J. Phys. Chem. 1995, 99, 905-915
905
Ab Initio and Density Functional Studies on Internal Rotation and Corresponding Transition States in Conjugated Molecules Tetsuro Oie Department 46, Building AP9A, Abbott Laboratories, One Abbott Park Rd., Abbott Park, Illinois 60064-3500
Igor A. Topol and Stanley K. Burt* Structural Biochemistry Program, Frederick Biomedical Supercomputing Center, PRI/Dyn Colporation, National Cancer Institute, Frederick Cancer Research and Development Center, Frederick, Maryland 21702 Received: April 26, 1994; In Final Form: September 8, 1994@
A comparative study between a high-level ab initio molecular orbital method and density functional theory (DFT) employing local density approximation with nonlocal gradient corrections to the exchange-correlation potential (NLGC) included has been performed on the rotational barriers around the single bond for 11 molecules. All of these molecules are constitutive parts of large biomolecules and have single bonds with varying degrees of partial double bond character. All conformers were optimized by the both methods, using comparable basis sets (double zeta plus polarization in valence orbital) including correlation effect, followed by single-point energy calculations using even larger basis sets. An excellent agreement between the two methods was obtained in locating the transition states. Although reasonable agreement between the two methods was obtained for the barriers in non-amide molecules, fairly large discrepancies were found for amide bonds.
I. Introduction In the past few years, density functional theory (DFT) under the local approximation has been applied to a wide variety of molecular systems which consist of only nonmetallic atoms.' When nonlocal gradient corrections to the exchange-correlation potential (NLGC) were included, the DFT results were found, in most cases, to be in good agreement with available experimental data and high-level ab initio calculations. Further, the lower computational cost and often improved results by DFT method (due to the inclusion of electron correlation effects) make DFT more applicable to large molecular systems than traditional ab initio Hartree-Fock (HF) molecular orbital method. The initial successes of DFT method indicate that this new methodology is becoming an acceptable tool and a viable alternative to ab initio molecular orbital methods for the study of molecular systems involving various light atoms. Most DFT applications for both intra- and intermolecular systems have been directed to the studies of minimum energy properties (e.g. molecular structures, vibrational frequencies, hydrogen bond energies, relative energies of conformational isomers, bond dissociation energies, and electronic properties). Few applications have been made to study transient molecular systems such as the transition state occurring upon internal rotations around a bond2a,bor during a chemical reaction.2c-fIf DFT is to be useful as an alternative to ab initio methods for molecular mechanics parameter development the method should correctly predict relatively low-lying energy conformations and provide reasonable estimates for the barrier to internal rotation. In an extensive study of ethylene glycol,la we have shown that DFT gives answers that are in quantitative agreement with ab initio results for the prediction of energy differences between low-lying conformers. Here we extend our comparison between DFT and ab initio methods to the estimation of barriers to internal rotation. In the present study, we have selected 11 molecules (Figure @
Abstract published in Advunce ACS Absrrucfs, November 15, 1994.
1) in order to test the applicability of DIT to the characterization of the transition states which occur during conformational changes. These molecules, shown in Figure 1, are butadiene (la),-acrolein (lb), vinylamine (IC), fo&c acid (ld), methyl formate (le), methyl acetate (If), formamide (lg), N-methylformamide (lh), acetamide (li), N-methylacetamide (lj) and N,N-dimethylformamide (lk). These molecules contain commonly found constituents in biological systems. In the equilibrium state all of these molecules have a conjugated single bond with partial double bond character. This bonding character will be completely lost at the transition state upon internal rotation of this bond. For vinylamine and amides, an additional conformational maximum arises due to inversion around the nitrogen atom. This inversion accompanies some degree of change in hybridization from a mixture of sp2 and sp3 hybridizations at the equilibrium state to an sp2 hybridization at the transition state. Since at these transition states the effect of electron correlation on both the geometries and energetics is expected to play a greater role than at the equilibrium state, testing of these molecules may pose more of a challenge to both ab initio and the DFT methods than testing of nonconjugated molecules where the changes in hybridization of atoms do not take place during the conformational change. The barriers to internal rotation can be obtained experimentally with an accuracy of 5% or better by the method of microwave spectroscopy for molecules with a relatively low , ~ the validation of the theoretically barrier (3-4 k ~ a l l m o l )and derived barriers for these molecules is rather straightforward. However, the barriers for the current molecules of interest are too high for the direct application of this method. The barriers reported in the literature for these molecules, which are derived either by solving the torsional Schroedinger equation for the adjustable analytic potential energy function (for most of the non-amide molecules) or by NMR kinetic study (for the amide molecules), need to be viewed with caution. In the former method, for example, the limited experimental data (Le., torsional excitation energies) fitted to the potential energy
QQ22-3654/95/2099-09Q5~Q9.QQlQ 0 1995 American Chemical Society
Oie et al.
906 J. Phys. Chem., Vol. 99, No. 3, 1995
(b)Acrolein (T)
(a) Butadiene (T)
(h) N-Methylformamide (S)
(g) Formamide (EQ)
He
(c) Vinylamine (EO)
: ,H
H I
H 03\
/c4
H5/
5 4
.H5
"7-5
'"H
it' (e) Methyl formate (S)
u) N-Methylacetamide(T)
(i)Acetamide (EO)
P ,J ~
03
'c,302
7
H%,
;'Sc
g 6-3 1G** was developed at the Hartree-Fock level. (b) Both basis sets used in the DFT calculation are optimized in the local spin density (LSD) approximation'. (c) Both basis sets for hydrogen atoms have a double zeta character in the DFT calculations; whereas the
6-31G** and 6-311G** basis sets have a double and a triple zeta character, respectively. In addition to the orbital basis sets, auxiliary basis sets were used in the DFT calculations to represent the electron density and the exchange-correlation potentials. In all our DFT calculations these auxiliary basis sets had (8/4/4) Gaussian representations for the heavy atoms and (4/1) for the H atoms. The NLGC to the LSD (NLSD) were self-consistently included in the exchange and correlation potentials according to Becke (exchange)8 and Perdew (c~rrelation).~ The geometries were fully optimized by an analytic gradient method at the MP2 level using a 6-31G** basis set (MP2/631G**) and at the NLSD level using a DZVP2 basis set (NLSD/ DZVP2). Symmetry constraints were used, when possible, in the ab initio calculations. With the above mentioned basis sets, the second derivatives of the energy at the optimized geometries were calculated analytically by ab initio and numerically by DFT to obtain harmonic vibrational frequencies, which were used to estimate the zero point vibrational energies (ZPVE). Single-point ab initio and DFT energy calculations were canied out for the MP2/6-31G** and NLSD/DZVP2 optimized geometries, respectively. At the highest ab initio level, frozen core Moller-Plesset perturbation calculations to full fourth Le., MP4(SDTQ), were carried out using the 6-311G** basis set, and the NLSD DFT calculations used a TZVP basis set. We believe that the current levels of theories used in this study are a reasonable compromise between accuracy and computational costs, and that employing the same levels of theories for all molecules will facilitate comparisons between the methods.
111. Results and Discussion In Figure 1 we show schematically only the most stable conformer for each of the eleven molecules. Other conformers can be easily identified by the optimized torsional angles given in Tables la-XIa. In Tables la-1 la, only selected geometrical
Density Functional Studies on Conjugated Materials
J. Phys. Chem., Vol. 99, No. 3, 1995 907
TABLE 1: (a) Optimized Geometries, Dipole Moments @), and Lowest Vibrational Frequencies (01) of Butadiene." (b) Relative Conformational Energies of Butadieng (a) Geometries, Dipole Moments and wl
T 1.455 123.7 180.0
Cl-C2 Cl-C2=C3 t(C1-C2)b
P
0.0
01
159
MP2/6-31G** G S 0.012 0.014 0.3 2.7 37.4 0.0 0.10 0.04 188 168i
NLSDIDZVP2 G S 0.016 0.015 1.4 3.5 38.0 0.0 0.12 0.08 95i 165
T 1.462 123.8 180.0
TS
0.026 -0.2 -101.5 0.07 175
0.0
123
TS 0.032 0.6 -101.2 0.06 190i
expt (g)' T(ED) 1.467 124.4 180.0 -
(b) ConformationalEnergies confg T
G S
TS
PG CU CZ CZ" CZ
MP4/A
ab initio' MP4B
0.
