세 가지 3-Chloro-1-butene 이형태체들의 진동 Frequency 계산에 대한 DFT 합동법 적용 연구

An Application of Combining DFT Methods to Calculate the Vibrational Frequencies of All Three Conformers of 3-Chloro-1-butene

INTRODUCTION

With the availability of fast small computers and quantum mechanical calculation programs such as Gaussian-98,1 it is now possible to carry out relatively accurate calculations on molecular structure, conformational stability and vibrational frequencies. Even though the quantum mechanical calculations are very useful to predict the structural parameters and vibrational frequencies, the calculated frequencies are considerably discrepant among those obtained by different methods.2-7 Therefore, some of scientists use the scaling factors to fit the theoretical frequencies to the observed frequencies for assigning the fundamental vibrational modes of molecules.4,8 And also some of scientist believe that the higher basis set may give the better frequencies and use the time consuming very high basis set such as MP2/6-311++G(d,p). But the results were not as satisfactory as expected.4,5,9-11

Therefore, it is necessary to find the calculation method(s) that gives very close values to the observed vibrational frequencies. For this purpose we performed forty-two sets of frequency calculations employing BLYP, B3LYP and MP2 methods on 3-chloro-1-butene. Because the 3-chloro-1-butene gives frequencies from three kinds of conformations.4 Therefore, this molecule will be the one of the best molecule as the representative one to find the best basis set for vibrational frequency calculation. The results of this study are reported herein.

 

CALCULATIONS

In this study all the calculations were carried out using the Gaussian-98 program1 using Gaussian-type functions. The energy minima with respect to the nuclear coordinates were obtained by the simultaneous relaxation of all the geometrical parameters of molecule using the gradient method of Pulay.12 The frequency calculations were performed analytically for the optimized structures of the conformer with the double bond eclipsing the H6 hydrogen atom (HE; Fig. 1) of 3-chloro-1-butene using the BLYP/6-31G and BLYP/6-311G basis sets, which are known as good methods for the frequency calculation2, including twelve kinds of depolarization functions of (d), (d,p), (d,2p), (d,3p), (2d), (2d,p), (2d,2p), (2d,3p), (3d), (3d,p), (3d,2p) and (3d,3p), respectively. And then the + and ++ diffuse functions were employed at the level of BLYP/6-31G and BLYP/6-311G respectively with the depolarization functions of (d), (d,3p) and (2d) that gave the least discrepant frequency differences. Finally the three basis sets that gave the best results among thirty-six BLYP calculations have been taken and with theses three basis sets the B3LYP and MP2 methods to obtain the optimized structures and frequencies for all three conformations of molecule have been performed. The percent discrepancies (Δ%) and standard deviations (σ) between the calculated and observed frequencies are listed in Table 1.

Fig. 1.Structural model and atom numbering of the HE form of 3-chloro-1-butene.

Table 1.a‘All’ refers to all fundamental modes of molecule excepting asymmetric torsion, ‘Light’ to fundamentals related to hydrogen atom(s) including C=C stretch and ‘Heavy’ to fundamentals related to heavier atoms including =CH bend (υ24) of 3-chloro-1-butene. The asymmetric torsion is not counted for Δ% and σ for the ‘All’, ‘Light’ and ‘Heavy’. bPercent difference between the calculated and observed frequencies as υcalc.-υobs.· cStandard deviation.

 

RESULT AND DISCUSSION

In Table 1 the Δ% and σ the BLYP/6-31G(d) basis set gives best result with -0.53% discrepancy for all of the fundamental frequencies exception an asymmetric torsion for the HE form of 3-chloro-1-butene. The BLYP/6-31G(d,3p) and B3LYP/6-31G(d) give 0.01% of Δ% for modes related to the hydrogen(s) and C=C stretch (‘Light’) and the heavier atoms and =CH bend (υ24) which has more potential energy distribution value of CCl stretch4 (‘Heavy’), respectively. The calculated and observed frequencies including differences (Δυ and Δ%) and standard deviations (σ) are listed in Table 2.

At the BLYP/6-31G(d) level calculation the D% excepting asymmetric torsion exist from -8.2 to 2.5% region and the total average error is -0.53%. And the average error for the ‘Light’ is 0.83% and for the one that related to the ‘Heavy’ is -4.09%. On the other hand the Δ% at the BLYP/6-31G(d,3p) exist from -8.6 to 2.2% regions and the total average error is -1.29% and the average error for the ‘Light’ is 0.01% and for the ‘Heavy’ is -4.71%. And at the B3LYP/6-31G(d) the Δ% exist from -1.9 to 5.3% region and the total average error is 2.84% and the average error for the ‘Light’ is 3.91% and for the ‘Heavy’ is 0.01%. These result clearly show that the BLYP/6-31G(d,3p) gives the best frequencies for the ‘Light’ modes of HE conformer of 3-chloro-1-butene and the B3LYP/6-31G(d) does for the ‘Heavy’ ones. Therefore, with combining the frequencies from the BLYP/6-31G(d,3p) and the B3LYP/6-31G(d) for the ‘Light’ and ‘Heavy’ modes the total average error comes down from -1.29 and 2.84, respectively, to 0.01% with standard deviation 1.60%. With this error and standard deviation the calculated frequencies are in excellent agreement with the observed ones (Table 2).

