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Optimized coordinates for anharmonic vibrational structure theories
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10.1063/1.4767776
/content/aip/journal/jcp/137/20/10.1063/1.4767776
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/20/10.1063/1.4767776

Figures

Image of FIG. 1.
FIG. 1.

The algorithm of the coordinate optimization.

Image of FIG. 2.
FIG. 2.

(a) The normal and (b) the optimized coordinates of the hydrogen fluoride tetramer.

Image of FIG. 3.
FIG. 3.

The VSCF zero-point energy of the water molecule as a function of the rotation angle (θ ij ) of the unitary transformation of two coordinates, , while the third remains to be the normal coordinate. At θ ij = 0, Q 1, Q 2, and Q 3 are the bending, symmetric stretching, and anti-symmetric stretching normal coordinates, respectively.

Image of FIG. 4.
FIG. 4.

The normal and optimized coordinates of the O–H stretching modes of the water molecule superposed on the two-dimensional cross-section of the PES. The contours are drawn with an interval of 0.01 hartree.

Image of FIG. 5.
FIG. 5.

The normal and the optimized coordinates of the water dimer and the associated harmonic frequencies (the intramolecular modes only). (a) The normal and the optimized coordinates for the bending modes, which coincide with each other. (b) The normal and (c) the optimized coordinates for the O–H stretching modes.

Image of FIG. 6.
FIG. 6.

The normal and the optimized coordinates of ethylene with the associated harmonic frequencies. (a) The normal and the optimized coordinates (which coincide with each other) for the C=C stretching, bending, and out-of-plane modes. (b) The normal and (c) the optimized coordinates for the CH stretching modes.

Tables

Generic image for table
Table I.

The zero-point energy (ZPE) and the fundamental frequencies (in cm−1) of the hydrogen fluoride tetramer obtained by VSCF, oc-VSCF, and VCI[4]-(8). The deviations and mean absolute deviations (MAD) from VCI[4]-(8) are given in the parentheses and in the last row, respectively.

Generic image for table
Table II.

The scaled force constants (in cm−1) of the O–H stretching modes of the water molecule in the normal and optimized coordinates.

Generic image for table
Table III.

The zero-point energy (ZPE) and the frequencies of the fundamentals, the first overtones, and combination tones (in cm−1) of the water molecule calculated by VSCF, oc-VSCF, VCI-(2), oc-VCI-(2), VCI[m]-(8) (m = 1 − 3), and oc-VCI[m]-(8) (m = 1 − 3). The deviations and mean absolute deviations (MAD) from the VCI[3]-(8) results are given in the parentheses and in the rows labeled by MAD, respectively.

Generic image for table
Table IV.

The frequencies of the fundamentals, the first overtones, and combination tones (in cm−1) of the water molecule calculated by oc-VCI-(2) with a QFF, a hybrid PES, and a grid PES and by oc-VCI[3]-(8) with the grid PES. The deviations and mean absolute deviations (MAD) from the experimental values are given in the parentheses and in the rows labeled by MAD, respectively.

Generic image for table
Table V.

The zero-point energy (ZPE) and fundamental frequencies (in cm−1) of the water dimer (intramolecular modes only) calculated by VSCF, oc-VSCF, VCI[m]-(8) (m = 1 − 4), oc-VCI[m]-(8) (m = 1 − 4), VCI-(8), and oc-VCI-(8). The deviations and mean absolute deviations (MAD) from the VCI-(8) results are given in the parentheses and in the rows labeled by MAD, respectively.

Generic image for table
Table VI.

The frequencies of the fundamentals, overtones, and combination tones (in cm−1) of the O–H stretching modes of the water dimer calculated by VCI-(1), oc-VCI-(1), VCI-(2), and oc-VCI-(2) as well as oc-VCI-(8). The deviations and mean absolute deviations (MAD) from the oc-VCI-(8) results are given in the parentheses and in the rows labeled by MAD, respectively. The assignments for the overtones and combination tones are based on the oc-VCI-(8) results.

Generic image for table
Table VII.

The zero-point energy (ZPE) and fundamental frequencies (in cm−1) of ethylene calculated by VSCF, oc-VSCF, VCI[m]-(6) (m = 1 − 5), oc-VCI[m]-(6) (m = 1 − 5), VCI-(6), and oc-VCI-(6). The deviations and mean absolute deviations (MAD) from the VCI-(6) results are given in the parentheses and in the rows labeled by MAD, respectively.

Generic image for table
Table VIII.

The deviations and mean absolute deviation (MAD) in the zero-point energy (ZPE) and fundamental frequencies (in cm−1) of ethylene obtained with nMR-QFF (n = 1 − 3) from those of 4MR-QFF.

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/content/aip/journal/jcp/137/20/10.1063/1.4767776
2012-11-28
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Optimized coordinates for anharmonic vibrational structure theories
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/20/10.1063/1.4767776
10.1063/1.4767776
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