0.
2.66 3.37 5.82
2.59 3.49 5.51
NLSDf
ZE 0. 0.05
-0.22 -0.30
EIZE) ~I
A'
B'
0.
0.
0.
2.64 3.27 5.21
3.82 3.74 7.09
3.74 3.74 6.90
ZE' 0.
-0.03 -0.12 -0.34
E(ZE') ~I
0.
3.71 3.62 6.56
0.
2.76(0.07) 3.94 5.88(0.09)
0.
-
3.29(0.16) 7.37(0.20)
a Optimized geometries at the MP2/6-31G** and NLSDIDZVP2 levels. Bond lengths in angstroms and angles in degrees; bond lengths and bond angles for the most stable conformer are in absolute values and those for other conformers are relative to those for the most stable one; dipole and NLSDTTZVPIINLSDIDZVP2levels for ab initio and DFT methods, moments @) in Debye calculated at the H-/6-311G**//MP2/6-31G** respectively; vibrational frequencies (wl) calculated at the MP2/6-3 1G** and NLSDIDZVP2 levels for ab initio and DFT methods, respectively; Codes adopted for the experimentalmethods for structure determination are ED (electron diffraction) and MW (microwave) with estimated experimental error in parenthesis. Dihedral angle for C4=Cl-C2=C3. In gas (g) phase. Reference 1lb. Energies in kcal/mol; frequencies in cm-'; Codes adopted for the experimental methods for energy measurement are IR (infrared), RA (Raman), UV (ultraviolet), MW (microwave), and NMR (nuclear magnetic resonance) with estimated experimental error in parentheses. e PG for point symmetry group; zero point vibrational energies (ZE) at MP2/6-31G**;MPUA at MP4SDTQ/6-31G**//MP26-3lG**; MP4/B at MP4SDTQ/6-311G**//MP2/6-31G**; E(ZE) as relative energies MP4/B plus ZE. f Zero point vibrational energies (ZE') at NLSDIDZVP2; A' at NLSDIDZVP2//NLSDIDZVP2; B' at NLSD/TZVP//NLSDIDZVP2; E(ZE') as relative energies at NLSD/B' plus ZE'. See optimized dihedral angles in part (a) for identification of conformers. * Reference 1la. The gauche and cis conformers are taken as the second stable isomer in the first and second columns, respectively.
TABLE 2: (a) Optimized Geometries, Dipole Moments @), and Lowest Vibrational Frequencies (wl)of Acrolein" and (b) Relative Conformational Energies of Acroleind (a) Geometries, Dipole Moments, and w 1 MP2/6-31G** Cl-C2 c2-c1=c4 Cl-C2=03 t(Cl-C2)b
P 01
T 1.470 120.4 124.1 180.0 3.79 164
NLSDIDZVP2 TS 0.023 1.8 -0.8 91.4 3.12 216i
S
0.010 0.3 -0.2 0.0
3.12 168
T 1.481 120.9 124.2 180.0 3.44 157
S
0.011 0.76 0.4 0.0
2.88 165
TS 0.026 2.5 -0.5 91.6 2.72 227i
expt (gY T(Mw) S(MW) 1.468 0.010 120.4 1.1 124.0 0.2 180.0 0.0 3.12 2.55
(b) ConformationalEnergies ab initioe
conf T S TS
PG
cs cs
C1
MP4/A
MP4B
0
0
1.31 7.74
1.40 7.51
expt (g),
NLSIY ZE
0 0.05
-0.41
E(ZE)
B'
A'
0
0
0
1.45
2.10 8.59
2.01 8.45
7.04
Same as in Table 1. Dihedral angle for C4=Cl-C2=03.
ZE' 0
-0.04
-0.68
E(ZE')
IRRA/UVh
0
0
1.97 7.77
1.72 1.29 8.08 7.87
Mw' 0 1.7(0.0)
-
Reference 12. d-g Same as in Table lb. Reference 13. ' Reference 14.
parameters for the fully optimized molecules studied are shown. As seen in the tables, excellent agreement was obtained between the ab initio and DFT methods for the torsion angles for each of the conformers for all 11 molecules. The optimized Cartesian coordinates for all the molecules studied are available upon request. In Tables la-1 la, the bond lengths for the rotatable bonds and the bond angles adjacent to those bonds are given for the most stable conformers. The bond lengths and the bond angles of less stable conformers are expressed relative to those of the most stable conformers. Excellent agreement was found between the two methods in prediction of relative bond length changes occurring during conformational change. However, absolute bond lengths calculated by the DFT method were found to be consistently longer than those calculated by ab initio and those measured by microwave spectroscopy. The lowest
vibrational frequency for each conformer is also shown in Tables la-lla and the presence of an imaginary frequency value means that there was only one imaginary frequency found. In Tables lb-llb, the calculated relative energies are compared with available experimental enthalpies. The ZPVE corrections were made for the energies calculated at the MP41 6-311G** and NLSD/TZVP levels, and the resulting energies, E(ZE) and E(ZE'), respectively, should correspond closely to the experimental enthalpies measured at 0 K. As seen in the tables, the ZPVEs calculated by both methods are quite comparable except for the inversion state of vinylamine, where the largest difference (0.46 kcaYmol) was found. In Table 12, the effect of the basis set and electron correlation on the relative energies of the most stable and second stable conformers is summarized. The energy changes due to the expansion of the basis set from 6-31G** to 6-31 1G** are 0.07-
Oie et al.
908 J. Phys. Chem., Vol. 99, No. 3, 1995
TABLE 3: (a) Optimized Geometries, Dipole Moments @), and Lowest Vibrational Frequencies (01) of Vinylamin@ and (b) Relative Conformational Energies of Vinylamineg-h
EQ 1.398 126.0 18.3 145.4 52.9 1.54 35 1
C2-N3 Cl=C2-N3 t(C2-N3)b t(C2-N3)' x(N3)* iu
Wl
(a) Geometries, Dipole Moments, and wl MP2/6-31G** INV EQ TS 1 TS2 -0.022 1.406 0.041 0.037 -0.3 -5.3 0.5 126.3 -58.1 122.6 0.0 17.3 -122.6 180.0 146.5 58.1 63.9 65.2 0.0 50.8 1.35 1.56 1.80 1.65 3941' 1871' 5291' 350
NLSDIDZVP2 TS 1 TS2 0.047 0.042 0.2 -5.3 -58.4 122.1 58.4 - 122.0 63.2 64.1 1.42 1.49 4281' 2722
INV -0.018 0.5 -0.3 179.8 0.1 1.93 460i
(b) Conformational Energies conf EQ TS1 TS2 INV
PG c1 CS CS
cs
MPWA
ab initio MP4B
0
0
6.49 5.16 2.19
6.65 5.17 2.45
ZE
EW)
0
-0.45 -0.46 -0.26
A'
B'
0
0
0
6.20 4.71 2.19
8.54 7.02 1.07
8.04 6.48 0.70
a Same as in Table la. b.cDihedral angles for Cl-C2-N3-H4 and Cl-C2-N3-H5, C2-H5. e-h Same as footnotes d-g in Table lb. Reference 15a. Reference 15b.
