Nonadiabatic Calculation of Dipole Moments

Fernández, Francisco M.; Echave, Julián

doi:10.1002/9783527633272.ch6

Cited by 3 publications

(6 citation statements)

References 52 publications

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“…The results are well known and have been discussed by several authors in different contexts (see, for example, the review by Fernández and Echave [5] and the references therein). The nonrelativistic Hamiltonian operator for a molecule can be written asĤ…”

Section: Molecular Hamiltonianmentioning

confidence: 54%

“…The explicit form of the interparticle distances r ij in terms of the new coordinates r ′ k may be rather cumbersome in the general case but there are particular choices that are suitable for the calculation of the integrals necessary for the application of the variational method [5,6]. The treatment of the simple model in Sec.…”

Section: Molecular Hamiltonianmentioning

confidence: 99%

“…For brevity, from now on we call those coordinates absolute and relative (or internal), respectively. By means of the variational method one obtains an approximate eigenfunction of H M that should be also eigenfunction of the operators that commute with H M , such as, for example, spin, angular momentum operator in relative coordinates, etc [4,5].…”

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confidence: 99%

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Particle correlation from uncorrelated non Born–Oppenheimer SCF wavefunctions

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Fernández

2012

J Math Chem

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We analyse a nonadiabatic self-consistent field method by means of an exactly-solvable model. The method is based on nuclear and electronic orbitals that are functions of the cartesian coordinates in the laboratory-fixed frame. The kinetic energy of the center of mass is subtracted from the molecular Hamiltonian operator in the variational process. The results for the simple model are remarkably accurate and show that the integration over the redundant cartesian coordinates leads to couplings among the internal ones.

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Section: Molecular Hamiltonianmentioning

confidence: 54%

Section: Molecular Hamiltonianmentioning

confidence: 99%

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Particle correlation from uncorrelated non Born–Oppenheimer SCF wavefunctions

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Fernández

2012

J Math Chem

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“…It is not difficult to take into account that the Hamiltonian is also parity-invariant. We simply apply equation (10) with the projection operators  u for the symmetry point group…”

Section: Exactly-solvable Three-particle Modelmentioning

confidence: 99%

“…In order to determine which non-relativistic spatial functions contribute to the antisymmetric spatial-spin ones, we proceed as in equation (10) adding an additional electron to that expression and choosing the projection operators for the symmetry point group O. In the case of four electrons we expect one quintuplet, three triplets and two singlets.…”

Section: Exactly-solvable Four-particle Modelmentioning

confidence: 99%

Allowed permutation symmetry in atomic and molecular wavefunctions: simple examples

Fernández

2020

J. Phys. B: At. Mol. Opt. Phys.

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It is well known that the allowed wavefunctions for an N-electron system should be antisymmetric with respect to the permutation of any pair of electron labels. On the other hand, the Hamiltonian for such a system is invariant under any permutation of electron labels and, consequently, its eigenfunctions are the basis for the irreducible representations of the symmetric group SN. Here, we investigate which symmetry species of the SN group are compatible with the antisymmetry principle. We illustrate the conclusions by means of simple N-particle one-dimensional models with harmonic interactions.

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Why are the low-energy protein normal modes evolutionarily conserved?

Echave

2012

Pure and Applied Chemistry

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Proteins fluctuate, and such fluctuations are functionally important. As with any functionally relevant trait, it is interesting to study how fluctuations change during evolution. In contrast with sequence and structure, the study of the evolution of protein motions is much more recent. Yet, it has been shown that the overall fluctuation pattern is evolutionarily conserved. Moreover, the lowest-energy normal modes have been found to be the most conserved. The reasons behind such a differential conservation have not been explicitly studied. There are two limiting explanations. A “biological” explanation is that because such modes are functional, there is natural selection pressure against their variation. An alternative “physical” explanation is that the lowest-energy normal modes may be more conserved because they are just more robust with respect to random mutations. To investigate this issue, I studied a set of globin-like proteins using a perturbed elastic network model (ENM) of the effect of random mutations on normal modes. I show that the conservation predicted by the model is in excellent agreement with observations. These results support the physical explanation: the lowest normal modes are more conserved because they are more robust.

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Nonadiabatic Calculation of Dipole Moments

Cited by 3 publications

References 52 publications

Particle correlation from uncorrelated non Born–Oppenheimer SCF wavefunctions

Particle correlation from uncorrelated non Born–Oppenheimer SCF wavefunctions

Allowed permutation symmetry in atomic and molecular wavefunctions: simple examples

Why are the low-energy protein normal modes evolutionarily conserved?

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