Potential energy surface study on glycine, alanine and their zwitterionic forms

Journal of Molecular Structure (Theochem) 671 (2004) 77–86 www.elsevier.com/locate/theochem

Potential energy surface study on glycine, alanine and their zwitterionic forms P. Selvarengan, P. Kolandaivel* Department of Physics, Bharathiar University, Coimbatore 641 046, India Received 5 July 2003; revised 5 July 2003; accepted 23 October 2003

Abstract The conformational stability of Glycine, Alanine and their zwitterionic forms have been studied using density functional theory (DFT) methods. The conformers have been predicted by the Potential energy surface scan employing the DFT methods, B3LYP, B3PW91 and B3P86 implementing 6-311þ þG** basis set. The rotational potential energy curves for neutral molecules and zwitterionic form have been determined at the above levels of theory. The Fourier decomposition potentials were analysed for the above molecules. The B3LYP level of theory predicts conformer 1 as the most stable one, but B3PW91 and B3P86 levels of theory have predicted conformers 2n, 2b for glycine and alanine respectively. The chemical hardness calculated at the HF/6-311þþ G** level of theory shows that the Maximum hardness principle fails to predict the conformational stability for hydrogen bonded systems. q 2004 Elsevier B.V. All rights reserved. Keywords: Glycine; Alanine; Zwitterions; Potential energy surface; Maximum hardness principle

1. Introduction Amino acids are an attracting target for computational chemists due to their variety of intramolecular interactions and moreover, they are conformationally flexible molecules. The experimental [1 –9] and theoretical studies [7 – 23] on the conformational behaviour of the amino acids, is not straightforward procedure. The different dipole moments of the stable rotamers and intramolecular interactions complicate the determination of the relative stabilities. The joint analysis of electron diffraction and microwave data [4] can provide a reasonable molecular structure for the different conformations of amino acids. Since most of the amino acids are found to be in the lower symmetry, they have many internal rotational degrees of freedom which leads to more number of conformations and the steric strain and repulsion of lone pair of electrons of N and O atoms which have a destabilization effect. So, it is a challenging problem to the theoretical chemists to predict the different conformations of the amino acids. * Corresponding author. Tel.: þ 91-422-2422222; fax: þ 91-4222422387. E-mail address: [email protected] (P. Kolandaivel). 0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2003.10.021

For the past three decades experimentalists and theoreticians are very much interested to study the conformational behaviours of the amino acids. Hu et al. [20] and Csa´sza´r [13,15] have reported the conformations of few amino acids using the high level ab initio calculations in which extensive correlation functions have been used. Many experimentalists [1 – 8] and theoreticians [10 – 21,23] have determined the conformations of glycine and alanine molecules. Some of the lower levels of the ab initio theory have predicted only less number of conformations for glycine and alanine molecules. Palla et al. [11] have made the comparative study using classical semiempirical and non-empirical methods to map the rotational energy surface of glycine and concluded that “if one compare numerical values of the relative depth of the potential holes and of the rotational barriers (of glycine), the accordance among the various methods vanishes almost completely”. Jensen and Gordon [12] have shown that the potential energy surface of glycine is not well reproduced by STO-2G, AM1 or PM3 methods. Csa´sza´r [13] have studied thirteen conformations obtained from PES of glycine molecule using correlated level ab initio calculations and predicted eight minimum energy conformers. Barone et al. [14] have examined the conformational behaviour of gaseous glycine molecule using the density functional theory (DFT), for their study,