NLSD ZE'
expt (81, AH MWJ
E(ZE')
0
0
-0.55 -0.55 -0.72
7.49 5.93 -0.02
Mw'
0
0
l.O(O.0)
7.3(0.6) 6.7(0.6) 2.0(0.3)
respectively. dImproper torsion angle for H4-N3-
J
TABLE 4: (a) Optimized Geometries, Dipole Moments @), and Lowest Vibrational Frequencies (wl) of Formic Acid" and (b) Relative Conformational Energies of Formic Acid (a) Geometries, Dipole Moments, and 01 S
c1-02 02-C P O 3 t(C1-02
1.349 125.2
iu
1.65 626
Wl
0.0
MP2/6-3 1G** T 0.006 -2.6 180.0 4.50 529
TS 0.029 -1.2 94.9 3.26 6241'
NLSDIDZVP2 T 0.007 -2.8 180.0 4.05 517
S
1.366 125.1 0.0
1.53 591
TS
0.029 -1.2 95.3 2.90 6371'
expt (8) TIMWV 1.343 0.009 124.9 -2.5 0.0 180.0 1.42' 3.79
S(MwY
(b) Conformation Energies conf
PG
S
cs cs
T TS
c1
MP4lA 0
5.49 14.06
ab initid MP4IB
0
5.28 13.78
ZE
0
-0.28 -1.37
Same as in Table la. Dihedral angle for 03=C1-02-H4. text for the discussion of the barrier.
E(ZE) 0
5.00 12.41
A'
0
4.63 13.86
Reference 18a.
0.25, and 0.07-0.21 kcaYmo1 at the MP2 and MP4 levels, respectively. The corresponding changes at the NLSD level are 0.08-0.49 kcaYmol upon going from DZVP2 to the TZVP basis set. The energy changes due to the addition of triple and quadruple excitations to the MP2 energies are 0.01-0.22 and 0.01-0.20 kcaVmol with the 6-31G** and 6-31 1G** basis sets, respectively. These small changes of less than 0.2 kcaYmol indicate that inclusion of even higher order correlation effects will have only small influence on the relative energies of the conformers. As expected, and as shown in Table 13, the basis set and electron correlation have greater influences on the calculated barrier heights than on the equilibrium energy differences. The energy changes upon going from the 6-31G** to 6-311G** basis set are 0.02-1.17 and 0.01-1.08 kcal/mol at the MP2 and MP4 levels, respectively. The corresponding changes at the NLSD level basis set are 0.00-0.75 kcal/mol on going from the DZVP2 to TZVP basis set. The energy changes when going from the MP2 to MP4 level are 0.01- 1.01 and 0.01-0.94 kcal/mol, with the 6-31G** and 6-31 1G** basis sets, respectively. In the discussion that follows, unless noted otherwise, the calculated energies will refer to the energies calculated at the
B' 0
4.63 13.91
NLSDh ZE' 0
-0.26 - 1.26
E(ZE') 0
4.37 12.65
expt (g)! AH MW 0
3.9(0.1) 12.9
Same as footnotes d-g in Table lb. j Reference 17. See the
MP4/6-311G** and NLSD/TZVP levels, and the corrected values for ZPVE, E(ZE) and E(ZE'), will be given in the parenthesis. A. Butadiene. The lowest energy conformer of butadiene has a trans form, but the identity of the next most stable conformer, gauche or cis, remains in doubt.1° The observed infrared (IR) and Raman spectra in the gas-phase for the second stable conformer cannot be unambiguously assigned either to the cis or gauche form. Therefore, two alternative potential energy functions with respect to the central C-C bond were derived from the experimental data1la resulting in the two sets of experimental energies shown in Table lb: (a) The first potential function finds a stable cis conformer separated by 3.29 kcaYmol from the trans form with a barrier of 7.37 kcaVmol at a torsion angle of 83.5" (trans-cis type); (b) The stable gauche conformer at a torsion angle of 43.2" is separated by 2.76 kcaY mol from the trans form with a barrier of 5.88 kcal/mol. The torsion angle at the transition state is 104.4". The second potential function finds the cis form as an unstable conformer separated by 1.18 kcal/mol from the gauche form (trans-gauche type). Our ab initio results find that the second stable conformer is
Density Functional Studies on Conjugated Materials
J. Phys. Chem., Vol. 99, No. 3, 1995 909
TABLE 5: (a) Optimized Geometries, Dipole Moments @), and Lowest Vibrational Frequencies (01) of Methyl Formate and (b) Relative Conformational Energies of Methyl Formatee (a) Geometries,Dipole Moments, and 01 MP2-6131G** NLSDDZVP2 c1-02 C 1=03 02-C1=03 tl(C1-02)b t2(02-04)'
S
TE
1.345 1.214 125.7
0.008 -0.007 -2.9 180.0
0.0
180.0 1.94 154
P
01
TS 0.027 -0.007 1.6 91.9 178.7 3.37 244i
0.0
4.81 24
PG
S TE TS
cs cs c1
MP4IA
MP4lB
0
0
5.96 14.26
ZE 0
5.87 13.93
-0.008 -3.4 180.0
0.0
180.0 1.98 117
0.0
4.36 74
(b) ConformationalEnergies NLSD8 E(ZE) A' B' ZE'
ab initid
cor&
1.360 1.225 126.0
0
-0.55 -0.92
0
5.32 13.01
Same as in Table la. b,c Dihedral angles for 03=C1-02-C4
0
4.57 14.61
4.69 14.56
and C1-02-C4-H6,
expt S(MW 1.334 1.200 125.9
TS 0.024 -0.009 -1.8 92.3 178.9 3.01 272i
TE 0.005
S
0.0
180.0 1.77
expt, AH E(ZE')
0 -0.40
0
0
4.29 13.77
-0.79
IR(g)'
zR(ArY 0
3.85(0.20)
-
4.75(0.19) 10-15
respectively. Reference 21a. e-h Same as footnotes d-g
in Table lb. Reference 23. j In argon (Ar) matrix. Reference 22.
