Molecular structure, conformational stability and cis effect of 1,4-dichlorobutadiene — a quantum chemical study

Journal of Molecular Structure (Theochem) 577 (2002) 69±79

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Molecular structure, conformational stability and cis effect of 1,4-dichlorobutadiene Ð a quantum chemical study K. Senthilkumar, P. Kolandaivel* Department of Physics, Bharathiar University, Coimbatore 641 046, India Received 24 April 2001; accepted 11 June 2001

Abstract The conformational equilibrium of 1,4-dichlorobutadiene molecule has been investigated using ab initio and density functional theory calculations at Hartree±Fock self consistent ®led theory (HF-SCF), Mùller±Plesset perturbation theory (MP2), B3LYP and B3PW91 levels of theory. The three larger basis sets have been used to study the cis effect of the molecule. The MP2 and B3PW91 methods predicted that the cis±cis conformer is more stable and the former method was able to predict the order of stability in accordance with the experimental results. The HF-SCF and B3LYP methods have failed to predict the cis± cis conformer of 1,4-dichlorobutadiene as the most stable structure even with the higher basis set 6-31111G pp. The relative stability of cis±cis conformer is found to be a consequence of the spectroscopic trans destabilization. The principle of maximum hardness has been tested for the cis effect. The complete frequency analysis has been performed for three isomers at MP2/6-31G p level of theory. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Ab initio; Density functional theory; 1,4-Dichlorobutadiene; cis effect; Maximum hardness principle

1. Introduction Theoretical conformational analysis becomes a very important tool for understanding the relationship between the geometrical arrangement of atoms and energy of molecules. In the 1,4-disubstituted butadiene molecule (X(CH)4X), if X is a small polar group, one would except that the molecule would prefer the anti conformation. However, both experimental and theoretical investigations have shown that the molecules prefer the cis conformation [1,2], the latter incorrectly expected on the basis of steric arguments. This has been termed as the cis effect. From the initial work of Viche et al. [1], the isomers of 1,4di¯uro and 1,4-dichloro butadienes are known to * Corresponding author. Fax: 191-422-422387. E-mail address: [email protected] (P. Kolandaivel).

have an unusual equilibrium relationship in which the cis±cis conformer is more stable, trans±trans conformer is the least stable and cis±trans conformer has intermediate stability. An even more interesting example for this effect is found among the isomers of 1,2-disubstituted ethane and 1,2-disubstituted ethene, where both the experimental and theoretical studies reveal that the gauche conformations were more stable than the anti conformations [3±6]. However, the origin of this apparent attraction between the polar atoms is not fully understood. Craig et al. [2] have studied the complete vibrational spectroscopy of isomers of 1,4-di¯urobutadiene employing the experimental (IR and Raman) and theoretical methods. The fundamentals for three isomers were assigned and the cis effect was studied. From the above study, it is observed that the cis±cis isomer is more stable than the cis±trans and trans±trans isomers, and the

0166-1280/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(01)00656-X

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K. Senthilkumar, P. Kolandaivel / Journal of Molecular Structure (Theochem) 577 (2002) 69±79

relative energies are 2.8 and 4.7 kJ mol 21, respectively. When one isomer of a molecule is more stable than the other, the ®rst may be stabilized or the second may be destabilized. The cis effect can be adequately and consistently interpreted in terms of spectroscopic trans destabilization [7], which arises from exchange repulsion associated with overlap between ®lled orbitals. Increasing the electronegativity of the butadiene substitutent lowers the pp energy level, thus destabilizing the bonding or anti bonding orbitals. Therefore, the net effect of delocalization will become energetically unfavorable and the preferred conformation of the butadiene derivative will switch from trans to cis. It is normally believed that the conformation of a molecule could be determined from electrostatic, exchange-repulsion and dispersion interactions between the substitutions. At the SCF level of approximation, only the ®rst two terms are present and both the exchange repulsion and electrostatic term must favor the anti and trans forms of the studied molecules. In the cis or gauche form, there is an overlap of the electron cloud of the substituent (polar) atoms leading to larger exchange repulsion and in the cis form, the polar atoms which have higher electronegativity will repel each other. Hence the quantum chemical calculations at the Hartree±Fock self consistent ®eld theory (HF-SCF) level could not explain the cis effect. Some of our recent studies and other studies indicate that the density functional theory (DFT) methods are capable of producing the results comparable to the high cost ab initio and experimental results [8,9]. In the present study, special emphasis has been given to study the cis effect presented in 1,4-dichlorobutadiene molecule employing higher level ab initio and DFT methods. The complete frequency analysis has been performed for three isomers at the Mùller± Plesset perturbation (MP2/6-31G p) level of theory. The DFT parameters, chemical hardness and chemical potential were calculated and the principle of maximum hardness has been tested for cis effect. 2. Computational methodology The geometries were optimized by using the restricted Hartree±Fock self consistent ®led theory and second order MP2 theory [10] of ab initio method.

