Viktor Szalay - Academia.edu (original) (raw)

Papers by Viktor Szalay

Research paper thumbnail of Aspects of the Eckart frame ro-vibrational kinetic energy operator

The Journal of Chemical Physics, 2015

A most decisive part of developing the Eckart frame ro-vibrational kinetic energy operator (KEO) ... more A most decisive part of developing the Eckart frame ro-vibrational kinetic energy operator (KEO) in terms of curvilinear internal coordinates is the introduction of vibrational displacements obeying the Eckart conditions. It is examined here, how such displacements may be constructed by orthogonal and nonorthogonal transformations, and how they can be employed in developing the KEO. In particular, it is shown analytically, by term by term comparison, that the Eckart KEOs obtained by employing Pickett's method and the gateway Hamiltonian method are equivalent. That is, although it may appear in the form of very different expressions, the general, exact ro-vibrational Eckart frame KEO is unique. As side result, it has been shown that the simple formula of the pseudo-potential derived by Watson for the exact KEO given in normal coordinates applies to any Eckart frame KEO, irrespective of the choice of the vibrational coordinates.

Research paper thumbnail of Determination of an isotope-independent puckering potential function of oxetane

Journal of Molecular Spectroscopy, 1987

A careful analysis of the experimental data and ab initio quantum chemical results for oxetane (t... more A careful analysis of the experimental data and ab initio quantum chemical results for oxetane (trimethylene oxide) has been carried out and led us to the conclusion that the isotopic dependence of the empirically determined puckering potential functions has at least two sources: (a) The kinetic anharmonicity affecting primarily the quartic potential term, and (b) the zero-point energy contribution of small-amplitude vibrations giving about one-half of the quadratic term of the puckering potential function. Neither of the corrections for these effects is sufficient to obtain an isotope-invariant potential function, but their simuhaneous application resuhs in a near-equilibrium puckering potential for the Oxetane mOkCuk. 0 1987 Academic PBS, Inc.

Research paper thumbnail of A paradox of grid-based representation techniques: accurate eigenvalues from inaccurate matrix elements

Journal of Mathematical Chemistry, 2012

Several approximately variational grid-based representation techniques devised to solve the time-... more Several approximately variational grid-based representation techniques devised to solve the time-independent nuclear-motion Schrödinger equation share a similar behavior: while the computed eigenpairs, the only results which are of genuine interest, are accurate, many of the underlying Hamiltonian matrix elements are inaccurate, deviating substantially from their values in a variational basis representation. Examples are presented for the discrete variable representation and the Lagrange-mesh approaches, demonstrating that highly accurate eigenvalues and eigenfunctions can be obtained even if some or even all of the Hamiltonian matrix elements in these gridbased representations are inaccurate. It is shown how the apparent contradiction of obtaining accurate eigenpairs with far less accurate individual matrix elements can be resolved by considering the unitary transformation between the representations. Furthermore, the relations connecting orthonormal bases and the corresponding Lagrange bases are generalized to relations connecting nonorthogonal, regularized bases and the corresponding nonorthogonal, regularized Lagrange bases.

Research paper thumbnail of The Force Field of Bromoform:  A Theoretical and Experimental Investigation

The Journal of Physical Chemistry, 1996

... Fernández-Liencres, Amparo Navarro, Juan J. López, and Manuel Fernández. ... Viktor Szalay. R... more ... Fernández-Liencres, Amparo Navarro, Juan J. López, and Manuel Fernández. ... Viktor Szalay. Research Laboratory for Crystal Physics, Hungarian Academy of Sciences, PO Box 132, 1502 Budapest, Hungary. Teresa de los Arcos, José V. García-Ramos, and Rafael M. Escribano* ...