TABLE 6: (a) Optimized Geometries, Dipole Moments @), and Lowest Vibrational Frequencies (wl) of Methyl Acetate and (b) Relative Conformational Energies of Methyl Acetate'
S
c1-02 C1=03 02-C 1=03 tl(C1-02)b t2(CI-C5)C t3(02-04)d P
01
1.357 1.218 123.5 0.0 0.0
180.0 1.98 70
(a) Geometries,Dipole Moments, and wl MP2/6-31G** NLSDDZVP2 T TS S T 0.029 1.372 0.007 0.008 -0.005 -0.005 -0.007 1.229 -2.3 123.5 -5.4 -4.9 180.0 -103.3 0.0 180.0 0.0 0.0 0.0 8.1 180.0 180.0 180.0 179.4 4.70 5.12 3.88 1.92 127 120i 41 54
TS 0.028 -0.009 -2.6 - 100.6 4.6 179.7 3.46 135
expt (gY S(ED) 1.360 1.209 123.0
(bl Conformational Energies
S
T TS
cs cs c1
0
8.49 13.86
0
8.45 13.46
0
-0.15 -0.65
0
0
8.30 12.81
7.29 14.08
Same as in Table la. b-d Dihedral angles for C4-02-C1=03.03%1-C5-H7, as footnotes d-g in Table lb. j Reference 22. (2
the gauche form and the calculated potential energy surface is quite consistent with the trans-gauche type. The cis form is a maximum lying 0.90 (0.63) kcal/mol above the gauche form. The trans to gauche barrier was calculated to be 5.51 (5.21) kcallmol with a torsion angle for the gauche form of 37.4' and 101.5' for the transition state. At the NLSDDZVP2 levels, the cis and gauche forms were also found to be the energy maximum and minimum, respectively. The calculated torsion angles for the gauche (38.0') and for the energy maximum (101.2') are in very good agreement with the MP2/6-31G** result and are very similar to those found experimentally, indicating that the potential energy surface is of the trans-gauche type. However, the potential energy surface between the cis and gauche regions is extremely flat (within numerical accuracy) and is more consistent with a potential energy surface of trans-cis rather than trans-gauche type. B. Acrolein. The molecular structures for both cis- and trans-acroleinhave been determined by microwave spectroscopy using eight single D-, 13C-,and 180-substitutedspecies for each conformer.13 Although the C=O and C=C double bonds were found to be equal within experimental uncertainties for both
0
0
7.21 13.85
0
-0.06 -0.57
and C1-02-C4-H6,
7.15 13.28
0
8.5( 1.O)
-
respectively. e Reference 21b. f - i Same
conformers, a significant increase in the central C-C bond by O.OlO(4) A was found upon going from the trans to the cis form. The calculated increase in the C-C bond length, 0.010 and 0.011 A at the MP2/6-31G** and NLSDDZVP2 levels, respectively, is in very good agreement with the experimental results. It is interesting to note that after the preparation of this manuscript, the study of the rotational barrier of acrolein was published by Andzelm and co-workerszbin which they optimized both the cis and trans conformers using DGauss with the basis set DZVPP(621/41;41/1),which is slightly smaller than DZVP2, at the LSD level without the NLGC. Their calculated C-C bond lengths for the trans and cis forms, 1.462 and 1.474 A respectively, are in good agreement with the respective experimental values of 1.468 and 1.478 A.12 However, comparison with our calculations shows that inclusion of the NLGC makes the bond length longer, 1.481 and 1.492 A. Th'is increase in the bond length between the heavy atoms, seen with inclusion of the NLGC, is quite consistent with other reported studies in the literature, including our previous study on ethylene glycol.la The experimental barrier height and cis-trans energy dif-
Oie et al.
910 J. Phys. Chem., Vol. 99, No. 3, 1995
TABLE 7: (a) Optimized Geometries, Dipole Moments @), and Lowest Vibrational Frequencies (01) of Formamidd and (b) Relative Conformational Energies of Formamidd
(a) Geometries, Dipole Moments, and wl MP2/6-31G** TS 1 TS2 0.081 0.075 -0.007 -0.011 0.6 -2.0 55.5 123.6 111.0 -112.7 1.70 4.27 518i 45 li
EQ 1.360 1.223 124.8 -3.6 172.0 4.30 94
Nl-C2 C2=03 Nl-C2=03 t(N1-C2)b x(N1)' @
01
NLSDIDZVP2 TS 1 TS2 0.081 0.076 -0.011 -0.015 1.3 -2.1 55.3 123.9 110.7 -112.2 1.42 3.87 566i 534i
EQ 1.375 1.234 124.6 -3.8 171.7 4.05 76
INV 0.OOO O.Oo0
0.0 0.0 180.0 4.31 66i
expt (9) EQ(MW)d EQ(ED)C 1.352 1.368 1.219 1.212 124.7 125.0
INV -0.001 0.000
0.1 0.1 179.8 4.07 78i
(b) Conformational Energies ab initid
conf EQ TS1 TS2 INV f-i
PG c1 c2
cs cs
MP4lA
MP4B 0
0
15.56 17.82 0.01
14.87 16.86 0.01
ZE 0
-0.46 -0.65 -0.13
E(ZE) ~I
0
14.41 16.21 -0.12
A' 0
17.82 19.75 0
B'
NLSDh ZE
0
18.57 20.31 0
0
-0.29 -0.49 -0.07
Same as in Table la. Dihedral angle for H5-Cl-C2-03. Improper torsion angle for H5-Nl-C2-..H4. Same as footnotes d-g in Table lb. j Reference 29a. 9.4 mol% in methyl propyl ketone solution.
expt (sol), AH NMR
E(ZE') \
,
0
0
18.28 19.82 -0.07
18.5(0.4) -
-
Reference 27. e Reference 26.
TABLE 8: (a) Optimized Geometries, Dipole Moments (p), and Lowest Vibrational Frequencies (01) of N-Methylformamidd and (b) Relative Conformational Energies of N-Methylformamidd
S
Nl-C2 C2=03 Nl-C2=03 tl (N1-C2)b t2(N1-C5)' x(Nl)d
1.360 1.226 125.3 0.0
-0.1 180.0 4.23 35
@ Wl
(a) Geometries, Dipole Moments, and 01 MP2/6-31G** NLSDIDZVPZ T S T TS 1 S(Me) TS 1 0.000 0.079 -0.004 1.374 -0.002 0.080 -0.001 -0.009 0.001 1.238 -0.001 -0.013 -0.4 -0.3 -1.3 125.1 -0.3 0.5 179.9 56.4 0.0 0.0 180.0 56.4 0.1 -54.0 -59.9 -0.1 -0.1 -53.9 179.9 116.2 180.0 -179.9 - 179.9 116.4 4.53 1.91 4.30 4.02 4.40 1.66 75 3271 90i 130 98 383i
expt (g)C S(ED) 1.366 1.219 124.6
S(Me) -0.004
0.001 -1.1 0.0
-59.5 -179.9 4.14 92i
(b) Conformational Energies ab initio8
con? S T TS 1 S(Me)
PG c1 c1 c1 C1
MP4/A 0
1.28 18.45 0.21
MP4B 0
1.18 17.53 0.23
ZE 0
-0.06 -0.61 -0.26
ECE) . . 0
1.12 16.92 -0.03
A'
B'
0
0
0.66 21.56 0.11
0.85 21.96 0.12
NLSD" ZE'
E(ZE') . ,
0
0
-0.20 -0.77 -0.31
0.65 21.19 -0.19
expt (sol), AH NMR 0
lS(0.2) 22.1(0.2)
-
Same as in Table la. tl(Nl-C2). b,c Dihedral angles for C5-Nl-C2=03 and H6-C5-Nl-C2, respectively. Improper torsion angle for C5-Nl-C2-H4. e Reference 26. f-i Same as footnotes d-g in Table lb. j Reference 29b. In 1,2-dichloroethane solution. ference for both conformers of acrolein has been determined in the gas-phase by IR, Raman, and UV spectro~copy.'~The two sets of relative energies, 1.72 and 1.29 kcal/mol for the cistrans energy difference, and 8.08 and 7.87 kcal/mol for the barrier (Table 2b), are consequences of the fact that two sets of potential energy curves which fit the experimental data equally well were derived. Furthermore, microwave spectroscopy intensity measurements also found a cis-trans energy difference of 1.7 kcaUm01.'~ The calculated cis-trans energy differences by ab initio and DFT methods, 1.40 (1.45) and 2.01 (1.97) kcal/mol, respectively, are in reasonable agreement with the observed values. The calculated barrier by the DFT method, 8.45 (7.77) kcal/mol, is in slightly better agreement with experimental values than those obtained by the ab initio method, 7.51(7.04) kcal/mol. C. Vinylamine. The geometrical structure of vinylamine in the gas-phase has not yet been determined, and an accurate experimental estimate of the barrier to the inversion of the NH2 group and to rotation about the C-N bond still remains to be determined, despite a number of spectroscopic studies. The
most recent spectroscopic study by Brown and c o - ~ o r k e r s ~ ~ ~ shows that the equilibrium conformation is nonplanar around the nitrogen atom. In the same study they estimated the inversion barrier to be 1.O kcallmol and challenged the previous estimate of 2.0 kcaYmol by Hamada and c o - ~ o r k e r s .The ~~~ experimental estimate of the rotational barrier is greatly hampered by the limited spectroscopic data and only a crude estimate of about 7 kcal/mol was made by the latter group. The ab initio MP2/6-31G** level calculated A, B, and C rotational constants are in good agreement with the recent spectroscopic measurement by Brown and coworkers,15awhereas all three calculated rotational constants were underestimated by DFT at the NLSDDZVP2 level. The respective experimental values of A, B , and C are 56 319, 10 035, and 8565 M H z . ~ ~ ~ These are compared with 56 261 (-O.l%), 10 032 (O.O%), 8603 (0.4%) MHz found by ab initio and 55 285 (-leg%), 9826 (-2.1%), and 8425 (-1.6%) MHz found by DFT. The deviation in the negative direction found for the rotational constants by DFT is consistent with longer bond lengths calculated with the NLGC.
