Exact quantum molecular Hamiltonians

Chapuisat, Xavier; Nauts, André; Brunet, Jean-Phillippe

doi:10.1080/00268979100100011

Cited by 76 publications

(51 citation statements)

References 10 publications

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“…Most methods of deriving kinetic energy operators follow one of two routes: (1) obtain the classical kinetic energy expression and then quantize it (usually using the procedure of Podolsky [105]) or (2) use the chain rule to transform a known quantum mechanical KEO (usually the space-fixed Cartesian KEO) to derive a new KEO. Chapuisat and co-workers [99][100][101][106][107][108] have advocated the first route. Sutcliffe and Tennyson [109][110][111][112][113] and Handy [114] were early proponents of the second route.…”

Section: Representations Of the Kinetic Energy Operatormentioning

confidence: 99%

Variational quantum approaches for computing vibrational energies of polyatomic molecules

2008

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In this article we review state-of-the-art methods for computing vibrational energies of polyatomic molecules using quantum mechanical, variationally-based approaches. We illustrate the power of those methods by presenting applications to molecules with more than four atoms. This demonstrates the great progress that has been made in this field in the last decade in dealing with the exponential scaling with the number of vibrational degrees of freedom. In this review we present three methods that effectively obviate this bottleneck. The first important idea is the n-mode representation of the Hamiltonian and notably the potential. The potential (and other functions) are represented as a sum of terms that depend on a subset of the coordinates. This makes it possible to compute matrix elements, form a Hamiltonian matrix, and compute its eigenvalues and eigenfunctions. Another approach takes advantage of this multimode representation and represents the terms as sum of products. It then exploits the powerful multiconfiguration Hartree time dependent method to solve the time-dependent Schrödinger equation and extract the eigenvalue spectrum. The third approach we present uses contracted basis functions in conjunction with a Lanczos eigensolver. Matrix vector products are done without transforming to a direct-product grid. The usefulness of these methods is demonstrated for several example molecules, e.g., methane, methanol and the Zundel cation.2

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Section: Representations Of the Kinetic Energy Operatormentioning

confidence: 99%

Variational quantum approaches for computing vibrational energies of polyatomic molecules

2008

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“…e., x Å x(q) depends parametrically on qЉ 0 ] tensor with constraints (14). of component Alternatively, q Å q (x) and 0 Å C(x) can be used.…”

Section: Hamiltonians For Rigidlymentioning

confidence: 99%

“…2 ) The dynamics of an N-particle system in terms of curvilinear coordinates rests on the relations between the 3N body-({gggЉ} Å {xyz}, {yzx}, {zxy}) fixed (BF) Cartesian atomic coordinates x Å (x 1 (13)(14)(15). The following must be known: either 3N relationships of the type x Å x(q) and the BF frame is…”

Section: Hamiltonians For Rigidlymentioning

confidence: 99%

Quantum-Mechanical Description of Rigidly or Adiabatically Constrained Molecular Systems

Gatti

Justum

Menou

et al. 1997

Journal of Molecular Spectroscopy

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“…͑2͒ is a pseudopotential 37 which arises from the volume element used in normalizing the wave function. 38 In this paper we have used the Wilson normalization, 38,39 which has the advantage that the volume element is simply expressed as…”

Section: Effective 1d Potential Energy Function and Kinetic Energymentioning

confidence: 99%

Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: Umbrella motion in NH3

Luis

Reis

Παπαδόπουλος

2009

The Journal of Chemical Physics

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A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella ͑inversion͒ motion of NH 3 it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described.

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Exact quantum molecular Hamiltonians

Cited by 76 publications

References 10 publications

Variational quantum approaches for computing vibrational energies of polyatomic molecules

Variational quantum approaches for computing vibrational energies of polyatomic molecules

Quantum-Mechanical Description of Rigidly or Adiabatically Constrained Molecular Systems

Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: Umbrella motion in NH3

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