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they considered only nine conformers. Among the nine conformers, five are planar heavy atom arrangement and four are nonplanar heavy atom arrangement and concluded that DFT methods produce results close to the most sophisticated Hartree –Fock methods. Stephanian et al. [7] have determined the molecular structure using the low temperature matrix isolation technique for glycine isolated in solid argon leads to identification of three low energy conformers of glycine. The three possible substitutions of methyl group in glycine lead to a-alanine. The gaseous electron diffraction experimental studies indicate the lowest energy form have a bifurcated H-bond between NH2 and carbonyl group. Godfrey et al. [16] have reported the molecular parameters for six conformers of alanine. Gronert and Hair [17] have reported ten conformers of alanine at HF and MP2 level of calculations. Cao et al. [19] again determined the 13 conformers for the alanine molecules. Stephanian et al. [8] have studied the a-alanine isolated in solid argon using the low temperature matrix isolation technique to study the structure of two conformations of a-alanine molecule. They have also used DFT-B3LYP method for the spectral characterization of glycine and a-alanine and reported the DFT results appeared to be even more accurate than the MP2 results. Csa´sza´r [15] have reported thirteen conformations for alanine molecules using ab initio and density functional theory (B3LYP) methods. The conformers were built up from the eight conformers of glycine corresponding to minima on its potential energy surface. So all the previous DFT studies could not predict eight conformers of glycine and the thirteen conformers of a-alanine from their respective PES, which were predicted by the ab initio methods. The DFT have reached a level of reliability and competitive with most sophisticated Post Hartree –Fock methods for a number of properties of the molecule. Recently, there have been excellent progress have been achieved in the exchange and correlation functions, which are giving quiet promising results in the molecular properties. The aim of the present study is try to locate as many as conformations using the DFT using the potential energy surfaces governing the conformational transitions. For the above purposes different exchange correlation functionals have been used and tested the validity of DFT functional in the low energy conformers. We have made the rotational analysis through Ca –N, Ca – C and C –O bond to locate all the conformers and we tried to find which potential function is more valid in this process. For the past few years, the chemical hardness and chemical potential have been used to study the conformational stability of the molecules. The more number of low energy conformations of alanine and glycine is one of the challenging problems for the chemical hardness to predict the stability of a molecule and it is a good problem to test the maximum hardness principle in these conformers. Further, the most stable conformer of zwitterions of the glycine and alanine has been studied using the B3LYP level of theory.

2. Computational details The different conformers of glycine and alanine molecules have been studied by the Potential energy surface scan using the DFT methods. The main chain torsional angles (HNCaC and NCaCO) are varied in steps of 308 between 08 and 3608 generating 169 points. The geometries were optimized for all the minimum energy conformers at the B3LYP, B3PW91 and B3P86 levels of theory implementing the 6-311þ þ G** basis set. For the zwitterionic form, all the calculations have been performed using B3LYP level of theory with same basis set employed in the neutral form. In DFT methods, Becke’s three parameter hybrid functional [24] combined with gradient corrected functional of Lee, Yang and Parr (LYP) [25], Becke’s three parameter hybrid functional with Perdew and Wang’s 1991 gradient corrected correlation functional (PW91) [26] and Becke’s three parameter hybrid functional with Perdew 86 gradient corrected correlation functional (P86) [27] were used with implementing the 6-311þ þ G** basis set. To derive the potential function for the internal rotation of neutral glycine and alanine molecules along with the zwitterionic form, the six-term truncated Fourier expansion [28] were considered. The potential function, VðaÞ may be given as, X VðaÞ ¼ 1=2VNi ð1 2 Cos iN aÞ i

where a is the angle of rotation and N represents the degree of symmetry of the molecule. The potential energy function VðaÞ describing the internal rotation of one part of a molecule (rotor) relative to the remainder (frame work). The conformational stability of the molecules have been studied using the Chemical hardness, which have been calculated using the EHOMO and ELUMO energy calculated at HF/ 6-311þ þ G** level of theory. All the calculations have been performed using GAUSSIAN 98W program package [29].

3. Results and discussion Table 1 contains the selected optimized geometrical parameters of conformer 1 of neutral glycine and alanine molecules calculated at B3LYP/6-311þ þ G**, B3PW91/ 6-311þ þ G** and B3P86/6-311þ þ G** levels of theory along with the available experimental results [4,30]. It has been noticed that all the levels of theory underestimate the bond lengths Ca – N and H – N and at the same time they have predicted the CyO and O –H bond lengths very accurately as like the high level ab initio method. The CCaN bond angle in glycine is smaller by , 28 from the experimental values and in alanine it is higher by , 3:58 at all the levels of theory. This is due to the presence of lone pair electrons in nitrogen atom, which causes difficulty in determining the bond lengths Ca –N and H – N, and bond angles in ab initio and DFT methods. The same has been confirmed in the earlier studies [31] also, but the DFT

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Table 1 ˚ , bond angle in degrees) for the most stable conformer (I) of glycine and Selected theoretical and experimental geometrical parameters (bond lengths in A a-alanine Geometrical parameters