Density Functional Studies on Conjugated Materials
TABLE 9: (a) Optimized Geometries, Dipole Moments or), and Lowest Vibrational Frequencies (01) of Acetamide and (b) Relative Conformational Energies of Acetamide
J. Phys. Chem., Vol. 99, No. 3, 1995 911
be further reduced to 12.9 k c d m o l since the ZPVE for the torsional mode was neglected at the potential energy minimum. This energy lowering can be estimated to be about 0.9 kcaY mol from the experimentally measured torsional frequencylg of (a) Geometries,Dipole Moments, and 01 638 cm-'. MP2/6-31G** N L S D ~ Z V P ~ expt (gy As shown in Tables 4, a and b, agreement among the EQ TS EQ TS EQ(ED) experiment and the calculated results by both methods is good Nl-C2 1.371 0.084 1.386 0.086 1.380 with respect to the structural parameters and relative energies. C2=03 1.227 -0.008 1.239 -0.010 1.220 The calculated rotational barriers, 13.78 (12.41) and 13.91 N1-C2=03 122.2 1.1 121.8 1.4 122.0 tl(N1-C2)b 10.3 54.7 (12.65) kcdmol by the ab initio and D l T methods, respectively, 54.7 10.9 t2(C2-C6)c -6.6 0.0 0.0 -6.2 are in good agreement with the experimental estimate of 12.9 x(Nl)d 109.4 -154.3 109.4 -155.2 kcaYmo1. A fairly large difference in dipole moments was n(Cl)e 180.0 -177.4 -177.1 180.0 measured experimentally between the syn (1.42 D)20and anti 4.19 1.82 4.00 1.52 c1 (3.79 D)18aforms. Although the dipole moments calculated at Wl 17 4261' 33 4491' the HF/6-311G** and NLSD/TZVP levels (Table 4a) are (b) Conformational Energies overestimated, it is interesting to note that the anti/syn ratio of ab initioh NLSD' the dipole moments between the two conformers, 2.7 and 2.6 at the former and latter level, respectively, are in surprisingly conf PG MP4/A MP4B ZE E(ZE) A' B' ZE' E(=') good agreement with the experimental ratio of 2.7. EQ C1 0 0 0 0 0 0 0 As shown in Table 4b, the calculated syn-anti energy TS CS 13.34 12.69 -0.46 12.23 14.69 15.40 -0.34 15.06 difference of 4.63 (4.37) kcdmol obtained with D l T is in better Same as in Table la. b.c Dihedral angles for H5-Nl-C2=03 and agreement with the experimental value of 3.9 kcdmol than that H7-C6-C2=03. d,e Improper torsion angles for N5-Nl -C2-H4 and of 5.28 (5.00) kcdmol calculated by the ab initio method. Since C6-C2=03-N1, respectively. f Reference 26. x-' Same as footnotes the repulsive interaction between the lone pair electrons of the d-g in Table lb. two oxygen atoms is greater in the anti form than in the syn Upon rotation around the C-N single bond, two transition form, the basis set for the oxygen atom is expected to play a states were found by both ab initio and DFT methods. In one significant role in the calculated energy difference. Our transition state the amino hydrogens are syn to the C=C bond, additional MP4SDTQ single point energy calculation, using a and in the other transition state the amino hydrogen are anti to 6-31l+G** basis set5jwith diffuse function on the heavy atoms, the C=C bond. The C-N bond lengths at these two transition reduced this energy difference to 4.52 kcaYmo1. This suggests states were calculated to be significantly longer by 0.037-0.047 that the 6-31 1G** basis set is still not sufficiently large enough 8, than in the equilibrium state by both methods. to accommodate the lone pair electrons of two oxygen atoms The calculated inversion barriers, 2.45 (2.19) and 0.70 situated in the anti form. (-0.02) kcal/mol, by the ab initio and DFT methods, respecE. Methyl Formate and Methyl Acetate. Methyl formate tively, are not in good agreement with each other. However, and methyl acetate exist almost completely in the syn conformaboth estimates with ZPVE corrections are off by about 1 kcaY tion at room temperature. In this case the syn conformation mol from the most recent experimental value of 1.0 k ~ a l / m o l . ~ ~ ~ refers to the relative orientation between the C=O and 0 - C The inversion barrier is known to be sensitive to the basis sets bonds. Although gas-phase structures of the syn form were used. For example, Head-Gordon and Pople16ademonstrated determined for both esters?l only the existence of the anti form that the inversion barrier of vinylamine could be reduced by could be detected.22 0.73 kcaYmol on changing from the 6-311G** to the It is interesting to note that a fairly good agreement between 6-311+G(2d,p) basis set at the MP2 level. A substantial the two methods was obtained in the geometrical parameters underestimation of the inversion barrier at the D l T level was changes of the syn conformers of the acid and esters. Specifalso found in our additional ab initio and DFT calculations for ically, the effect of the methyl substitution on the 0-C=O NH3,16band in a recent D I T study1&by Dixon and Matsuzawa group is described reasonably well by both methods. On going on the inversion barrier for urea in which they also found the from formic acid to methyl formate, the decrease in the central barrier to be sensitive to the DFT basis set used. The calculated C 0 bond length by 0.009 8, and increase in the O-C=O bond rotational barriers, 5.17 (4.71) and 6.48 (5.93) kcdmol, obtained angle by 1.0" were observed experimentally (Tables 4a and 5a). by the ab initio and DFT methods, respectively, are somewhat Although smaller changes were calculated at the MP2/6-31G** lower than the gross experimental estimation of about 7 k c d level (0.004 8, and 0.5") and the NLSDDZVP2 level (0.006 8, and 0.9"), compared with the observed differences, the directions D. Formic Acid. At room temperature formic acid is known of changes were correctly predicted. to exist predominantly in the syn conformation, where syn and For the 0-C=O group, larger differences were found anti refer to the relative orientation of the C=O and 0-H bonds. between methyl formate and methyl acetate than between formic The existence of the anti conformer was unequivocally identified acid and methyl formate. It was observed by both experiment by microwave spectroscopy in the gas-pha~e.'~Further, the and the two theoretical methods that both the C - 0 and C=O structures of both conformers, including the complete r, structure bonds are lengthened, and the 0-C=C bond angles are of the anti form, were also determined by microwave spectrosdecreased by the methyl substitution at the carbonyl carbon copy.'* The energy difference between the ground vibrational (Tables 5a and 6a). Changes in the C-0 and CEO bond states of both conformers was determined to be 3.9 Z!C 0.1 kcaY lengths (in A), and the 0-C=O bond angles (in degrees) are mol by microwave relative intensity measurement^.'^ In the 0.026, 0.009, and 2.9 in the experiment; 0.012, 0.004, and 2.2 same experiment the syn to anti barrier to internal rotation at the MP2/6-31G** level; and 0.012, 0.004, and 2.5 at the around the C - 0 bond was determined to be 13.8 kcdmol. This NLSDDZVP2 level. value was estimated from the difference between the energy The increase in both bond lengths by the methyl substitution maximum and minimum of the one-dimensional torsional can be explained by hyperconjugation between the methyl and potential function. However, this experimental barrier should
Oie et al.