Research paper thumbnail of General derivative relations for anharmonic force fields

Molecular Physics, 1996

The brace notation, introduced by Allen and Csa! sza! r ( , J. chem. Phys., 98, 2983, provides a ... more The brace notation, introduced by Allen and Csa! sza! r ( , J. chem. Phys., 98, 2983, provides a simple and compact way to deal with derivatives of arbitrary non-tensorial quantities. One of its main advantages is that it builds the permutational symmetry of the derivatives directly into the formalism. The brace notation is applied to formulate the general nth-order Cartesian derivatives of internal coordinates, and to provide closed forms for general, nthorder transformation equations of anharmonic force ® elds, expressed as Taylor series, from internal to Cartesian or normal coordinate spaces.

Research paper thumbnail of Derivation of rotational-vibrational Hamiltonian matrices of real elements

Molecular Physics, 1992

... Madrid, Spain and SAMANTHA LANE Department of Chemistry, Monash University, Clayton, Victoria... more ... Madrid, Spain and SAMANTHA LANE Department of Chemistry, Monash University, Clayton, Victoria 3168, Australia (Received 11 March 1991; accepted 12 August 1991) It has ... Applications, Voi. 8 (Addison-Wesley) p. 316. [7] COLLADO ...

Research paper thumbnail of Adiabatic Jacobi corrections for H2 + -like systems

where m+=m3/m2+m3 and m=m2/m2+m3 .I fm3 is cho- sen to be dm2, then

Research paper thumbnail of Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator

The Journal of Chemical Physics, 2015

A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic... more A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, Tˆ, is presented. It is in the Eckart frame and it is of the same form as Watson's normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact Tˆ given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.

Research paper thumbnail of Eckart-Sayvetz conditions revisited

The Journal of chemical physics, Jan 21, 2014

It is shown that vibrational displacements satisfying the Eckart-Sayvetz conditions can be constr... more It is shown that vibrational displacements satisfying the Eckart-Sayvetz conditions can be constructed by projection of unconstrained displacements. This result has a number of interesting direct and indirect ramifications: (i) The normal coordinates corresponding to an electronic state or an isotopologue of a molecule are transformed to those of another state or isotopologue by a linear and, in general, non-orthogonal transformation. (ii) Novel interpretation of axis switching. (iii) One may enhance the separation of rotational-large-amplitude internal motions and the vibrational motions beyond that offered by the standard use of the Eckart-Sayvetz conditions. (iv) The rotational-vibrational Hamiltonian given in terms of curvilinear internal coordinates may be derived with elementary mathematical tools while taking into account the Eckart conditions with or without enhancement.

Research paper thumbnail of About the variational property of generalized discrete variable representation

The journal of physical chemistry. A, Jan 15, 2013

It is explained why the generalized discrete variable representation is variational neither with ... more It is explained why the generalized discrete variable representation is variational neither with respect to the size (truncation) of the basis set nor with respect to the selection of grid points.

Research paper thumbnail of Vibrations of H+(D+) in stoichiometric LiNbO3 single crystal

Chemical Physics, 2011

A first principles quantum mechanical calculation of the vibrational energy levels and transition... more A first principles quantum mechanical calculation of the vibrational energy levels and transition frequencies associated with protons in stoichiometric LiNbO3 single crystal has been carried out. The hydrogen contaminated crystal has been approximated by a model one obtains by translating a supercell, i.e., a cluster of LiNbO3 unit cells containing a single H+ and a Li+ vacancy. Based on the

Research paper thumbnail of CALCULATION OF THE ROTATIONAL PART OF THE INVERSE OF THE FOUR DIMENSIONAL GENERALIZED TENSOR OF INERTIA OF MOLECULES WITH ONE LARGE-AMPLITUDE INTERNAL MOTION

Research paper thumbnail of CALCULATION OF THE VIBRATIONAL ENERGY LEVELS OF TRIATOMIC MOLECULES

Research paper thumbnail of Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry-The internal axis system of molecules with one large amplitude internal motion

Research paper thumbnail of Theoretical Methods and Algorithms-Iterative and direct methods employing distributed approximating functionals for the reconstruction of a potential energy surface from its sampled values