Ca –N CyO O –H N –H N–Ca –C a b c

Glycine

Alanine

B3LYP

B3PW91

B3P86

MP2a

Expt.b

B3LYP

B3PW91

B3P86

MP2a

1.448 1.205 0.969 1.015 115.98

1.443 1.204 0.968 1.014 115.91

1.441 1.203 0.968 1.014 115.86

1.447 1.209 0.968 1.014 115.6

1.466 1.204 0.966 1.001 113.0

1.455 1.206 0.969 1.015 113.59

1.449 1.205 0.968 1.014 113.56

1.447 1.204 0.968 1.014 113.53

1.452 1.211 0.968 1.016 113.7

Expt.c 1.471 1.192 – – 110.1

6-311þ þG** basis set have been used for all theoretical calculations. From Ref. [18]. From Ref. [4]. From Ref. [30].

methods predicted the above bond lengths and bond angles much better than the ab initio methods. The geometrical parameters calculated by the B3LYP level of theory are somewhat closer to the available experimental results and at the same time the results of B3PW91 and B3P86 levels of theory are closer to the available theoretical results [13]. In summary all the theoretical studies indicate that the introduction of methyl group for alanine to replace one of the hydrogens of glycine have rather small effect on the geometry of the alanine. The accuracy of the geometrical parameters of a molecule depends on the performance of the exchange and electron correlation functional that have been used in the DFT methods. In order to find all the conformers of glycine and alanine, which were predicted by the high level ab initio computations, the different levels of theory of DFT methods have been used for the potential energy surface scan and the results are presented in the Table 2. Figs. 1 and 2 shows all

the conformers of glycine and alanine molecules, which were available in the literature [21], and Fig. 3 shows the zwitterionic forms of glycine and alanine considered in this study. The numbering of the conformers in Table 2 as given by Csa´sza´r in Ref. [21]. Fig. 4 shows that the potential energy surface map computed at B3LYP level of theory, and these conformers except 3n and 7p are present in glycine and, in alanine 3b and 7 are not found in all the levels of theory except 3b is found in B3P86 level of theory. The DFT functionals considered in this study, could not predict the conformers 3n and 7p in glycine, that are the minimum energy structures predicted by MP2 method [13]. The B3LYP level of theory has predicted the conformer 1 as the most stable structure for glycine and predicts the order of stability as 1 . 2n . 2p . 4n . 3p . 5n . 4p . 5p . 6 . 8n . 8p and the order of stability predicted at MP2 (full) is 1 . 2n . 2p . 4n . 3n . 3p . 5n . 4p . 5p . 6 . 7 . 8n . 8p and for alanine, the order of stability predicted at B3LYP level

Table 2 Relative energies (in kcal/mol) for the conformers predicted at the PES of glycine and alanine Conformers

Glycine

Alanine

B3LYP

B3PW91

B3P86

HF

h

B3LYP

B3PW91

B3P86

HF

h

1 2a 2b 3a 3b 4a 4b 5a 5b 6 7 8a 8b

0.00 0.43 0.43 * 1.52 1.45 4.49 2.67 4.96 5.62 * 7.09 10.75

0.00 20.03 20.03 * 1.53 1.48 4.63 2.84 5.04 5.55 * 7.03 10.85

0.00 20.23 20.23 * 1.53 1.42 4.66 2.81 5.05 5.59 * 6.98 10.92

0.00 2.83 2.98 1.86 1.91 1.60 4.94 2.61 5.56 6.59 8.40 8.31 12.36

6.11 6.16 6.09 5.98 5.99 5.99 5.93 6.01 5.93 6.04 5.92 5.96 5.86

0.00 0.03 0.02 1.07 * 1.31 1.46 1.98 2.25 5.72 * 6.93 6.94

0.00 20.51 20.58 1.15 * 1.34 1.50 2.15 2.41 5.60 * 6.83 6.76

0.00 20.72 20.80 1.18 1.25 1.29 1.39 2.06 2.42 5.64 * 6.79 6.62

0.00 2.42 2.48 1.20 1.47 1.55 1.66 1.85 2.19 6.72 8.05 8.26 8.54

6.06 6.14 6.11 5.96 5.96 5.95 5.94 5.98 5.97 6.01 5.89 5.93 5.93

Ea

2284.52961

2284.41685

2285.24066

2282.92502

2323.85608

2323.72869

2324.71342

2321.97093

*–not found; for glycine ‘a’ refers to nonplanar, ‘b’ refers to planar structure. 6-311þþ G** basis set have been used for all the levels of theory. Chemical hardness h (in eV) calculate at HF level of theory. a Total energy E (in hartrees) refers to the conformer (1).