912 J. Phys. Chem., Vol. 99, No. 3, 1995
TABLE 10: (a) Optimized Geometries, Dipole Moments @), and Lowest Vibrational Frequencies (01) of N-Methylacetamidd and (b) Relative Conformational Energies of N-Methylacetamideh
T 1.366 1.231 123.1 1.o -4.2 41.1 -178.2 178.4 4.12 36
Nl-C2 C2=03 Nl-C2=03 tl(N1-C2)b t2(Nl-C5)C t3(C2-C6)d x(N1)’ X(C2Y P
01
(a) Geometries, Dipole Moments, and wl MP2/6-31G** NLSDDZVP2 TS1 T S S TS1 TS2 0.002 0.089 0.080 1.380 0.005 0.086 -0.013 -0.001 -0.01 1 -0.014 1.243 0.001 -3.1 122.8 -1.8 0.2 -1.7 -0.1 54.1 55.6 122.2 1.4 -172.2 -168.2 -54.5 -51.6 -59.0 -4.4 -51.3 -53.6 0.0 9.7 40.8 2.1 -1.1 2.1 115.4 -177.7 - 166.9 -160.7 115.1 - 120.3 178.9 178.8 -179.7 178.2 179.2 179.4 4.41 2.01 4.39 3.94 4.27 1.73 108 17% 172i 66 48 191i
expt (gY T(ED) 1.386 1.225 121.8
TS2 0.082 -0.018 -2.7 122.4 -61.0 7.5 - 119.9 179.6 4.06 19%
(b) Conformational Energies conf
PG c1 c1 c1 c1
T S
TS1 TS2
MP4/A 0
2.27 15.81 19.94
ab initio‘ MP4B
NLSIY
ZE
E(ZE)
0
0
2.11 14.85 18.84
0.21 -0.32 -0.50
0
2.32 14.53 18.34
A’
B‘
0
0
2.16 18.27 21.82
ZE’ 0
2.65 19.03 22.57
-0.09 -0.39 -0.61
E(ZE’) 0
expt (sol),’ M NMR 0
2.56 18.64 21.96
2.8(1.8) 22.6(1.8) -
Same as in Table la. tl(Nl-C2). b-d Dihedral angles for C5-Nl-C2=03, H8-C5-Nl-C2, and H7-C6-C2=03, respectively. ‘f Improper torsion angles for C5-Nl-C2-H4 and C6-C2=03-N1. g Reference 26. h-k Same as footnotes d-g in Table lb. Reference 29c. 35 mol % in 1,2-dichloroethane solution.
TABLE 11: (a) Optimized Geometries, Dipole Moments @), and Lowest Vibrational Frequencies (01) of Nfl-Dimethylformamidd and (b) Relative Conformational Energies of Nfl-Dimethylformamidee (a) Geometries, Dipole Moments, and w 1 MP2/6-31G** EW TS 1.363 0.076 125.5 -0.8 0.0 -60.5 0.0 -62.5 0. 62.5 4.32 2.08 98 2661’
Nl-C2 Nl-C2=03 tl(N1-C2)b t(N1-N4)c t3(N1-C5)d P
01
NLSDDZVP2 EO1.375 125.7
TS 0.078 -0.1 -61.6 -63.3 63.3 1.85 321i
0.0 0.0 0.0
4.25 121
(b) ConformationalEnergies conf EQ TS
PG c1
MP4/A 0
cs
19.57
ab initid MP4B
0
18.49
ZE
E(ZE)
0
-0.77
0
0
17.22
Same ase in Table la. b-d Dihedral angles for C4-Nl-C2=03, d-g in Table lb. Reference 28.
’
A’
23.08
H-C4-Nl-C2,
B‘ 0
23.37
NLSD8 ZE’ 0
- 1.06
and H-C5-Nl-C2,
E(ZE’) 0
22.31
expt (g),’AH NMR 0
19.7(0.3)
respectively. e-h Same as footnotes
TABLE 12: Effects of Basis Set and Correlation on Equilibrium Energy Difference@ dE(6-31lG**,6-31G**)* dE(TZVP,DZVP2)’ dE(MP4,MP2)d MP2 MP4 NLSD 6-31G** 6-311G** CH2CH-CHCH2 (GI -0.07 -0.07 -0.08 0.01 0.01 CHzCH- CHO (SI 0.11 0.09 -0.09 -0.14 -0.16 HCO-OH (TI -0.25 -0.21 0.00 -0.15 -0.11 HCO-OCHs (TE) -0.12 -0.09 0.12 -0.20 -0.17 CHsCO-OCH3 (TI -0.06 -0.04 -0.08 -0.22 -0.20 CH3NH-CHO (TI -0.09 -0.10 -0.19 -0.06 -0.07 CH3NH-CH3CO (9 -0.19 -0.16 0.49 -0.09 -0.06 a Energies in kcal/mol. The energy calulated with 6-311G** basis set minus the energy calculated with 6-31G** basis set at the MP2 and MP4SDTQ levels. The energy calculated at the NLSD/TZVP level minus the energy at the NLSDDZVP2 level. The energy calculated at the MP4SDTQ level minus the energy at the MP2 level using the 6-31G** and 6-311G** basis sets. OCO groups. Due to the interaction between the high-lying occupied n type orbital (made of p orbital of carbon and s orbitals of two hydrogens off the OCO plane) of the methyl group and the low-lying vacant n* orbital of the OCO group, charge transfer will occur from the former to the latter orbital.