Research paper thumbnail of ON THE METHYL INTERNAL ROTATION PROBLEM

Research paper thumbnail of EQUILIBRIUM MOLECULAR STRUCTURE AND SPECTROSCOPIC PARAMETERS OF METHYL CARBAMATE

Research paper thumbnail of Toward complete spectroscopy of small molecules

Research paper thumbnail of Elméleti módszerek molekulák forgási-rezgési mozgásainak leírása= Theoretical methods for describing the rotational-vibrational motions of molecules

Research paper thumbnail of Variational properties of the discrete variable representation: Discrete variable representation via effective operators

A variational finite basis representation/discrete variable representation (FBR/DVR) Hamiltonian ... more A variational finite basis representation/discrete variable representation (FBR/DVR) Hamiltonian operator has been introduced. By calculating its matrix elements exactly one obtains, depending on the choice of the basis set, either a variational FBR or a variational DVR. The domain of grid points on which the FBR/DVR is variational has been shown to consist of the subsets of the set of grid points one obtains by diagonalizing commuting variational basis representations of the coordinate operators. The variational property implies that the optimal of the subsets of a fixed number of points, i.e., the subset which gives the possible highest accuracy eigenpairs, gives the DVR of the smallest trace. The symmetry properties of the variational FBR/DVR Hamiltonian operator are analyzed and methods to incorporate symmetry into FBR/DVR calculations are discussed. It is shown how the Fourier-basis FBR/DVR suitable to solving periodic systems arise within the theory presented. Numerical examples are given to illustrate the theoretical results. The use of variational effective Hamiltonian and coordinate operators has been instrumental in this study. They have been introduced in a novel way by exploiting quasi-Hermiticity.

Research paper thumbnail of Aspects of the Eckart frame ro-vibrational kinetic energy operator

The Journal of Chemical Physics, 2015

A most decisive part of developing the Eckart frame ro-vibrational kinetic energy operator (KEO) ... more A most decisive part of developing the Eckart frame ro-vibrational kinetic energy operator (KEO) in terms of curvilinear internal coordinates is the introduction of vibrational displacements obeying the Eckart conditions. It is examined here, how such displacements may be constructed by orthogonal and nonorthogonal transformations, and how they can be employed in developing the KEO. In particular, it is shown analytically, by term by term comparison, that the Eckart KEOs obtained by employing Pickett's method and the gateway Hamiltonian method are equivalent. That is, although it may appear in the form of very different expressions, the general, exact ro-vibrational Eckart frame KEO is unique. As side result, it has been shown that the simple formula of the pseudo-potential derived by Watson for the exact KEO given in normal coordinates applies to any Eckart frame KEO, irrespective of the choice of the vibrational coordinates.

Research paper thumbnail of Determination of an isotope-independent puckering potential function of oxetane

Journal of Molecular Spectroscopy, 1987

A careful analysis of the experimental data and ab initio quantum chemical results for oxetane (t... more A careful analysis of the experimental data and ab initio quantum chemical results for oxetane (trimethylene oxide) has been carried out and led us to the conclusion that the isotopic dependence of the empirically determined puckering potential functions has at least two sources: (a) The kinetic anharmonicity affecting primarily the quartic potential term, and (b) the zero-point energy contribution of small-amplitude vibrations giving about one-half of the quadratic term of the puckering potential function. Neither of the corrections for these effects is sufficient to obtain an isotope-invariant potential function, but their simuhaneous application resuhs in a near-equilibrium puckering potential for the Oxetane mOkCuk. 0 1987 Academic PBS, Inc.