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Fig. 1. Conformers of glycine available in the literature.

of theory is 1 . 2b . 2a . 3a . 4a . 4b . 5a . 5 b . 6 . 8b . 8a and Cao et al. [18] predicted the order of stability for alanine as 1 . 2b . 2a . 3a . 3b . 4a . 4 b . 5a . 5b . 6 . 7 . 8a . 8b in ab initio theory. So the order of stability for glycine and alanine predicted at B3LYP level of theory is similar to the earlier results. But B3P86 and B3PW91 levels of theory have predicted the second stable conformer in B3LYP is the most stable conformer in both the molecules. These results are not surprising, because the difference in energy between the conformers is very small so it is very difficult to distinguish these types of conformers in

these levels of theory. More sophisticated exchange and correlation functionals to be developed to solve the low energy barrier problem. So, again, the DFT methods have predicted only six minimum energy conformers (1, 2n, 4n, 5n, 6p, 8n) for glycine out of eight and eleven conformers (1, 2a, 2b, 3a, 4a, 4b, 5a, 5b, 6, 8a, 8b) for alanine molecules out of thirteen conformers were predicted by the ab initio method and earlier DFT studies. It is an important problem and one should be very careful to choose the DFT functional and basis sets for the biomolecules. The present system is a good platform to test the DFT functionals. The B3P86 level of theory have predicted

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81

Fig. 2. Conformers of a-alanine available in the literature.

one more conformer 3b for the alanine molecule. So the present levels of theory are found to be suitable for these types of conformations. The relative energies of the conformers arises due to the rotation of Ca – N, Ca – C and C – O, of neutral glycine and alanine molecules, the Ca –N, Ca –C bond rotation of

the zwitterionic form of these molecules at different torsional angles computed at B3LYP, B3PW91 and B3P86 levels of theory are shown in Tables 3 and 4. The study has been restricted to B3LYP level of theory for zwitterionic form to save the computer time. Since the zwitterionic form is not found minimum energy in

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Fig. 3. Zwitterionic form of glycine and alanine conformer is taken in this study.

the potential energy surface in the gas phase, the study has been performed only for the comparative purpose. First, we considered the rotation around the Ca – N bond in neutral glycine where the dihedral angle D3(NCaCO) and D5(HOCO) are fixed and D6(HNCaC) is varied from 0 to 1808. The minimum energy structure has been obtained at D6 ¼ 608 and the rotational barrier is 3.74 kcal/mol at B3LYP level of theory. The barrier height computed at HF level of theory is 8.1 kcal/mol., which is higher when compared with the DFT methods. The barrier heights predicted at the B3P86 and B3PW91 levels of theory in glycine are 3.86, 3.85 kcal/mol, respectively. The high level

ab initio and experimental methods have predicted the conformer, which have a planar heavy-atom structure and a bifurcated hydrogen bridge between the hydrogen atoms of the amino group and the oxygen atom of the carbonyl group is the minimum energy structure of neutral glycine in gas phase. The B3LYP/DZP and B3LYP/TZ2P levels of theory of DFT methods have also determined the same conformer as the most stable one [14]. But the other DFT methods BLYP/DZP and LDA/DZP levels of theory favour the other conformer as the most stable structure, which contrasts all the theoretical methods. The standard functionals of DFT overestimate the electron energy. The Gradient corrections

Fig. 4. Potential energy surfaces of glycine and alanine computed at B3LYP/6-311þ þ G** level of theory.