This orbital is antibonding, resulting in the weakening of both bonds. For methyl formate, the syn-anti energy difference was found to be 3.85 & 0.20 k c d m o l from an IR intensity study using a temperature-drift technique.23 An energy difference of 4.75 f
Density Functional Studies on Conjugated Materials
J. Phys. Chem., Vol. 99, No. 3, 1995 913
TABLE 13: Effects of Basis Set and Correlation on Rotational and Inversion Barrier@ dE(6-311G**,6-3lG**)b dE(TZVP.DZVP2)' MP2 MP4 NLSD -0.27 CHzCH-CHCHz -0.3 1 -0.19 -0.23 -0.24 -0.14 CHzCH- CHO -0.05 CHzCH-NHz 0.01 -0.54 0.27 0.26 -0.37 -0.38 HCO-OH -0.28 0.05 -0.47 HCO-OCH3 -0.05 -0.33 -0.51 CH3CO-OCH3 -0.40 -0.23 -0.76 NHz-CHO 0.75 -0.69 0.02 0.00 0.00 -1.00 CH3NH-CHO 0.40 -0.92 -1.04 CHJ'T"HCHX0 -0.96 0.76 -1.17 - 1.OS (CH3)zNH-CHO (TS)' 0.29 Same as in Table 12. 0.19 k c d m o l was also measured by another IR intensity study using thermal molecular beam trapping in AI matrices.22 In that experiment the syn to anti barrier was estimated to be 1015 kcdmol. For methyl acetate only the syn-anti energy difference of 8.5 f 1.O kcdmol was estimated>2and no barrier measured in the gas-phase has been reported. For both esters, the dipole moments of the syn forms were calculated to be much smaller by both methods than for the anti or transition state forms. As a result, a significant solvent effect is expected on both the syn-anti energy difference and barrier height. In comparison to the above mentioned gas state data, a smaller syn-anti energy difference (1.9-2.9 kcal/mol) and lower syn to anti barrier (7.6 kcal/mol) were measured ultrasonically in the liquid phase for methyl formate.24 By the same technique, an energy difference of 4.3 kcdmol and a syn to anti barrier of 6.0 k c d m o l were measured for liquid methyl acetatesz4 These solvent effects can be qualitatively explained by dipole-dipole interactions and are consistent with the recent MP2/6-3 1+G**//HF/6-3 lG* level calculations in the reaction field approximation of Wiberg and Wongz5for these two esters. In their study, by changing the dielectric constant of the media around the cavity from 1 to 35.9 (correspondingto the dielectric constant of acetonitrile), the syn-anti energy differences decreased by 3.6 and 3.4 kcal/mol for methyl formate and methyl acetate, respectively. They also found that the barrier height decreased by at least 1 kcal/mol for both esters. As shown in Tables 5b and 6b, our calculated syn to anti barriers for both esters agree well with each other. The differences in the barriers between the ab initio and DFT levels are 0.63 (0.76) and 0.39 (0.47) k c d m o l for methyl formate and methyl acetate, respectively. Furthermore, for methyl formate the calculated barriers, 13.93 (13.01) and 14.56 (13.77) kcal/mol by the ab initio and D l T method, respectively, are also within the experimental range of 10-15 kcdmo1.22 For both esters the calculated syn-anti energy differences at the MP4/6-311G** level are greater than those at the NLSD/TZVP level. This is most likely due to the same basis set problem discussed in the previous section. However, when zero point vibrational energies are taken into account the calculated values by both methods are still within 0.5 kcal/mol of the experimental estimates. F. Amides. The equilibrium structures of the amides molecules studied here were primarily determined by gas-phase electron diffraction,26 except for N,N-dimethylformamide for which no gas-phase data is available. For formamide a microwave was also done and the equilibrium conformation was interpreted in terms of a planar structure. The rotational barrier around the amide C-N bond measured in the
dE(MP4,MP2)d 6-31G** 6-311G** -0.20 -0.39 -0.55 0.42 -0.27 -0.25 -0.28 -1.01 0.01 -0.99 -0.89 -0.82
-0.24 -0.38 -0.49 0.41 -0.17 -0.11 -0.17 -0.94 -0.01 -0.91 -0.81 -0.73
gas-phase is available only for N,N-dimethylformamide,28 and the barriers for other amides were measured only in solution.29 This experimental data is included in Tables 7b-lob. Of the 11 molecules studied here, both methods found the largest C-N bond stretch for the amide. The calculated bond length increases for five amide molecules are shown in Tables 7a-lla. Respective values of 0.076-0.086 8, and 0.078-0.089 A at the MP2/6-31G** and NLSDIDZVP2 levels were calculated. As discussed for methyl formate and n-methyl formate, the effects of methyl substitution on the 0-C-N were also predicted to be qualitatively correct by both methods. Comparing formamide to acetamide, the respective changes in the C=O and C-N bond lengths (A) and the O=C-N bond angles (degree) are, 0.008, 0.012, and 2.7 by electron diffraction (ED) measurement; 0.004,0.011, and 2.6 at the MP2/6-31G** level; and 0.005, 0.011, and 2.8 at the NLSDDZVP2 level. Between N-methylformamide and N-methylacetamide, the corresponding changes are 0.006, 0.020, and 2.8 by the ED measurement; 0.005, 0.006, and 2.2 at the MP2/6-31G** level; and 0.005, 0.006, and 2.3 at the NLSDIDZVP2 level. The lengthening of the two bonds can be explained by the flow of electron density from the high-lying n type orbital of CH3 group (made of p orbital of C atom and two s orbital of hydrogens) to low-lying n* antibonding orbital of 0 4 - N group through hyperconjugation, thereby weakening the bond. The discrepancies in the calculated rotational barriers between the two theoretical methods were found to be largest for the amide molecules (Tables 7- 1lb). The barriers were always calculated to be lower by the ab initio method than by the DFT method. These discrepancies are significantly smaller with the 6-31G** basis set at the MP4SDTQ level. It should be noted that the discrepancies are larger for those with a N-methyl substitution. At the transition state the distance between the methyl group and the carbonyl oxygen is found to be smaller than the van der Waals distance. Although it may be speculated that the longer bond lengths calculated by the DFT method may exaggerate the steric hindrance at the transition state, further studies are needed to explain the origin of this large discrepancy. Despite these large differences, qualitative agreements between the two methods were obtained in the influence of the methyl substitution at the amino nitrogen and carbonyl C atom on the change in barrier heights. The N-methyl substitution was found to increase the barrier by 2.66 (2.51) and 3.39 (2.91) kcaYmol by the ab initio and DFT methods, respectively, between formamide and N-methylformamide. Between acetamide and N-methylacetamidethe increases are 2.16 (2.30) and 3.63 (3.58) kcal/mol by the respective methods. This increase in barrier can be attributed to the steric hindrance caused by the methyl group and reduction of the energetically favorable
Oie et al.
914 J. Phys. Chem., Vol. 99, No. 3, 1995
dipole-dipole interaction between the NH and CO bond at the transition state. However, the C-methyl substitution was found to decrease the barrier height by 2.18 (2.18) and 3.17 (3.22) kcaYmol by the ab initio and DFT methods, respectively, between formamide and acetamide. Between N-methylformamide and N-methylacetamide, the respective decreases by the two methods are 2.68 (2.39) and 2.93 (2.55) kcal/mol. This decrease in barrier height is also consistent with the already discussed elongation of the C-N amide bond at the ground state found by both experiments and the two theoretical methods. The calculated barriers around the C-N amide bonds by DFT method were found to be in much better agreement with those measured in solutions of formamide (9% in methyl propyl ketone),29aN-methylformamide (in 1,2-di~hloroethane)?~~ and than those N-methylacetamide (35 % in 1,2-di~hloroethane)~~~ calculated by the ab initio method. The experimental barriers are 18.5, 22.1, and 22.6 kcdmol, respectively, whereas the calculated barriers are 18.57 (18.28), 21.96 (21.19), and 19.03 (18.64) kcaVmol by the DFT method and 14.87 (14.41), 17.53 (16.92), and 14.85 (14.53) kcal/mol by the ab initio method. Although validation of these theoretical barrier heights cannot be done without relevant experimental measurement in the gas phase, it should be expected that the barrier measured in the gas phase is lower than that measured in solution. Besides possible self-association due to hydrogen bonding, two additional factors may account for the barrier increase in solution: (1) For all five amides the calculated dipole moments for 'the equilibrium ground states are much larger than those for the rotational transition states by factors of 2.0-2.5 and 2.32.9 by the ab initio and DFT methods, respectively. This indicates that in a polar medium the polar ground state is stabilized more than the less polar transition state. (2) The internal pressure of the solvent, arising from local packing forces in solution, may hinder the rotation. These two expected medium effects are consistent with the comparative study done by Ross and c o - w ~ r k e r son~ ~the experimental barrier heights (AH) measured in various media for N,N-dimethylacetamide: 15.8 f 1.1 (gas phase), 16.3 (15% in CC14), 19.0 (neat), 19.0 (in 10% in acetone), 19.1 (10% in DzO), 20.0 (10% in DMSO), and 20.3 (10% in formamide) kcaVmo1. As shown in Table l l b , the experimental barrier (AH) for N,N-dimethylformamidewas measured to be 19.7 f 0.3 k c d mol in the gas-phase by a NMR kinetic study.28 The calculated barriers (AH) at 0 K are 17.72 and 22.31 kcdmol by the ab initio and DFT methods, respectively. This is an underestimation and overestimationof 1.98 and 2.61 kcal/mol, respectively. This discrepancy of 2-3 k c d m o l in barrier between both methods and experiment is much greater than that found for the other molecules (butadiene, acrolein, formic acid, and methyl formate). More experimental data for gas-phase barriers are needed for validation of theoretically derived barriers of amides. Also, further ab initio studies need to be undertaken, at least for small amides like formamide, to investigate the influence of higher levels of theory on the accuracy of calculated barrier heights. Although this undertaking is beyond the current focus of this study, we performed additional calculations to investigate the effect of electron correlation on the barrier for formamide. In order to obtain further correction for electron correlation effects beyond fourth-order perturbation theory (MP4SDTQ), quadratic configuration interaction (QCI) calculations were done using the 6-311G** basis set for the MP2/6-31G** optimized geometries, in which single, double, and an estimate of triple excitations were included, i.e. QCISD(T).31 As expected, the calculated barrier of 14.59 kcaVmol at the QCISD(T) level was
changed slightly from that of 14.87 kcal/mol at the MP4SDTQ level. However, at the same MP4SDTQ level, the calculated barrier was increased to 15.27 kcal/mol by changing from the 6-31 1G** basis set to the 6-31 l+G** basis set which includes additional diffuse functions on the heavy atoms. Obviously, further and more systematic studies are needed. Especially, the effect of the basis sets needs to be studied in detail since, as seen in Table 13, the opposite effect was obtained by the both methods when the basis sets were increased; the barriers were decreased by 0.65- 1.08 kcal/mol on going from the 6-31G** to 6-311G** basis set at the MP4SDTQ level, whereas the barriers were increased by 0.29-0.75 kcal/mol on going from the DZVP2 to TZVP basis set.