In the hybrid DFT methods, Becke's three parameter exchange functional (B3) [11] combined with nonlocal correlation functions of Lee±Yang±Parr (LYP) [12] and Predew±Wang 91 (PW91) [13], by notation B3LYP and B3PW91, respectively were used for the geometry optimization. Addition of polarization and diffuse functions to the basis sets play a dominant role to predict the exact structural and energetic parameter. Four types of basis sets 6-31G p, 6-311G p, 6-3111G pp and 6-31111G pp have been used in ab initio and DFT methods. The complete frequency calculation has been performed for three isomers at MP2/6-31G p level of theory and the calculated frequencies were scaled with the standard value of 0.9427. The DFT parameters chemical hardness (h ) and chemical potential (m ) have been calculated using the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies calculated from ab initio methods. The chemical hardness and chemical potential can be expressed as

hˆ

I2A ; 2

hˆ

I2A ; 2

where the ionization potential I ˆ 2EHOMO and the electron af®nity A ˆ 2ELUMO : All the calculations were performed with the gaussian 94W computational package [14]. 3. Results and discussion The calculated geometrical parameters, total energies and relative energies employing ab initio and DFT methods are summarized in Tables 1±4. The schematic representation of isomers of 1,4-dichlorobutadiene molecule is presented in Fig. 1. The relative energies calculated by MP2 method were able to predict the stable structure even with the moderate basis set 6-31G p. It shows that the cis±cis conformer is found to be the most stable, and the relative energy of cis±trans conformer (0.26 kcal mol 21) is found to be higher than the trans±trans conformer (0.11 kcal mol 21). The correct description of electron correlation and dispersion energy requires at least one set of diffuse and polarization functions to be added to split valence shell type basis functions. The relative energies calculated by the MP2/6-311G p level of theory could able to predict the stable structure

Parameters

R(C±H) R(CyC) R(C±C) R(Cl±C) u (H±CyC) u (CyC±C) u (C±C±H) u (Cl±CyC) RA RB RC mm h m 2 E (1070 1 ) DE

HF/6-31G p

HF/6-31 1 G p

HF/6-311 1 G pp

HF/6-31111G pp

cis±cis

cis±trans

trans±trans cis±cis

cis±trans

trans±trans cis±cis

cis±trans

trans±trans cis±cis

cis±trans

trans±trans

1.073 1.321 1.468 1.728 119.2 125.1 115.7 126.3 10.618 0.783 0.729 0.000 5.89 2 3.18 2.71944 0.00

1.073 1.320 1.468 1.727 120.6 121.0 114.1 125.1 7.515 0.764 0.693 2.399 5.90 2 3.13 2.71946 2 0.0125

1.074 1.319 1.468 1.728 121.8 121.4 116.9 123.9 29.664 0.572 0.561 0.000 5.91 2 3.10 2.72042 2 0.6149

1.074 1.322 1.469 1.727 120.6 121.1 114.2 125.1 7.502 0.764 0.693 2.354 5.47 2 3.64 2.72432 0.1129

1.074 1.321 1.468 1.728 121.8 121.4 116.8 123.9 29.627 0.571 0.560 0.000 5.48 2 3.61 2.72507 2 0.3577

1.074 1.319 1.468 1.729 120.7 120.9 114.2 125.0 7.479 0.765 0.694 2.311 5.40 2 3.76 2.80898 0.0502

