(2df, p) results). Finally, the addition of

K. Kim, K.D. Jordan /Chemical Physics Letters 218 (1994) 261-269

266

diffuse “+” s functions to the H atoms results in a 25 cm-’ decrease in the barrier height. The importance of higher-order correlation effects is estimated by means of MP4SDTQ calculations with the 6-3 lG*, 6-3 1 +G**, and 6-3 1+ G [ 2df, p] basis sets. The 6-3 1 + G [ 2df, p] basis set retains the full 2df polarization set of the 6-3 1 + G (2df, p) basis set on the Ci, CZ, and C6 atoms, but retains only the two d polarization functions on the 0 atom and a single d polarization function on the other C atoms. In addition, the 6-31 +G [ 2df, p] basis set retains the hydrogen p polarization function on only the hydroxy hydrogen atom. The MP2 barrier height obtained with the 6-31 +G[ 2df, p] basis set is only 28 cm-’ below that obtained with the full 6-31 +G( 2df, p) basis set, and most of this discrepancy can be traced to the omission of the p polarization functions on the CH hydrogen atoms. The use of the 6-3 1+ G [ 2df, p] basis set in place of the 6-3 1 + G (2df, p) basis set results in considerable computational savings. The barrier heights obtained at various levels of MBPT are summarized in Table 3. The results ob-

tained with the 6-3 1G* basis set are considered first. With this basis set, the barrier height is predicted to be 1106, 1104, and 1083 cm-’ in the MP3, MP4D, and MP4DQ approximations, respectively, as compared to the MP2 result of 1280 cm-‘. Thus, although the MP2 approximation overestimates the contribution of double excitations to the barrier height, the perturbation expansion in the double excitations converges quite rapidly (as evidenced by the good agreement between the MP3, MP4D, and MP4DQ results). The inclusion of single and triple excitations acts so as to increase the barrier height, with the result that the MP4SDTQ calculations give a barrier height nearly identical to the MP2 value (and 64 cm-’ larger than that deduced from the experiments). The near equivalence of the MP2 and MP4SDTQ barrier height persists with the 6-3 1 + G” and 6-3 1+ G [ 2df, p] basis sets, with the MP4SDTQ barrier height is only 8 and 2 1 cm- ’ less than the MP2 value, with the 6-3 1 + G” and 6-3 1 + G [ 2df, p ] basis sets, respectively. Because the contribution of double excitations is

Table 3 Total energies (hattree) and rotational barriers, AE (cm-‘), of phenol calculated quadratic CI methods and employing the MP2/6-3 lG* optimized geometries Method

using the many-body

Total energy

perturbation

AE”

minimum

transition

MP2/6-31G’ MP3/6-31G* MP4D/6-3 1G’ MP4DQ/6-31G’ MP4SDQ/6-31G* MP4SDTQ/6-31G’ QCISD/6-31G’ QCISD(T)/6-31G*

- 306.47954 -306.50763 -306.53006 -306.50755 -306.51675 - 306.55903 -306.51987 -306.55775

-306.47371 -306.50259 - 306.52503 -306.50261 -306.51135 -306.55324 -306.51448 -306.55221

1280 1106 1104 1083 1186 1271 1184 1214

MP2/6-31 +G” MP3/6-31 +G* MP4D/6-3 1 +Ga MP4DQ/6-3 1 + G-+ MP4SDQ/6-3 1 + G” MP4SDTQ/6-3 1 +G-

-306.55131 -306.57981 - 306.60287 -306.57818 - 306.58749 - 306.63373

-306.54656 -306.57571 -306.59878 -306.57417 -306.58308 -306.62903

1041 901 897 881 967 1031

MP2/6-31 +G[2df, p] MP3/6-31+G[2df,p] MP4D/6-31 +G[Zdf, p] MP4DQ/6-31+G[Zdf,p] MP4SDQ/6-31 +G[Zdf, p] MP4SDTQ/6-31 +G[Zdf, p]

- 306.60872 - 306.63486 -306.65913 - 306.63074 - 306.64064 - 306.69402

- 306.60352 - 306.63033 -306.65461 - 306.62632 - 306.63586 - 306.68892

1140 993 992 971 1048 1119

’ The barrier heights were calculated

from total energies to ten significant

figures.