Table 3 Relative energies (in kcal/mol) of Ca –N, Ca –C and C –O rotations on most stable conformer of glycine at different torsional angles Torsional angles

Ca –N

Ca –C

C–O

B3PW91

B3P86

ZWa

B3LYP

B3PW91

B3P86

ZWa

B3LYP

B3PW91

B3P86

0 30 60 90 120 150 180

2.184 0.734 0.000 0.822 2.271 3.263 3.740

2.165 0.709 0.000 0.816 2.271 3.294 3.846

2.096 0.678 0.000 0.784 2.215 3.263 3.859

0.000 1.625 2.968 4.053 4.411 3.759 3.244

0.000 0.847 2.366 2.817 2.196 1.958 2.102

0.000 0.885 2.516 3.056 2.378 2.014 2.115

0.000 0.910 2.585 3.131 2.435 2.020 2.083

1.412 1.393 6.287 9.500 7.737 3.815 0.000

6.601 8.295 12.179 13.635 9.450 3.018 0.000

6.475 8.251 12.292 13.829 9.581 3.050 0.000

6.519 8.289 12.355 13.911 9.990 3.093 0.000

Eb

2284.52960

2284.41685

2285.24066

2284.54580

2285.52960

2284.41685

2285.24066

2284.54580

2284.52960

2284.41685

2284.24066

a b

Gas phase Zwitterionic forms computed at B3LYP level of theory. Total energy E in hartrees.

Table 4 Relative energies (in kcal/mol) of Ca –N, Ca –C and C –O rotations on most stable conformer of alanine at different torsional angles Torsional angles

Ca –N

Ca –C

C–O

B3LYP

B3PW91

B3P86

ZWa

B3LYP

B3PW91

B3P86

ZWa

B3LYP

B3PW91

B3P86

0 30 60 90 120 150 180

1.989 0.000 0.571 2.742 4.656 5.716 7.461

1.933 0.000 0.628 2.868 4.844 5.973 7.787

1.933 0.000 0.665 2.980 4.988 6.118 7.937

3.589 3.175 2.591 2.861 1.537 0.439 0.000

0.000 3.909 6.607 5.616 3.156 1.994 2.830

0.000 3.903 6.657 5.748 3.288 2.071 2.880

0.000 3.928 6.739 5.873 3.407 2.115 2.868

0.069 4.505 8.320 10.065 6.814 0.671 0.000

6.795 8.841 12.775 13.955 9.381 2.780 0.000

6.613 8.709 12.813 14.112 9.519 2.842 0.000

6.620 8.703 12.819 14.143 9.556 2.855 0.000

Eb

2323.78685

2323.65720

2324.64142

2323.86327

2323.78523

2323.65548

2324.63967

2323.86101

2323.85606

2323.72867

2324.71341

a b

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B3LYP

Gas phase Zwitterionic forms computed at B3LYP level of theory. Total energy E in hartrees.

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to the correlation function improve the accuracy of the energy. The different correlation functionals combined with the exchange functionals have been used in the present study to arrive a conclusion about the functionals in the bio molecules. In alanine molecule, the barrier heights have been measured for Ca – N rotation, and the values are 7.46, 7.79 and 7.94 kcal/mol at B3LYP, B3PW91 and B3P86 levels of theory, respectively. The minimum energy structure exists at D6 ¼ 08 and for alanine zwitterions, the minimum energy exists at D6 ¼ 1808 at B3LYP level of theory. We again considered the rotation around the Ca –C bond in glycine ðD6; D5 are fixed and D3 ¼ 0 – 1808Þ: The most stable structure exists at 08 and the barrier height computed at B3P86 level of theory is 3.13 kcal/mol which is found to be the maximum among all the three levels of theory, the lowest one is B3LYP level of theory (2.82 kcal/ mol) which exist at D3 ¼ 908: So these results are comparable with the available theoretical results. For alanine, the minimum energy structure exists at D3 ¼ 08 and the barrier height is maximum at 608 and the values are 6.61, 6.66 and 6.74 kcal/mol at B3LYP, B3PW91 and B3P86 levels of theory, respectively. For the zwitterionic form of glycine, the minimum energy exists at D3 ¼ 1808 and the barrier energy is maximum, 12.16 kcal/mol at B3P86 level of theory and for alanine, it is 3.59 kcal/mol at D3 ¼ 08: This large value of the barrier energy shows that these molecules could not have free internal rotation about the Ca – C bond due to attractive interaction between the 2 hydrogen atom in – NHþ 3 and oxygen atom in –CO group. For the C – O bond rotation ðD3; D6 fixed and D5 ¼ 0 – 1808Þ the minimum energy exists at 1808. The barrier height is found to be higher than Ca – N, Ca – C bond rotations. It is computed at B3LYP, B3PW91 and B3P86 levels of theory and the values are 13.64, 13.83 and 13.91 kcal/mol, respectively. For alanine, the barrier height is computed at the above levels of theory and the values are 13.96, 14.11, and 14.14 kcal/mol, respectively. This increase in values may be due to the presence of hydrogen bonding interaction between the amine and carboxyl groups. During this intramolecular interaction, oxygen atom in the carboxyl group strongly interacts with hydrogen in amine