1.074 1.318 1.468 1.731 121.9 121.3 116.8 123.8 29.579 0.572 0.561 0.000 5.43 2 3.71 2.80982 2 0.4769

1.074 1.319 1.468 1.729 120.7 120.9 114.2 125.0 7.480 0.765 0.694 2.326 5.08 2 4.00 2.80918 0.0627

1.074 1.318 1.468 1.731 121.9 121.3 116.8 123.8 29.585 0.572 0.561 0.000 5.12 2 4.01 2.81000 2 0.4518

1.073 1.323 1.469 1.728 119.2 125.0 115.8 126.3 10.605 0.782 0.729 0.001 5.56 2 3.61 2.72450 0.00

1.073 1.320 1.469 1.731 119.3 125.0 115.8 126.2 10.583 0.784 0.730 0.000 5.35 2 3.72 2.80906 0.00

1.073 1.320 1.469 1.731 119.3 125.0 115.8 126.2 10.582 0.784 0.730 0.000 5.16 2 4.04 2.80928 0.00

K. Senthilkumar, P. Kolandaivel / Journal of Molecular Structure (Theochem) 577 (2002) 69±79

Table 1 Ê , bond angle in degrees), rotational constants RA ; RB ; RC (in GHz), dipole moment mm (in Debye), chemical hardness h (in eV), chemical Geometrical parameters (bond length in A potential m (in eV), total energy E (in Hartree) and relative energy DE (in kcal mol 21) calculated by HF level of theory

71

72

Parameters

R(C±H) R(CyC) R(C±C) R(Cl±C) u (H±CyC) u (CyC±C) u (C±C±H) u (Cl±CyC) RA RB RC mm h m 2 E (1070 1 ) DE

MP2/6-31G p

MP2/6-31 1 G p

MP2/6-311 1 G pp

MP2/6-31111G pp

cis±cis

cis±trans

trans±trans cis±cis

cis±trans

trans±trans cis±cis

cis±trans

trans±trans cis±cis

cis±trans

trans±trans

1.085 1.345 1.454 1.724 119.4 124.3 116.3 125.6 10.519 0.784 0.730 0.00 5.70 2 3.16 3.48537 0.00

1.086 1.345 1.453 1.722 120.5 120.8 115.1 124.7 7.396 0.765 0.693 2.364 5.70 2 3.12 3.48495 0.2635

1.087 1.343 1.453 1.723 121.4 121.0 117.5 123.8 28.908 0.570 0.559 0.00 5.71 2 3.09 3.48519 0.1129

1.087 1.347 1.454 1.722 120.4 120.8 115.3 124.7 7.385 0.764 0.692 2.306 5.37 2 3.53 3.49793 0.4392

1.088 1.346 1.454 1.723 121.4 121.1 117.5 123.8 28.854 0.569 0.558 0.00 5.38 2 3.50 3.49789 0.4643

1.086 1.347 1.455 1.719 120.4 120.8 115.4 124.4 7.364 0.768 0.696 2.241 5.28 2 3.63 3.64290 0.407

1.087 1.346 1.456 1.720 121.3 121.1 117.6 123.6 28.769 0.570 0.559 0.00 5.31 2 3.58 3.64272 0.5208

1.086 1.347 1.455 1.719 120.4 120.8 115.4 124.4 7.350 0.769 0.696 2.259 4.96 2 3.95 3.64346 0.4643

1.087 1.346 1.455 1.720 121.3 121.1 117.6 123.6 28.759 0.570 0.559 0.00 5.00 3.89 3.64327 0.5835

1.086 1.348 1.454 1.723 119.3 124.3 116.4 125.6 10.505 0.783 0.729 0.00 5.45 2 3.50 3.49863 0.00

1.085 1.346 1.455 1.720 119.3 124.1 116.6 125.3 10.462 0.788 0.733 0.00 5.36 2 3.59 3.64355 0.00

1.085 1.348 1.455 1.720 119.3 124.1 116.6 125.3 10.458 0.789 0.733 0.00 5.04 2 3.91 3.64420 0.00

