Numerical solving of the vibrational time-independent Schrödinger equation in one and two dimensions using the variational method

Stare, Jernej; Mavri, Janez

doi:10.1016/s0010-4655(01)00457-x

Cited by 52 publications

(62 citation statements)

References 51 publications

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“…The PES scans provided a set of proton potential functions which were used to solve the vibrational Schrçdinger equations. [71] The OÀH stretching envelope was constructed on the basis of the obtained solutions (eigenvalues). Next, the one-and two-dimensional potentials of mean force (1D and 2D pmf) were calculated to obtain a free-energy profile for the intramolecular bridge dynamics.…”

Section: Methodsmentioning

confidence: 99%

Spectroscopic Properties of a Strongly Anharmonic Mannich Base N‐oxide

2008

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Car-Parrinello molecular dynamics simulations in vacuum and in the solid state are performed on a strongly anharmonic system, namely, 2-(N-diethylamino-N-oxymethyl)-4,6-dichlorophenol, to investigate its molecular and spectroscopic properties. The investigated compound contains two slightly different molecules in the crystal cell with very short intramolecular hydrogen bonds (of 2.400 and 2.423 A), as determined previously by neutron diffraction. The vibrational properties of the compound are studied on the basis of standard approaches, that is, Fourier transformation of the autocorrelation functions of the atomic velocities and dipole moments. Then, the trajectory obtained from ab initio molecular dynamics is sampled and the obtained snapshots are used to solve the vibrational Schrödinger equations and to calculate the O--H stretching envelope as a superposition of the 0-->1 transition. Using an envelope method, the a posteriori quantum effects are included in the O--H stretching. In addition, NMR spectra are calculated also using the obtained snapshots. One- and two-dimensional potentials of mean force (1D and 2D pmf) are derived to explain the details of the proton dynamics. The computational results are supported by NMR experimental data. In addition, the calculated results are compared with previously published X-ray, neutron diffraction, and spectroscopic descriptions. A detailed analysis of the bridged proton's dynamics is thus obtained. The application of 1D and 2D pmf in a system with a strong bridged-proton delocalization is also demonstrated.

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Section: Methodsmentioning

confidence: 99%

Spectroscopic Properties of a Strongly Anharmonic Mannich Base N‐oxide

2008

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“…In the experimental infrared spectrum of PANO isolated in an Ar matrix, however, Szczepaniak et al [85] found no intense absorption band within 1200 cm [86]. Here, we present a 2D analysis using the potential surfaces for PANO calculated by Stare and Balint-Kurti [25] and by Stare and Mavri [84]. The first PES was calculated using the Car-Parrinello Molecular Dynamics program [25,87].…”

Section: D Hénon-heiles Potentialmentioning

confidence: 93%

“…However, Stare and Balint-Kurti found that the O · · · O distance in the optimized gas-phase geometries was always greater than 2.5 Å, no matter what level of theory was used [25]. Furthermore, harmonic frequency calculations at B3LYP/6-311++G(3df, 3pd), B3LYP/6-31+G(d, p) and B3LYP/6-31G(d, p) levels yield O-H stretching frequencies ν OH of 2977 cm −1 [25], 2965 cm −1 [84], and 2991 cm −1 [85] respectively. In the experimental infrared spectrum of PANO isolated in an Ar matrix, however, Szczepaniak et al [85] found no intense absorption band within 1200 cm [86].…”

Section: D Hénon-heiles Potentialmentioning

confidence: 96%

Solving the vibrational Schrödinger equation on an arbitrary multidimensional potential energy surface by the finite element method

Stare

Cooksy

2009

Computer Physics Communications

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“…The anharmonic vibrational energy levels and wave functions were calculated for the proton motion in the OÀ ÀH Á Á Á S hydrogen bond. 62 The assumed model, using fixed positions of all other atoms, reduces the problem to a onedimensional case of a particle in a specified potential. This allows the use of standard one-dimensional kinetic energy operator with reduced mass of the particle set to the mass of proton (see eq.…”

Section: Methods and Technical Detailsmentioning

confidence: 99%

“…(1) of ref. 62). Finally, potential energy distribution (PED) analysis was performed to assign the normal modes corresponding to the bridge vibrations.…”

Section: Methods and Technical Detailsmentioning

confidence: 99%

Investigations of an OH · · · S hydrogen bond via Car‐Parrinello and path integral molecular dynamics

Jezierska

Panek

2008

J Comput Chem

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The presence of intramolecular hydrogen bonds influences the binding energy, tautomeric equilibrium, and spectroscopic properties of various classes of organic molecules. This article discusses the O-H...S bridge, one of the less commonly investigated types of intramolecular interactions. 3-mercapto-1,3-diphenylprop-2-en-1-one was considered as the model structure. This compound exhibits photochromic properties. Car-Parrinello molecular dynamics (CPMD) was applied to investigate the spectroscopic and molecular properties of this compound in the gas phase and in the solid state. The second part of the study is devoted to the effects of the quantization of nuclear motions, with special attention to the O-H...S moiety. Path integral molecular dynamics (PIMD) of the molecular crystal of 3-mercapto-1,3-diphenylprop-2-en-1-one was carried out for this purpose. The employment of this fully quantum mechanical technique enables one to study, in a time-averaged sense, the zero-point motion important for flat potential energy surfaces. Finally, the potentials of mean force (Pmfs) were calculated from the CPMD and PIMD data obtained for the solid-state calculations. The effect of including quantum nuclear motion was investigated. In the studied compound, quantum effects shortened the H-bridge and provided a better description of the free energy minimum. The computational results place this uncommon intramolecular H-bonding among the class of strong hydrogen bonds with large red shifts of O-H stretching modes, which correspond well with previously presented experimental data in the literature concerning this structure.

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Numerical solving of the vibrational time-independent Schrödinger equation in one and two dimensions using the variational method

Cited by 52 publications

References 51 publications

Spectroscopic Properties of a Strongly Anharmonic Mannich Base N‐oxide

Spectroscopic Properties of a Strongly Anharmonic Mannich Base N‐oxide

Solving the vibrational Schrödinger equation on an arbitrary multidimensional potential energy surface by the finite element method

Investigations of an OH · · · S hydrogen bond via Car‐Parrinello and path integral molecular dynamics

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