Research paper thumbnail of A paradox of grid-based representation techniques: accurate eigenvalues from inaccurate matrix elements

Journal of Mathematical Chemistry, 2012

Several approximately variational grid-based representation techniques devised to solve the time-... more Several approximately variational grid-based representation techniques devised to solve the time-independent nuclear-motion Schrödinger equation share a similar behavior: while the computed eigenpairs, the only results which are of genuine interest, are accurate, many of the underlying Hamiltonian matrix elements are inaccurate, deviating substantially from their values in a variational basis representation. Examples are presented for the discrete variable representation and the Lagrange-mesh approaches, demonstrating that highly accurate eigenvalues and eigenfunctions can be obtained even if some or even all of the Hamiltonian matrix elements in these gridbased representations are inaccurate. It is shown how the apparent contradiction of obtaining accurate eigenpairs with far less accurate individual matrix elements can be resolved by considering the unitary transformation between the representations. Furthermore, the relations connecting orthonormal bases and the corresponding Lagrange bases are generalized to relations connecting nonorthogonal, regularized bases and the corresponding nonorthogonal, regularized Lagrange bases.

Research paper thumbnail of The Force Field of Bromoform:  A Theoretical and Experimental Investigation

The Journal of Physical Chemistry, 1996

... Fernández-Liencres, Amparo Navarro, Juan J. López, and Manuel Fernández. ... Viktor Szalay. R... more ... Fernández-Liencres, Amparo Navarro, Juan J. López, and Manuel Fernández. ... Viktor Szalay. Research Laboratory for Crystal Physics, Hungarian Academy of Sciences, PO Box 132, 1502 Budapest, Hungary. Teresa de los Arcos, José V. García-Ramos, and Rafael M. Escribano* ...

Research paper thumbnail of General derivative relations for anharmonic force fields

Molecular Physics, 1996

The brace notation, introduced by Allen and Csa! sza! r ( , J. chem. Phys., 98, 2983, provides a ... more The brace notation, introduced by Allen and Csa! sza! r ( , J. chem. Phys., 98, 2983, provides a simple and compact way to deal with derivatives of arbitrary non-tensorial quantities. One of its main advantages is that it builds the permutational symmetry of the derivatives directly into the formalism. The brace notation is applied to formulate the general nth-order Cartesian derivatives of internal coordinates, and to provide closed forms for general, nthorder transformation equations of anharmonic force ® elds, expressed as Taylor series, from internal to Cartesian or normal coordinate spaces.

Research paper thumbnail of Derivation of rotational-vibrational Hamiltonian matrices of real elements

Molecular Physics, 1992

... Madrid, Spain and SAMANTHA LANE Department of Chemistry, Monash University, Clayton, Victoria... more ... Madrid, Spain and SAMANTHA LANE Department of Chemistry, Monash University, Clayton, Victoria 3168, Australia (Received 11 March 1991; accepted 12 August 1991) It has ... Applications, Voi. 8 (Addison-Wesley) p. 316. [7] COLLADO ...

Research paper thumbnail of Adiabatic Jacobi corrections for H2 + -like systems

where m+=m3/m2+m3 and m=m2/m2+m3 .I fm3 is cho- sen to be dm2, then

Research paper thumbnail of Understanding nuclear motions in molecules: Derivation of Eckart frame ro-vibrational Hamiltonian operators via a gateway Hamiltonian operator

The Journal of Chemical Physics, 2015

A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic... more A new ro-vibrational Hamiltonian operator, named gateway Hamiltonian operator, with exact kinetic energy term, Tˆ, is presented. It is in the Eckart frame and it is of the same form as Watson's normal coordinate Hamiltonian. However, the vibrational coordinates employed are not normal coordinates. The new Hamiltonian is shown to provide easy access to Eckart frame ro-vibrational Hamiltonians with exact Tˆ given in terms of any desired set of vibrational coordinates. A general expression of the Eckart frame ro-vibrational Hamiltonian operator is given and some of its properties are discussed.