K. Senthilkumar, P. Kolandaivel / Journal of Molecular Structure (Theochem) 577 (2002) 69±79

Table 2 Ê , bond angle in degrees), rotational constants RA ; RB ; RC (in GHz), dipole moment mm (in Debye), chemical hardness h (in eV), chemical Geometrical parameters (bond length in A potential m (in eV), total energy E (in Hartree) and relative energy DE (in kcal mol 21) calculated by MP2 level of theory

Parameters

R(C±H) R(CyC) R(C±C) R(Cl±C) u (H±CyC) u (CyC±C) u (C±C±H) u (Cl±CyC) RA RB RC mm 2 E (1070 1 ) DE

B3LYP/6-31G p

B3LYP/6-31 1 G p

B3LYP/6-311 1 G pp

B3LYP/6-31111G pp

cis±cis

cis±trans

trans±trans

cis±cis

cis±trans

trans±trans

cis±cis

cis±trans

trans±trans

cis±cis

cis±trans

trans±trans

1.085 1.341 1.456 1.740 119.5 125.0 115.4 126.0 10.537 0.772 0.719 0.003 5.18516 0.00

1.086 1.341 1.455 1.738 120.6 121.4 114.3 125.0 7.347 0.756 0.685 2.055 5.18496 0.1255

1.086 1.340 1.456 1.738 121.6 121.5 116.9 124.1 29.012 0.564 0.554 0.000 5.18556 2 0.2510

1.856 1.344 1.457 1.739 119.4 125.1 115.5 126.0 10.533 0.770 0.717 0.003 5.19387 0.00

1.087 1.343 1.457 1.738 120.6 121.4 114.4 125.1 7.344 0.754 0.684 2.025 5.19350 0.2322

1.087 1.342 1.457 1.739 121.6 121.5 116.8 124.1 28.982 0.563 0.552 0.000 5.19397 2 0.0627

1.083 1.338 1.455 1.739 119.5 125.0 115.5 125.9 10.549 0.774 0.721 0.003 5.28694 0.00

1.084 1.337 1.455 1.738 120.7 121.4 114.3 125.0 7.343 0.758 0.687 1.956 5.28659 0.2196

1.084 1.336 1.455 1.739 121.7 121.5 116.8 124.0 29.113 0.565 0.555 0.000 5.28703 2 0.0565

1.083 1.338 1.454 1.739 119.5 125.0 115.5 125.9 10.548 0.774 0.721 0.003 5.28711 0.00

1.084 1.337 1.454 1.738 120.6 121.4 114.3 125.0 7.350 0.758 0.687 1.967 5.28675 0.2259

1.084 1.336 1.455 1.739 121.7 121.5 116.8 124.0 29.117 0.565 0.555 0.001 5.28718 2 0.0439

K. Senthilkumar, P. Kolandaivel / Journal of Molecular Structure (Theochem) 577 (2002) 69±79

Table 3 Ê , bond angle in degrees), rotational constants RA ; RB ; RC (in GHz), dipole moment mm (in Debye), total energy E (in Hartree) and relative Geometrical parameters (bond length in A energy DE (in kcal mol 21) calculated by B3LYP level of theory

73

74

Parameters

R(C±H) R(CyC) R(C±C) R(Cl±C) u (H±CyC) u (CyC±C) u (C±C±H) u (Cl±CyC) RA RB RC mm 2 E (1070 1 ) DE

B3PW91/6-31G p

B3PW91/6-31 1 G p

B3PW91/6-311 1 G pp

B3PW91/6-31111G pp

cis±cis

cis±trans

trans±trans

cis±cis

cis±trans

trans±trans

cis±cis

cis±trans

trans±trans

cis±cis

cis±trans

trans±trans

1.086 1.341 1.452 1.727 119.4 125.0 115.6 126.0 10.610 0.777 0.724 0.002 5.01961 0.00

1.087 1.341 1.452 1.726 120.5 121.3 114.5 125.0 7.429 0.760 0.690 2.023 5.01934 0.1694

1.087 1.340 1.452 1.726 121.5 121.4 117.1 124.1 29.113 0.568 0.558 0.000 5.01987 2 0.1631

