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Numeric kinetic energy operators for molecules in polyspherical coordinates
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10.1063/1.4729536
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Affiliations:
1 Theoretische Chemie, Ruprecht-Karls-Universität, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
2 CNRS, Laboratoire de Chimie Physique (UMR 8000), Université Paris-Sud, F-91405 Orsay, France
3 CTMM, Institut Charles Gerhardt (UMR 5253), CC 1501, Université Montpellier II, F-34095 Montpellier Cedex 05, France
a)
c) E-mail: gatti@univ-montp2.fr.
d)
J. Chem. Phys. 136, 234112 (2012)
/content/aip/journal/jcp/136/23/10.1063/1.4729536
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/23/10.1063/1.4729536

Figures

FIG. 1.

Shown is HONO in trans-geometry. The cis-geometry is reached by increasing the dihedral angle φ by π, i.e., by rotating R 1 with respect to R 2 around R 3.

FIG. 2.

Spectrum of HONO. (a) Spectrum of HONO calculated by propagation of an initial wavepacket (see text). Displayed are the Fourier transforms of autocorrelation functions obtained by using analytical (continuous line) and cluster expansion (dotted line) KEOs. The two spectra lie on top of each other and their difference can hardly be seen in this figure. (b) Enlarged view on the high energy part of the above spectrum, tiny differences can now be observed.

FIG. 3.

Polyspherical coordinates for C2H4. G is the center of mass of the system. denotes the center of mass of the H2 subsystem. Reprinted with permission from M. R. Brill, F. Gatti, D. Lauvergnat, and H.-D. Meyer, Chem. Phys.338, 186 (2007)10.1016/j.chemphys.2007.04.002. Copyright 2007, Elsevier B.V.

FIG. 4.

Absorption spectrum of π → π* of ethene. The lower curve is obtained with the first-order cluster expansion of the KEO and the upper curve is the spectrum of Ref. 15, i.e., calculated using the analytical main term and zeroth order cluster for the correction term Eq. (26).

Tables

Table I.

DVR type and size for the various degrees of freedom. The distances are given in atomic units. HO denotes a harmonic oscillator (hermite) DVR and exp denotes an exponential DVR. N is the number of grid points.

Table II.

Vibrational levels A (even quanta for ν6) and A (odd quanta for ν6) for trans-HONO. ν1 is OH stretching, ν2 is NO stretching, ν3 is NOH bending, ν4 is ONO bending, ν5 is ON stretching, and ν6 is torsional mode. The first column in the table shows the assignment of the state. The second column displays the eigenvalues obtained with analytical KEO, the third column shows the population of , the fourth column is energy above ground state, fifth column shows the eigenvalues obtained by using cluster expanded numerical KEO, and the last column gives their difference. The last row shows the energies of the OH-stretch fundamental. All energies are in cm−1.

Table III.

Vibrational levels A and A for cis-HONO. See caption of Table II.

Table IV.

DVR type and size for the various degrees of freedom. Distances are given in atomic units. sin denotes sine DVR. Compare with Table I for further explanation.

Table V.

Single particle function basis sets used for propagation and eigenenergy calculations.

Table VI.

Energy states for ethene. The first column shows the eigenenergies for Hamiltonian with analytic main term KEO, the second column gives excitation energies, i.e., energies of the first column minus the zero point energy. The third column shows the eigenenergies for Hamiltonian with numerical KEO, and the fourth column displays the differences. All energies are in cm−1.

/content/aip/journal/jcp/136/23/10.1063/1.4729536
2012-06-21
2014-04-21

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