Research paper thumbnail of Eckart-Sayvetz conditions revisited

The Journal of chemical physics, Jan 21, 2014

It is shown that vibrational displacements satisfying the Eckart-Sayvetz conditions can be constr... more It is shown that vibrational displacements satisfying the Eckart-Sayvetz conditions can be constructed by projection of unconstrained displacements. This result has a number of interesting direct and indirect ramifications: (i) The normal coordinates corresponding to an electronic state or an isotopologue of a molecule are transformed to those of another state or isotopologue by a linear and, in general, non-orthogonal transformation. (ii) Novel interpretation of axis switching. (iii) One may enhance the separation of rotational-large-amplitude internal motions and the vibrational motions beyond that offered by the standard use of the Eckart-Sayvetz conditions. (iv) The rotational-vibrational Hamiltonian given in terms of curvilinear internal coordinates may be derived with elementary mathematical tools while taking into account the Eckart conditions with or without enhancement.

Research paper thumbnail of About the variational property of generalized discrete variable representation

The journal of physical chemistry. A, Jan 15, 2013

It is explained why the generalized discrete variable representation is variational neither with ... more It is explained why the generalized discrete variable representation is variational neither with respect to the size (truncation) of the basis set nor with respect to the selection of grid points.

Research paper thumbnail of Vibrations of H+(D+) in stoichiometric LiNbO3 single crystal

Chemical Physics, 2011

A first principles quantum mechanical calculation of the vibrational energy levels and transition... more A first principles quantum mechanical calculation of the vibrational energy levels and transition frequencies associated with protons in stoichiometric LiNbO3 single crystal has been carried out. The hydrogen contaminated crystal has been approximated by a model one obtains by translating a supercell, i.e., a cluster of LiNbO3 unit cells containing a single H+ and a Li+ vacancy. Based on the

Research paper thumbnail of CALCULATION OF THE ROTATIONAL PART OF THE INVERSE OF THE FOUR DIMENSIONAL GENERALIZED TENSOR OF INERTIA OF MOLECULES WITH ONE LARGE-AMPLITUDE INTERNAL MOTION

Research paper thumbnail of CALCULATION OF THE VIBRATIONAL ENERGY LEVELS OF TRIATOMIC MOLECULES

Research paper thumbnail of Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry-The internal axis system of molecules with one large amplitude internal motion

Research paper thumbnail of Theoretical Methods and Algorithms-Iterative and direct methods employing distributed approximating functionals for the reconstruction of a potential energy surface from its sampled values

Research paper thumbnail of ON THE METHYL INTERNAL ROTATION PROBLEM

Research paper thumbnail of EQUILIBRIUM MOLECULAR STRUCTURE AND SPECTROSCOPIC PARAMETERS OF METHYL CARBAMATE

Research paper thumbnail of Toward complete spectroscopy of small molecules

Research paper thumbnail of Elméleti módszerek molekulák forgási-rezgési mozgásainak leírása= Theoretical methods for describing the rotational-vibrational motions of molecules

Research paper thumbnail of Variational properties of the discrete variable representation: Discrete variable representation via effective operators

A variational finite basis representation/discrete variable representation (FBR/DVR) Hamiltonian ... more A variational finite basis representation/discrete variable representation (FBR/DVR) Hamiltonian operator has been introduced. By calculating its matrix elements exactly one obtains, depending on the choice of the basis set, either a variational FBR or a variational DVR. The domain of grid points on which the FBR/DVR is variational has been shown to consist of the subsets of the set of grid points one obtains by diagonalizing commuting variational basis representations of the coordinate operators. The variational property implies that the optimal of the subsets of a fixed number of points, i.e., the subset which gives the possible highest accuracy eigenpairs, gives the DVR of the smallest trace. The symmetry properties of the variational FBR/DVR Hamiltonian operator are analyzed and methods to incorporate symmetry into FBR/DVR calculations are discussed. It is shown how the Fourier-basis FBR/DVR suitable to solving periodic systems arise within the theory presented. Numerical examples are given to illustrate the theoretical results. The use of variational effective Hamiltonian and coordinate operators has been instrumental in this study. They have been introduced in a novel way by exploiting quasi-Hermiticity.