1.086 1.343 1.452 1.726 119.3 125.0 115.7 126.0 10.609 0.776 0.723 0.002 5.02583 0.00

1.087 1.342 1.453 1.725 120.5 121.4 114.6 125.1 7.426 0.759 0.689 1.984 5.02541 0.2635

1.087 1.341 1.452 1.726 121.5 121.5 117.0 124.1 29.088 0.568 0.557 0.000 5.02580 0.0188

1.084 1.338 1.450 1.726 119.4 124.9 115.6 125.9 10.614 0.781 0.728 0.002 5.11463 0.00

1.085 1.337 1.450 1.725 120.6 121.3 114.5 125.0 7.422 0.764 0.692 1.901 5.11458 0.2573

1.085 1.336 1.450 1.726 121.6 121.4 117.0 124.1 29.194 0.570 0.559 0.001 5.11458 0.0314

1.084 1.338 1.450 1.726 119.4 124.9 115.6 125.9 10.613 0.781 0.728 0.002 5.11484 0.00

1.085 1.337 1.450 1.725 120.6 121.3 114.5 125.0 7.423 0.764 0.692 1.916 5.11441 0.2698

1.085 1.336 1.450 1.726 121.6 121.4 117.0 124.1 29.199 0.570 0.559 0.001 5.11476 0.0502

K. Senthilkumar, P. Kolandaivel / Journal of Molecular Structure (Theochem) 577 (2002) 69±79

Table 4 Ê , bond angle in degrees), rotational constants RA ; RB ; RC (in GHz), dipole moment mm (in Debye), total energy E (in Hartree) and relative Geometrical parameters (bond length in A energy DE (in kcal mol 21) calculated by B3PW91 level of theory

K. Senthilkumar, P. Kolandaivel / Journal of Molecular Structure (Theochem) 577 (2002) 69±79

Fig. 1. Schematic representation of the isomers of 1,4-dichlorobutadiene.

and also the order of stability among the three isomers. The cis±cis conformer is the most stable, trans±trans conformer is the least stable and cis± trans conformer is the intermediate form with the relative energies 0.46 and 0.44 kcal mol 21, respectively. Tabulated values (Table 2) show that the relative energies calculated by employing the higher basis sets also give the same results and increasing the size of the basis set leads to an increase in the relative energies. Hence, in 1,4-dichlorobutadiene, the MP2 method was able to predict the cis effect completely. The HF-SCF method could not predict the stable structure. Even with the higher basis set 631111G pp, the trans±trans conformer has been identi®ed as the most stable structure, cis±trans conformer the least stable and cis±cis, the intermediate form. The calculated relative energies are presented in Table 1. At the HF-SCF level, only the electrostatic and exchange repulsion terms are considered, which favor the trans±trans conformer

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of the 1,4-dichlorobutadiene molecule. The relative energies calculated by the hybrid DFT method B3LYP are summarized in Table 3. The tabulated values show that the B3LYP method was not able to predict the cis effect and it completely fails to determine the order of stability too. In most of the earlier studies, the B3LYP level of theory has succeeded in predicting the stability of conformers and the geometrical parameters related to the atoms having lone pair electrons, with greater accuracy [8,15]. Even with the higher basis set 631111G pp, the trans±trans conformer has been found to be the most stable form with the relative energy 20.04 kcal mol 21, cis±trans, the least stable with the relative energy 0.23 kcal mol 21 and cis±cis, the intermediate one. The same trend has also been found for SiC2 molecule, in which B3LYP theory fails to predict the stable structure [16]. The higher level hybrid DFT method B3PW91 with 6-311G p basis set predicts the stable structure, but fails to predict the order of stability even with the more ¯exible 6-31111G pp basis set. The relative energies calculated by B3PW91/6-31111G pp level of theory (Table 4) show that the cis±cis structure is more stable and the relative energy of cis±trans structure (0.27 kcal mol 21) is higher than the trans±trans structure (0.05 kcal mol 21), which is contradictory to the experimental result. In general, the failure of HF-SCF and DFT methods to predict the cis effect in 1,4-dichlorobutadiene is due to the poor prediction of geometrical parameters associated with the omission of electron correlation in HF-SCF and dispersion interaction term in DFT methods. The optimized geometrical parameters of the isomers of 1,4-dichlorobutadiene molecule employing the different levels of theory of ab initio and DFT methods are summarized in Tables 1±4. It has been observed that there is no signi®cant change in structural parameters due to increase in the size of the basis set. The difference in bond lengths between the isomers in all the levels is found to be very small. The structural parameters predicted by restricted Hartree±Fock (RHF) and DFT methods are different from the values predicted by the MP2 method. Bond lengths R(C±H), R(C±C) and R(C± Cl) calculated by the RHF method differ approxiÊ , and for R(CyC), a large difference mately by 0.01 A Ê of 0.028 A is observed. A maximum difference of

