Density Functional Calculations for Amino Acids

Density Functional Calculations for Amino Acids

I) Brief introduction

Within the framework of a diploma thesis [1] the structure of three amino acids (glycine, alanine, serine) has been studied, using density functional methods. Utilizing the Car-Parrinello technique [2], the calculations are based on It has been demonstrated (see e.g. [7]) that for given exchange-correlation functional the spectroscopic constants obtained with normconserving pseudopotentials agree excellently with the corresponding all-electron data, if (i) sufficiently conservative cut-off radii are used and (ii) nonlinear core corrections [8] are taken into account. However, the inclusion of nonlinear core corrections mainly affects dissociation energies, it is less relevant for all geometrical aspects. Moreover, a suitable choice of the cut-off radii is straightforward. The quality of the present results is thus only controlled by the form of the exchange-correlation functional and two technical parameters, The latter size has been chosen so that atoms belonging to different molecules are separated by roughly 10 Bohr.

The results can be summarized as follows:






II) Results for Glycine

II.1) Ground state: Glycine Ip (planar)

Calculational parameters
xc-functional LDA [5]
cut-off energy 100 Rydberg
pseudopotential Troullier-Martins [3]
nonlinear core corrections no
supercell size 23 Bohr
Results
bond lengths
[Angstroms]
bond angles
[degrees]
bond expt. [9] LDA angle expt. [9] LDA
N-H (1.001) 1.020 H-N-H (110.3) 106.5
N-C 1.467 1.431 H-N-C (113.3) 111.0
C-H (1.081) 1.101 N-C-C 112.1 115.9
C-C 1.526 1.506 H-C-H (107.0) 104.4
C-O 1.355 1.332 C-C-O 111.6 114.9
C=O 1.205 1.200 C-C=O 125.1 125.7
O-H (0.966) 0.976 C-O-H (112.3) 104.7
  • experimental results in brackets are based on estimates
  • reasonable agreement between LDA and experiment
  • however: LDA erroneously predicts conformer IIp to be energetically lower than the Ip state by 0.14 eV
glycine: ground state of neutral structure



II.2) Energetically lowest conformer: Glycine IIp

Calculational parameters
xc-functional LDA [5]
cut-off energy 60 and 100 Rydberg
pseudopotential Troullier-Martins [3]
nonlinear core corrections no
supercell size 23 Bohr
Results
bond lengths
[Angstroms]
bond angles
[degrees]
bond LDA
60 Ryd
LDA
100 Ryd
angle LDA
60 Ryd
LDA
100 Ryd
N-H 1.026 1.019 H-N-H 107.9 108.7
N-C 1.453 1.449 H-N-C 113.1 113.7
C-H 1.103 1.099 N-C-C 109.9 110.4
C-C 1.518 1.518 H-C-H 106.2 106.1
C-O 1.338 1.324 C-C-O 112.2 112.0
C=O 1.228 1.203 C-C=O 122.5 123.1
O-H 1.046 1.023 C-O-H 100.0 101.8
  • A bond contraction is observed, when increasing the basis set size from 60 to 100 Rydberg: The oxygen bonds are affected most strongly.
  • Results for 80 Rydberg are almost identical with those for 100 Rydberg.
glycine: conformer IIp

Calculational parameters
xc-functional GGA [6]
cut-off energy 80 Rydberg
pseudopotential Troullier-Martins [3]
nonlinear core corrections no
supercell size 23 Bohr
Results
bond lengths
[Angstroms]
bond angles
[degrees]
bond GGA angle GGA
N-H 1.013 H-N-H 107.9
N-C 1.453 H-N-C 112.8
C-H 1.088 N-C-C 110.5
C-C 1.518 H-C-H 106.4
C-O 1.344 C-C-O 112.8
C=O 1.224 C-C=O 122.7
O-H 1.020 C-O-H 101.1
  • GGA contracts bonds slightly compared to LDA: Effect of gradient corrections is less dramatic than for many inorganic molecules and for solids.
glycine: conformer IIp



II.3) Glycine IIn

Calculational parameters
xc-functional LDA [5]
cut-off energy 80 Rydberg
pseudopotential Troullier-Martins [3]
nonlinear core corrections no
supercell size 23 Bohr
Results
bond lengths
[Angstroms]
bond angles
[degrees]
bond LDA angle LDA
N-H 1.021 H-N-H 108.5
N-C 1.452 H-N-C 113.7
C-H 1.099 N-C-C 110.3
C-C 1.518 H-C-H 106.2
C-O 1.330 C-C-O 112.0
C=O 1.206 C-C=O 123.1
O-H 1.029 C-O-H 101.3
glycine: conformer IIn

glycine: conformer IIn






III) Results for Alanine

III.1) Neutral structure

Calculational parameters
xc-functional LDA [5]
cut-off energy 60 Rydberg
pseudopotential Troullier-Martins [3]
nonlinear core corrections no
supercell size 23 Bohr
Results
bond lengths
[Angstroms]
bond angles
[degrees]
bond LDA angle LDA
N-C 1.458 - -
C-C 1.526 N-C-C 108.3
C-O 1.334 C-C-O 112.6
C=O 1.230 C-C=O 122.3
  • The LDA predicts the neutral structure to be the ground state configuration if alanine, in contrast to quantum chemical results [10]. The LDA energy difference to the zwitterionic state is 0.94 eV.
alanine: neutral structure



III.2) Zwitterion

Calculational parameters
xc-functional LDA [5]
cut-off energy 60 Rydberg
pseudopotential Troullier-Martins [3]
nonlinear core corrections no
supercell size 23 Bohr
Results
bond lengths
[Angstroms]
bond angles
[degrees]
bond LDA angle LDA
N-C 1.481 - -
C-C 1.564 N-C-C 106.6
C-O 1.287 C-C-O 115.5
C=O 1.251 C-C=O 116.6
alanine: zwitterion






IV) Results for Serine

IV.1) Ground state

Calculational parameters
xc-functional LDA [5]
cut-off energy 60 Rydberg
pseudopotential Troullier-Martins [3]
nonlinear core corrections no
supercell size 23 Bohr
Results
bond lengths
[Angstroms]
bond angles
[degrees]
bond LDA angle LDA
N-H 1.028 H-N-H 108.6
N-C 1.452 H-N-C 113.2
C-H 1.107 N-C-C 107.0
C-C 1.528 H-C-H 109.0
C-O 1.333 C-C-O 112.4
C=O 1.232 C-C=O 122.3
O-H 1.054 C-O-H 99.4
serine: ground state






References

  1. G. Iseri, Diploma thesis, University of Frankfurt (2003).
  2. M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992).
  3. N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 (1991).
  4. L. Kleinman and D. M. Bylander, Phys. Rev. Lett. 4, 1425 (1982).
  5. S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980).
  6. J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B 46, 6671 (1992).
  7. E. Engel, A. Höck, R. N. Schmid, R. M. Dreizler, and N. Chetty, Phys. Rev. B 64, 125111 (2001).
  8. S. G. Louie, S. Froyen, and M. L. Cohen, Phys. Rev. B 26, 1738 (1982).
  9. Iijima, Tanaka, Onuma, J. Mol. Struct. 246, 257 (1991).
  10. F. R. Tortonda, J.-L. Pascual-Ahuir, E. Silla, and I. Tunon, J. Chem. Phys. 109, 592 (1998).


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