group, which may restrict the free internal rotation of CO group. This type of bond rotation does not exist in zwitterionic form. In Tables 3 and 4 it has been noticed that the total energy of the most stable structure is same in all the bond rotations (Ca –N, Ca –C and C – O) for glycine, where as for alanine, it could not so, due to the nonplanarity of the structure. In glycine, the most stable conformer is planar, but for alanine all the heavy atoms does not arrange in an exact plane. During the scanning process, the torsional angle between 0 and 1808 and the step size 308 has been used and the total energy for the most stable structure of alanine is obtained for all the bond rotations. The six term potential coefficients V1 – V6 for the conformers of glycine and alanine molecules have been calculated at B3LYP, B3PW91 and B3P86 levels of theory along with the zwitterionic form computed at B3LYP level of theory are shown in Tables 5 and 6. The potential energy function for the internal rotation can be obtained by fitting the energies calculated for different conformational positions to a truncated Fourier expansion. The rotation of Ca –N bond from 0 to 1808 in glycine and alanine shows that V1 potential is found to have maximum value. This may be due to the interaction between –NH2 and CyO group. In the Ca –C bond rotation the V2 potential is found to have maximum value in both neutral and zwitterionic forms. This may be due to the repulsive interaction of nitrogen lone pair with the n-lone pair electrons of the carboxyl group. The rotation around the C–O bond shows that V2 potential has the larger value due to the presence of repulsive force between –OH and – CaH2 groups. Similar type of trends has been observed at all levels of theory. The obtained potential curves of glycine and alanine molecules show that, the V1; and V2 coefficients significantly contribute to the torsional potentials. The conformational stability of the molecule has been studied using Maximum hardness principle. The chemical hardness is defined as
 h ¼ 1=2 d2 E=dN 2 VðrÞ

where E is the total energy: VðrÞ is the external potential, and N is the number of electrons, in a finite difference

Table 5 Fourier fitted torsional potentials of Ca –N, Ca – C and C –O bond rotations of glycine Potential coefficientsa

V1 V2 V3 V4 V5 V6 a b

Ca –N

Ca – C b

C–O b

B3LYP

B3PW91

B3P86

ZW

B3LYP

B3PW91

B3P86

ZW

B3LYP

B3PW91

B3P86

3.453 21.268 20.268 0.289 0.555 0.220

3.532 21.316 20.232 0.266 0.547 0.208

3.517 21.339 20.190 0.243 0.532 0.194

2.794 2.286 0.119 0.471 0.330 0.145

1.285 1.763 0.814 20.123 0.003 0.003

1.311 1.997 0.797 20.144 0.007 0.001

1.285 2.089 0.795 20.132 0.003 0.000

1.882 9.272 20.967 0.077 20.915 0.228

23.956 12.528 1.820 1.891 2.137 1.106

23.907 12.744 1.807 1.839 2.100 1.086

23.897 12.819 1.795 1.859 2.102 1.092

6-311þ þG** basis set have been used in all the levels of theory. In kcal/mol. Gas phase Zwitterionic forms computed at B3LYP level of theory.

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Table 6 Fourier fitted torsional potentials of Ca –N, Ca –C and C –O bond rotations of Alanine Potential coefficientsa

V1 V2 V3 V4 V5 V6 a b

Ca –N

Ca –C b

C–O b

B3LYP

B3PW91

B3P86

24.631 12.815 2.263 1.956 2.368 1.340

24.475 13.004 2.196 1.887 2.289 1.111

24.464 13.034 2.175 1.882 2.289 1.109

B3LYP

B3PW91

B3P86

ZW

B3LYP

B3PW91

B3P86

ZW

3.032 1.305 21.031 0.561 20.011 0.147

3.180 1.429 21.002 0.605 20.001 0.150

3.252 1.539 20.991 0.623 20.001 0.155

21.931 2.079 0.703 0.673 1.228 0.782

21.302 1.201 0.561 0.377 0.980 0.287

21.221 4.196 3.206 0.514 0.895 0.112

21.201 4.327 3.177 0.525 0.892 0.112

22.716 10.029 1.004 0.060 1.712 0.036

6-311þ þG** basis set have been used in all the levels of theory. In kcal/mol. Gas phase Zwitterionic forms computed at B3LYP level of theory.