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K. Senthilkumar, P. Kolandaivel / Journal of Molecular Structure (Theochem) 577 (2002) 69±79

Table 5 Ê ) and Calculated principal moments of inertia IA ; IB ; IC (in amu A asymmetric parameter k of the isomers of 1,4-dichlorobutadiene at MP2/6-31G p level of theory Isomers

IA

IB

IC

ka

cis±cis cis±trans trans±trans

7.98 11.36 2.91

107.18 109.84 147.49

115.12 121.27 150.39

2 0.9890 2 0.9785 2 0.9992

a

Asymmetry parameter k ˆ …2B 2 A 2 C†=…A 2 C†; where A ˆ h=…8p2 IA †; etc.

Ê is observed in the case of C±Cl approximately 0.02 A bond length calculated by the B3LYP method. The B3LYP level of theory with higher basis sets 63111G pp and 6-31111G pp underestimates the CyC

Ê . The bond length, and the difference is around 0.01 A B3PW91 level of theory with higher basis set 631111G pp underestimates the CyC bond length compared to the value predicted by the MP2 method. As like B3LYP method, the B3PW91 level of theory overestimates the C±Cl bond Ê ). The length but the difference is small (0.006 A bond angles u (CyC±Cl), u (CyC±C) calculated by the RHF and DFT methods are higher than the value calculated by MP2 method and the difference is approximately 0.68. For bond angle u (C± C±H), the reverse is the case where the values calculated by RHF and DFT methods are lower than the value calculated by MP2 method, and the difference is nearly 0.88. Hence, the poor prediction of geometrical parameters by RHF and

Table 6 Calculated vibrational frequencies (cm 21) and assignments for cis±cis and trans±trans 1,4-dichlorobutadiene along with the experimental values Approximate description a

Symm. species

cis±cis

trans±trans

Calculated

Exp. b,c

Calculated

Expt. b,c

3086 3068 1612 1363 1226 726 1053 657 174

3085 3040 1625 1415 1232 733 1063 670 186

3060 3052 1615 1280 1255 804 1125 357 254

3068 3030 1625 1295 1285 825 1140 375 225

ag

g1 g2 g3 g4 g5 g6 g7 g8 g9

Sym CHt str Sym CHc str Sym CyC str Sym CHc bd Sym CHt bd Sym CCl str CC ctr Sym CyC±C bd Sym CCl bd

au

g 10 g 11 g 12 g 13

Sym CHc ¯ap Sym CHt ¯ap Sym CCl ¯ap Torsion

891 686 268 55

932 703 [320] [47]

938 725 197 80

955 760 [176] [71]

bg

g 14 g 15 g 16

Asym CHc ¯ap Asym CHt ¯ap Asym CCl ¯ap

865 751 488

913 [746] 500

885 871 312

[919] 860 270

bu

g 17 g 18 g 19 g 20 g 21 g 22 g 23 g 24

Asym CHt str Asym CHc str Asym CyC str Asym CHc bd Asym CHt bd Asym CCl str Asym CCl bd Asym CyC±C bd

3088 3071 1542 1299 1175 783 486 134

3095 3058 1574 1305 1185 777 495 [114]

3061 3057 1555 1287 1181 775 482 107

3075 3030 1572 1295 1245 810 495 [114]

a b c

Sym ˆ symmetric; asym ˆ antisymmetric with respect to center of C±C bond; str ˆ stretching; bd ˆ bending; t ˆ terminal; c ˆ central. Taken from Ref. [19]. Values given in bracket were computed in normal coordinate analysis [19].