state

theory

and the

K. Kim. K.D. Jordan /Chemical PhysicsLetters218 (1994) 261-269

overestimated in the MP2 approximation, it is anticipated that the contributions of single and triple excitations are overestimated in the MP4 approximation (since these excitations enter into the fourthorder expression for the energy via mixing with the double excitations). QCISD( T) calculations show that this is indeed the case. With the 6-3 1G* basis set the QCISD(T) calculations give a barrier height of 1214 cm-‘, which is 66 cm-’ below the MP2 value and which is nearly identical with the experimental value. QCISD (T) calculations were not performed with the larger bases sets due to the high computational cost. The MP4SDTQ/6-3 1 + G [ 2d, f], MP4SDTQ/631G*, QCISD(T)/6-31G*, MP2/6-31 +G(2d, f), MP2/6-31 +G[2d, f], and MP2/6-31+ +G” results can be combined to estimate the QCISD (T) /631+ +G(Zdf, p) barrier height #5. This approach gives an estimated barrier height of about 1076 cm-‘, which is 131 cm-’ smaller than the experimental value of the barrier height reported in ref. [ 3 1. The discrepancy between the theoretical and experimental values for the barrier height could be due to either approximations in the calculations or to assumptions made in the analysis of the experimental data. With regard to the calculations, one possible source of error is the use of the MP2/6-31G* optimized geometries. However, the barrier height at a given level of theory (e.g., MP2/6-3 1+G( 2df, p) is relatively insensitive to whether the MP2/6-3 1G’, and MP2/6-31+G(Zdf, p) optiMP2/6-31G”, mized geometries are used. Thus, it appears that the use of MP2/6-3 1G* optimized geometries does not introduce sizable errors in the calculated barrier height. Several assumptions were made in the procedures used to deduce the barrier height from the rotational and vibrational data [ 3-5 1, and we believe that these led to an overestimation of the barrier height. In particular, we note that in the determination of the exa5 The

QCISD(T)/6-31 +G(Zdf, p) barrier height is estimated from E(MP4SDTQ/6-31 +G[Zdf, p] -E(MP2/6-31 +G[Zdf, p)+O.78{E(QCISD(T)/6p])+E(MP2/6_31++G(2df, 3lG*-E(MP4SDT/6-3lG*)}, where the factor of 0.78 included in the last term accounts for the fact that the change in the barrier height in going from the MP4DQ to the MP4SDTQ approximation is 78% as large with the 6-3 1+ G [ 2df, p ] as with the 6-3 1+ G” basis set.

267

perimental barrier height in ref. [ 31 it was assumed that the HOCiC,, atoms remain fixed (and retain C, symmetry) and that the Cz, CX,C5, and C6 atoms and the attached hydrogen atoms retain CzVsymmetry as they are rotated with respect to the HOC,C, plane. In addition, only the I’, term was retained in the Fourier expansion of the rotational potential In order to estimate the magnitude of the error in the barrier height resulting from the geometrical constraints imposed in analyzing the rotational data, the planar structure was also optimized at the MP2/63 1G’ level of theory with Czy symmetry imposed for the Cz, Cs, C5, and C6 atoms and the associated H atoms. The corresponding constrained TS structure was generated by rotating the plane containing the Cz, Cs, C5, and Cs atoms and the attached H atoms by 90” with respect to the HOC&, plane, keeping all other geometrical parameters frozen at the values they had in the planar structure. This procedure gives a barrier height 72 cm-’ greater than that obtained from the MP2/6-31G* calculations without constraints. Separate calculations revealed that nearly all of this increase is due to the use in the TS structure of the CO bond length obtained for the minimum energy structure. In the unconstrained MP2/6-3 lG* calculations the CO bond length is 0.019 A longer in the TS structure than in the minimum energy structure. The increase in the CO bond length accompanying rotation away from the planar equilibrium structure is due to the loss of the conjugation between the 0 pXorbital and the TCorbitals of the ring. Singlepoint MP2/6-3 1+ G( 2df, p) calculations carried out using the constrained geometries give a barrier height 37 cm-’ larger than that obtained from the MP2/63 1 + G (2df, p) calculations using the unconstrained geometries. The above analysis indicates that the rigid-rotor approximation could introduce an error on the order of 40 cm- ’ in the barrier height, thus accounting for roughly one-third of the difference between the calculated and experimental barrier heights. It is also possible that the retention of only the V, term in the potential may have acted so as to give too high a value of the barrier height deduced from analysis of the spectroscopic data. The LSD and NLSD calculations using the DZVPP basis set and the MP2/6-3 lG* optimized geometries, give barrier heights of 1544 and 1341 cm- *, respec-