Table 2.a‘All’ refer to the all modes; ‘Light’ to the modes related to the H atom(s) and C=C stretch; ‘Heavy’ to the modes related to the heavier atoms and =CH bend (υ24). ‘All’, ‘Light’ and ‘Heavy’ all together not include the asymmetric torsion. bTaken from reference 4 and frequencies are in cm−1. cFrequency difference between the calculated and observed frequencies as υcalc.-υobs.· dPercent difference between the calculated and observed frequencies as υcalc.-υobs.· eValues for the ‘Light’ are taken from BLYP/6-31G(d,3p) and those for the ‘Heavy’ from B3LYP/6-31G(d).

Table 3.a‘All’ refer to the all modes; ‘Light’ to the modes related to the H atom(s) and C=C stretch; ‘Heavy’ to the modes related to the heavier atoms and =CH bend (υ24). ‘All’, ‘Light’ and ‘Heavy’ all together not include the asymmetric torsion. bTaken from reference 4 and frequencies are in cm−1. cFrequency difference between the calculated and observed frequencies as υcalc.-υobs.· dPercent difference between the calculated and observed frequencies as υcalc.-υobs.· eValues for the ‘Light’ are taken from BLYP/6-31G(d,3p) and those for the ‘Heavy’ from B3LYP/6-31G(d).

Table 4.a‘All’ refer to the all modes; ‘Light’ to the modes related to the H atom(s) and C=C stretch; ‘Heavy’ to the modes related to the heavier atoms and =CH bend (υ24). ‘All’, ‘Light’ and ‘Heavy’ all together not include the asymmetric torsio bTaken from reference 4 and frequencies are in cm−1. cFrequency difference between the calculated and observed frequencies as υcalc.-υobs.· dPercent difference between the calculated and observed frequencies as υcalc-υobs.· eValues for the ‘Light’ are taken from BLYP/6-31G(d,3p) and those for the ‘Heavy’ from B3LYP/6-31G(d).

With these BLYP/6-31G(d,3p) and B3LYP/6-31G(d) basis sets the frequency calculations for the higher energy conformers, the conformer with the double bond eclipsing the methyl group (ME) and the conformer with the double bond eclipsing the chlorine atom (ClE), of 3-chloro-1-butene also carried out and the results are listed in Table 3 and 4. The error, Δ%, of the ‘Light’ modes at the BLYP/6-31G(d,3p) obtained as -0.70 and -0.91% and the Δ% of the ‘Heavy’ ones at the B3LYP/6-31G(d) as 0.65 and 0.34% for the ME and ClE form, respectively. By applying the combining method for the ME and ClE the Δ%s for all modes come down to -0.16 and -0.37%, respectively. And we found most of the calculated frequencies with this combing method of all three conformers are in fairly good agreement with the observed ones within about ±2% errors with exception of those of CCC bend and two CCl bends of ME form. Therefore, the combing the frequencies from BLYP/6-31G(d,3p) and B3LYP/6-31G(d) will be very useful to predict and assign the vibrational frequencies of molecules such as 3-chloro-1-butene. And it would be interest to reassign the CCC bend and two CCl bends of ME conformer of 3-chloro-1-butene using the frequencies from the B3LYP/6-31G(d) calculation.

Table 5.aTaken from reference 4.

The enthalpy differences, ΔH, among the HE, ME and ClE conformers of 3-chloro-1-butene in the vapor phase were also estimated from the BLYP/6-31G(d), BLYP/6-31G(d,3p) and B3LYP/6-31G(d). The ΔH values between the HE and ME form were obtained of 390 cm−1 (4.67 kJ/mol), 320 cm−1 (3.83 kJ/mol) and 353 cm−1 (4.22 kJ/mol) and those between the HE and ClE form were 685 cm−1 (8.19 kJ/mol), 600 cm−1 (7.18 kJ/mol) and 565 cm−1 (6.76 kJ/mol) with the HE being the most stable form from the BLYP/6-31G(d), BLYP/6-31G(d,3p) and B3LYP/6-31G(d), respectively (Table 5). These values are not significantly different from those obtained from the MP2/6-31G(d) and MP2/6-311++G(d).4

The structural parameters obtained from the BLYP/6-31G(d), BLYP/6-31G(d,3p) and B3LYP/6-31G(d) calculations are not significantly different from those experimentally obtained by electron diffraction (see Table 6).13 At the B3LYP/6-31G(d) level, the C-C and C-Cl bond lengths are about 0.6 and 1.8% shorter, respectively, than those at the BLYP/6-31G(d,3p) and closer to those of electron diffraction. The C-H bond lengths at the BLYP/6-31G(d,3p) are about 0.5% longer than those at the B3LYP/6-31G(d). This could explain the reason why the B3LYP/6-31G(d) gives the better frequencies of fundamentals on heavier atoms and the BLYP/6-31G(d,3p) gives the better frequencies of fundamentals related to hydrogen(s).

Table 6.aBond length in Å, bond angle in degrees, rotational constant (A, B, C) in MHz, dipole moment (μ) in Debyes and energy (E) in Hartrees. bFor the definition of atom numbers, see Fig. 1. cReference 13.

By utilizing combining density functional calculations with the BLYP/6-31G(d,3p) and B3LYP/6-31G(d) basis sets, we have found an excellent agreement between the calculated vibrational frequencies and those obtained experimentally for the 3-chloro-1-butene. Therefore, it is believed that the very high basis set, such as 6-311++G(d,3p), is not necessary to predict frequencies of this molecule and the combining method with the BLYP and B3LYP employing not a very high basis set, such as BLYP/6-31G(d,3p) and B3LYP/6-31G(d), can be valuable assigning the fundamental modes of 3-chloro-1-butene. And we found the combining technique presently discussed provides excellent estimates for the vibrational frequencies from the low to the high frequency modes of this molecule.