K. Senthilkumar, P. Kolandaivel / Journal of Molecular Structure (Theochem) 577 (2002) 69±79

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Table 7 Calculated vibrational frequencies (cm 21) and assignments for cis±trans 1,4-dichlorobutadiene along with the experimental values Symm. Species a0

a b c

g1 g2 g3 g4 g5 g6 g7 g8 g9 g 10 g 11 g 12

Approximate description a

Calc.

Exp. b,c

Symm. species

CHt str CHt str Sym CHc str Asym CHc str Sym CyC str Asym CyC str CHt bd CHt bd Sym CHc bd Asym CHc bd CCl str CCl str

3077 3070 3066 3055 1610 1545 1338 1290 1230 1182 848 767

3095 3073 3037 3037 1617 1572 1365 1340 1287 1235 855 765

a0

a 00

Approximate description a

Calc.

Expt. b,c

g 13 g 14 g 15 g 16 g 17

CC str Sym CyC±C bd CCl bd CCl bd Asym CyC±C bd

1082 582 377 259 85

1090 599 395 [257] [87]

g 18 g 19 g 20 g 21 g 22 g 23 g 24

Asym CHC ¯ap Sym CHC ¯ap CHt ¯ap CHt ¯ap yCHCl (cis) yCHCl (trans) Torsion

925 866 772 697 435 165 100

950 908 810 712 452 190 [104]

Sym ˆ symmetric; asym ˆ antisymmetric with respect to center of C±C bond; str ˆ stretching; bd ˆ bending; t ˆ terminal; c ˆ central. Taken from Ref. [19]. Values given in bracket were computed in normal coordinate analysis [19].

DFT methods leads to their inability to predict the curious cis effect in 1,4-dichlorobutadiene molecule. The DFT parameters chemical hardness (h ) and chemical potential (m ) calculated by ab intio method have been presented in Tables 1 and 2. The recent studies on maximum hardness principle (MHP) indicate that the MHP could predict the stable structure and order of stability among the geometrical isomers and it could not predict the order of stability among the positional isomers [17,18]. In the present study, the chemical hardness of 1,4-dichlorobutadiene isomers has been calculated using the orbital energies obtained from RHF and MP2 methods with different basis sets. The relative energies calculated by the MP2/6-31G p level of theory predicted that the cis±cis conformer is the most stable one, but the chemical hardness is found to be maximum for the trans±trans conformer, with a small difference 0.01 eV. The MP2/6-311G p level of theory and the other higher basis sets in the same level of theory predicted that the minimum energy conformer has maximum hardness. Nevertheless, the order of stability among the isomers could not be predicted on the principle of maximum hardness. Moreover, the chemical hardness difference between the isomers is very small, and therefore, it is very dif®cult to distinguish the conformers using the chemical hardness. In addition to the level of theory, the size of the

basis sets also plays a crucial role in determining the orbital energies. In this situation, when the difference of chemical hardness values is very small among the isomers, it is very dif®cult to test the MHP, where the chemical potential and external potential are not constant. Since the relative energies calculated by the HF-SCF method completely fail to predict the cis effect, it is irrelevant to discuss the DFT parameters calculated from this method. Two of the isomers of 1,4-dichlorobutadiene, the cis±cis and trans±trans isomers have the C2h symmetry, and thus the selection rules which have been applied for vibrational fundamentals of these two isomers are the same. Table 5 gives the moment of inertia and the corresponding asymmetry parameter, k, of all the three isomers calculated from the rotational constants obtained at the MP2/6-31G p level of theory. Both cis±cis and trans±trans isomers are prolate type with a k value of 20.9890 and 20.9992, respectively. For both the isomers, the fundamental modes consist of nine in-plane vibrations of the ag symmetry, four out-of-plane vibrations of the au symmetry, three out-of-plane vibrations of the bg symmetry and eight in-plane vibrations of the bu symmetry species. Since the cis±trans isomer has Cs symmetry, the selection rule for cis±trans isomer is different from other two isomers. Although this isomer has lower symmetry than the other two