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K. Kim, K.D. Jordan /Chemical PhysicsLetters218 (1994) 261-269

tively. The LSD and NLSD barrier heights are 30-49 cm-’ greater when the TZVP basis set is employed and about 56-92 cm-’ greater still when the ccpVTZ1 and cc-pVTZ2 basis sets are used. However, upon the addition of diffuse functions (s, p, and d on 0 and C and s on H) to the correlation-consistent basis sets, the LSD and NLSD barrier heights drop down to values close to those obtained with the TZVP basis set. The barrier heights obtained from NLSD calculations using the TZVP or aug-cc-PVTZ 1* basis sets are about 233 cm-’ greater than the MP2 values obtained with the 6-3 1 + G (2df, p) basis set and about 325 cm- ’ greater than our estimated QCISD (T) result. Thus, it is clear that NLSD calculations with the BP exchange-correlation potential give much too large a value of the barrier height. The LSD and NLSD results reported in Table 2 were obtained at the MP2/6-3 1G’ optimized geometries. However, this is not an important factor since the LSD and NLSD barrier heights calculated using the LSD/DZVPP optimized geometries agree to within 40 cm-’ of those calculated using the MP2/ 6-3 1G* geometries.

to the discrepancy between theory and experiment are the use of a rigid-rotor model and the retention of only the V, term in the potential in the analysis of the spectroscopic data. Based on the HF/6-31G’ frequency calculations, the inclusion of zero-point vibrational energy would lower the barrier height by about 175 cm-‘, nearly all of which is due to the torsional mode. The experimental value of the barrier height was deduced assuming that the zero-point energy in the non-torsional degrees of freedom is nearly the same at the minimum and transition state structures, and neglecting the ZPE in the torsional mode. Density functional calculations in the LSD approximation and using the aug-cc-PVTZl* basis set give a barrier 568 cm-’ higher than obtained from MP4SDTQ/6-3 1 + G** calculations. The barrier height is reduced by 207 cm- ’ upon inclusion of nonlocal corrections by means of the BP exchange-correlation functional. The error in the NLSD barrier height should be due primarily to inadequacies in the BP exchange-correlation potential.

4. Conclusions

This research was carried out with the support of a grant from the National Science Foundation. Some of the calculations were carried out on the Cray C90 at the Pittsburgh Supercomputing Center. We thank Professor D. Salahub for access to the demon program and Dr. A. St.Amant for many helpful discussions about demon. We also thank Professor D. Pratt for discussions about the rotational barriers in OH substituted aromatic compounds and P. Bolkovac for providing the MP2/6-3 lG* optimized geometries of phenol.

MP2 calculations using the 6-3 1+ G( 2df, p) basis set give a rotational barrier height of about 1168 cm- ‘, about 40 cm-’ below the most recent experimental estimates of the barrier height. Higher-order double excitations act so as to further decrease the barrier height, while single and triple excitations act so as to increase it, with the net result being that the MP4SDTQ and MP2 values of the barrier height are very close. The MP4SDTQ procedure overestimates the contributions of single and triple excitations to the barrier height; with the 6-31G* basis set, the QCISD(T) barrier height is 57 cm-’ below the MP4SDTQ value. Our best estimate of the barrier height, obtained by combining the results of MP4SDTQ/6-3 1 + G [ 2df, p], QCISD(T)/6-31G’ and MP4SDTQ/6-31G* calculations, as well as MP2 calculations with the 631++G(Zdf, p), 6-31+G(2df, p), and 63 1+G [ 2df, p] basis sets, is about 130 ‘cm-’ below the experimental value. Factors that may contribute

5. Acknowledgement

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