IV. Conclusions In the present conformational studies of the 11 molecules, energy maxima as well as minima due to rotation around the conjugated single bond were characterized geometrically and energetically by ab initio and DFT methods. For two molecules, additional energy maxima arising from inversion at the nitrogen atom were also studied. The following conclusions can be drawn from the current study: 1. For all molecules studied here, excellent agreement was obtained between the two theoretical methods in locating conformational maxima on the potential energy surface. The largest difference in torsion angle was found to be 2.7" for methyl acetate. Agreement was also good between the two methods in the degree of deformation of the central bond length upon rotation around it for both equilibrium states and transition states. 2. For butadiene the experimental data is not sufficient to determine if the cis or gauche form is the second stable conformer. The gauche and cis forms were unequivocally found to be the energy minimum and maximum, respectively, by the ab initio method, although the energy difference was only 0.63 kcaVmo1 after the ZPVE correction. However, the potential energy surface between the cis and gauche forms was found to be extremely flat by the DFT method and there is virtually no barrier between the two conformers. 3. Rotational barriers calculated at the highest levels for each method are in reasonable agreement for the six non-amide molecules. However, significantly large discrepancies were found for all five amide molecules. The differences are 0.131.39 kcaYmol for non-amide molecules and 2.71-4.88 kcaY mol for amide molecules between the MP4SDTQ/6-311G** and NLSDEZVP levels. The corresponding differences between the MP4/6-31G** and N L S D D Z W levels are 0.20-1.86 kcal/ mol and 1.35-3.51 kcaYmo1. 4. The discrepancies in the rotational barriers between the two methods and experiment are small for non-amide molecules (within 1 kcaVmol for butadiene, acrolein and formic acid), while for N,N-dimethylformamide the difference is increased to about 2 kcal/mol. 5. Rotational barriers calculated by the DFT method were always found to be greater than those calculated by the ab initio method, except for the barrier of formic acid calculated at the MP4/6-3 1G** and NLSDDZVP2 levels. However, for vinylamine the inversion barrier calculated by the former method was found to be significantly lower than that by the latter. 6. The results obtained by the DFT method in the current study are encouraging with respect to characterization of not only the equilibrium conformational states but also transient states. These results demonstrate that DFT can be useful as an alternative to ab initio methods for molecular mechanics parameter development. However, the large discrepancy found
Density Functional Studies on Conjugated Materials between the two methods for barriers of amides needs to be investigated further.
Acknowledgment. We thank the staff of the Frederick Biomedical Supercomputing Center, FCRDC, Frederick, MD, for their assistance. The content of this publication does not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products or organization imply endorsement by the U.S. Government. Supplementary Material Available: Complete listing of the MP2/6-31G** and NLSDfDZVP2 optimized Cartesian coordinates for all conformations are available (10 pages). Ordering information is given on any current masthead page. References and Notes (1) (a) Oie, T.; Topol, I. A.; Burt, S. K. J. Phys. Chem. 1994,98, 1121. (b) Topol, I. A.; Burt, S. K. Chem. Phys. Lett. 1993, 204, 611. (c) Holme, T. A.; Truong, T. N. Chem. Phys. Lett. 1993, 215, 53. (d) Mijoule, C; Latajka, Z.; Borgis, D. Chem. Phys. Lett. 1993, 208, 364. (e) Laasonen, K.; Parrinello, M.; Car. R.; Lee, C.; Vanderbilt, D. Chem. Phys. Lett. 1993, 207, 208. (f) Seminario, J. Chem. Phys. Lett. 1993,206,547. (9) Huhn, M. M.; Amos, R. D.; Kobayashi, R.; Handy, N. C. 1993, J. Chem. Phys. 1993, 98,7107. (h) Dickson, R. M.; Becke, A. D. J. Chem. Phys. 1993,99,3898. (i) Lee, C.; Fitzgerald,; Yang, W. G. J. Chem. Phys. 1993, 98, 2971. (j) Handy, N. C.; Murray, C. W.; Amos, R. D. J. Phys. Chem. 1993,97,4392. (k) Amos, R. D.; Murray, C. W.; Handy, N. C. Chem. Phys. Lett. 1993, 202,489. (1) Sim, F.; St-Amant, A,; Papai, I.; Salahub, D. R. J. Am. Chem. SOC.1992, 114,4391. (m) Chiavassa, T.; Roubin, P.; Pizzala, L.; Verlaque, P.; Allouche, A.; Marinelli, F. J. Phys. Chem. 1992,96, 10659. (n) Ignatyev, I. S.; Schaefer H. F. J. Phys. Chem. 1992, 96, 7632. (0)Fournier, R.; DePristo, A. E. J. Chem. Phys. 1992, 96, 1183. (p) Dixon, D. A.; Christe, K. 0. J. Phys. Chem. 1992, 96, 1018. (9) Laasonen, K. ; Csajka, F.; Parrinello, M. Chem. Phys. Lett. 1992,194, 172. (r) Handy, N. C.; Maslen, P. E.; Amos, R. D.; Andrew, J. S.; Murray, C. W.; Laming, G. J. Chem. Phys. Lett. 1992, 197, 506. (s) Merkle, R.; Savin, A. ; Preuss, H. Chem. Phys. Lett. 1992, 194, 32. (t) Becke, A. D. J. Chem. Phys. 1992, 97, 9173. (2) (a) Dixon, D. A,; Matsuzawa, N.; Walker, S. C. J. Phys. Chem. 1992, 96, 10740. (b) Andzelm, J.; Sosa, C.; Eades, R. A. 1993, 97,4664. (c) Kim, K.; Jordan, K. D. Chem. Phys. Lett. 1994, 218, 261. (d) Fan, L.; Ziegler, T. J. Am. Chem. SOC. 1992, 114, 10890. (e) Deng, L.; Ziegler, T.; Fan, L. J. Chem. Phys. 1993,99,3823.(0 Sosa, C.; Lee, C. J. Chem. Phys. 1993, 98, 8004. (3) Gordy, W.; Cook, R. L. In Techniques of Chemistry XVIII; Weissberger, A., Ed.; J. Wiley & Sons: New York, 1984; p 569. (4) Glasstone, S; Laidler, K. I.; Eyring, H. The Theory of Rate Processes; McGraw-Hill Book Co. Inc.: New York, 1941. (5) (a) Frisch, A. M.; Trucks, G. W.; Head-Gordon, M; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A,; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92, Gaussian, Inc., Pittsburg PA 15213. (b) Hehre, W. J.; Radom, L.; Schleyer, P.v.R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986. (c) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972,56, 2257. (d) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. (e) Krishnan, R; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980,
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