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K. Senthilkumar, P. Kolandaivel / Journal of Molecular Structure (Theochem) 577 (2002) 69±79

isomers, it has an asymmetric parameter value of 20.9785, which is close to the prolate type of symmetry. There are seventeen in-plane fundamentals belong to a 0 symmetry and the remaining seven belong to outof-plane vibrations of a 00 symmetry. Tables 6 and 7 provide the complete assignment for the fundamentals of cis±cis, trans±trans and cis±trans isomers calculated from MP2/6-31G p level of theory, respectively. It has been observed that the three isomers are stationary points in the potential energy surface without having imaginary frequencies. Although the frequencies predicted from the calculations have been compared with the experimental values [19], the majority of the assignments were secured by the application of the selection rules and standard frequency correlations. The agreement between the calculated and experimental frequencies is good. It is interesting to note that the fundamental corresponding to C±C bond torsion vibration for cis±cis isomer is small (55 cm 21) compared to the trans±trans (80 cm 21) and cis±trans (100 cm 21) isomers, which is a consequence of steric crowding in the cis±cis isomer, and leads to a minimum energy of the cis±cis isomer. The same result has been observed in the case of 1,4di¯urobutadiene molecule [2]. 4. Conclusions The higher level ab initio and DFT methods were used to study the cis effect in 1,4-dichlorobutadiene molecule. The following conclusions have been arrived: 1. The post Hartree±Fock method (MP2) could predict the cis effect present in the molecule and it can predict the order of stability as cis±cis . cis±trans . trans±trans isomers in accordance with the experimental result. 2. The RHF and B3LYP methods could not predict the cis effect and the order of stability. The B3PW91 method with 6-311G p basis set can predict the stable structure, but could not predict the order of stability even with the higher basis set 6-31111G pp. The failure of RHF and DFT methods may be due to the omission of electron correlation and dispersion interaction terms in the RHF and DFT methods, respectively.

3. The chemical hardness values calculated by MP2 method can determine the minimum energy structure, but the MHP fails to predict the order of stability. 4. The scaled vibrational frequencies calculated from second derivatives at the MP2/6-31G p level of theory agree well with the experimental values.

Acknowledgements The authors are thankful to Dr K.S. Viswanathan, RCL, Indira Gandhi Center for Atomic Research (IGCAR), Kalpakkam for allowing them to use the gaussian 94W, Revision E.1 program. One of the authors (K.S.) expresses his sincere thanks to the CSIR, New Delhi, for the award of Senior Research Fellowship. References [1] H.-G. Viche, E. Franchimont, Chem. Ber. 97 (1964) 602. [2] N.C. Craig, C.F. Neese, T.N. Nuguyen, C.M. Oertel, L. Pedraza, J. Phys. Chem. A 103 (1999) 6726. [3] D. Friesen, K. Hedberg, J. Am. Chem. Soc. 102 (1980) 3987. [4] M.W. Wong, K.B. Wiiberg, M.J. Frisch, J. Comput. Chem. 16 (1995) 385. [5] N.C. Craig, L.G. Piper, V.L. Wheeler, J. Phys. Chem. 75 (1971) 1453. È m, P.-O. Widmark, Chem. Phys. Lett. [6] O. Engkvist, G. KarlstrO 265 (1997) 19. [7] R.C. Bingham, J. Am. Chem. Soc. 98 (1976) 535. [8] P. Kolandaivel, K. Senthilkumar, J. Mol. Struct. (Theochem.) 535 (2001) 61. [9] K. Senthilkumar, P. Kolandaivel, Comput. Chem. (2001) in press. [10] C. Mùller, M.S. Plesset, Phys. Rev. A 46 (1934) 618. [11] A.D. Beke, Phys. Rev. A 38 (1988) 3098. [12] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [13] J.P. Predew, Y. Wang, Phys. Rev. B 45 (1992) 244. [14] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian Inc., Pittsburgh, PA, 1995. [15] P. Kolandaivel, N. Kuze, T. Sakaizumi, O. Ohashi, K. Lijima, J. Phys. Chem. A 101 (1997) 2873.

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