approximation, with the assumption that the energy varies quadratically with the number of electrons. This can be expressed with an orbital basis as

h ¼ ðI 2 AÞ=2 where I is the ionization potential and A is the electron affinity of a system. By applying the above equation, the chemical hardness is computed for the different conformers of glycine and alanine using HF/6-311þ þ G** basis set. The calculated values are tabulated in Table 2. The hardness values for the various torsional angle ðD3 and D6Þ are plotted in a 3D map and it is

given in Fig. 5. The chemical hardness value for the most stable conformer of alanine and glycine is 6.06 and 6.11 eV, respectively. These values are found to be less than the predicted maximum value. The maximum hardness value is obtained for conformer 2a (6.14 eV) of alanine, conformer 2n (6.16 eV) for glycine. According to the chemical hardness values the order of stability for glycine is 2n . 1 . 2p . 6 . 5n . 4n . 3p . 3n . 8n . 4p . 5 p . 7 . 8p and for alanine is 2a . 2b . 1 . 6 . 5a . 5 b . 3a . 3b . 4a . 4b . 8a . 8b . 7. So in these isomers, the MHP could not predict the most stable structure. The reason behind is, that glycine and alanine

Fig. 5. Hardness map for glycine and alanine computed at HF/6-311þþ G** level of theory.

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amino acids have variety of hydrogen bonding interaction in the conformers. This hydrogen bonding plays a major role for the molecular stability, and Chemical hardness values of a molecule depend on the strength of the hydrogen bonding. Due to the presence of the hydrogen bonding, the highest occupied molecular orbital and lowest unoccupied molecular orbital are strongly affected. If the hydrogen bond strength is high, the hardness value is high and it will decrease as the strength of hydrogen bonding decreases.

4. Conclusions The DFT methods have been used to study the conformational stability of the glycine and alanine molecules. The molecular geometries were optimized at the B3LYP/6-311þ þ G**, B3PW91/6-311þ þ G** and B3P86/6-311þ þ G** levels of theory. The 3D potential energy surface maps were drawn by varying wðD6Þ and cðD3Þ dihedral angles at the above levels of theory. B3LYP level of theory has predicted the most stable structure which is also the most stable structure in all high level ab initio theory, but other levels of theory have predicted the second most stable conformer as the most stable one. The potential energy curves have been obtained for Ca – N, Ca – C, and C – O rotational angles at the same levels of theory. For neutral glycine the minimum energy is found at 608, 08 and 1808 for Ca – N, Ca – C and C – O bond rotations and for the glycine zwitterion is 08 and 1808 for Ca – N and Ca –C rotations. For alanine the energy minimum is exist at 308, 08 and 1808 for the above rotations and 308, 08 for the zwitterionic form. Fourier fitted torsional potential coefficients calculated at the above levels of theory show that V1 and V2 terms are the major contributors. In glycine and alanine the MHP could not predict the correct conformational stability due to the presence of the hydrogen bonding. This hydrogen bonding interaction strongly affects the EHOMO and ELUMO values. Depending upon the hydrogen bonding strength the hardness values of the molecule changes. The DFT methods B3LYP, B3PW91 and B3P86 with 6-311þ þ G** have predicted the maximum of 6 minimum energy conformers out of 8 conformers for glycine and 11 minimum energy conformers out of 13 conformers for alanine which were predicted by the high level of ab initio theory. Even though the order of stability differs between the levels of theory, the over all performance of the methods are remarkably good. So the higher basis set with the DFT methods have predicted more number of low energy conformers. This study has given the valuable insight on the conformational behaviour of the glycine, alanine molecules and it is used as the testing bed for the DFT functionals for the Biomolecules.

Acknowledgements The authors are thankful to DST, Government of India, for the financial support for this work in the form of project (SP/S1/H-27/99).

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