The numerical method of K. E. Plokhotnikov for solving the Schrödinger equation is applied to spatial configurations of eleven proteinogenic amino acids (glycine, alanine, valine, leucine, isoleucine, proline, serine, threonine, cysteine, tyrosine, tryptophan) in their canonical PubChem geometries. The method combines stochastic Monte-Carlo discretization of configuration space with a finite-difference approximation of the kinetic energy operator. A scheme of valence-electron positioning with delocalization along covalent bonds and with the number of valence electrons fixed by the group number of the periodic table is employed. For all 11 structures, the relative deviation of the discrete-Hamiltonian eigenvalue Ω_I from the reference total-energy estimate E_ref is below 0.02 %, and Ω_I lies in the middle part of the spectrum in all cases. Tryptophan is examined as the most complex example (135 quantum particles; configuration-space dimension 405).
31.15.-p Calculations and mathematical techniques in atomic and molecular physics
87.15.-v Biomolecules: structure and physical properties
$^1$Moscow State University, Faculty of Physics, Department of Acoustics. A 5th year student of the specialty.
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