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Predicting accurate vibrational frequencies for highly anharmonic systems
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10.1063/1.2987712
/content/aip/journal/jcp/129/16/10.1063/1.2987712
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/16/10.1063/1.2987712

Figures

Image of FIG. 1.
FIG. 1.

Optimized geometries of (a) at CCSD level of theory with the cc-pVTZ basis set in symmetry; (b) at CCSD(T) level of theory with the cc-pVTZ basis set in symmetry; (c) at CCSD(T) level of theory with the cc-pVDZ basis set in symmetry. Geometry parameters are listed in the set of internal coordinates that were used as the basis for the decomposition of the normal mode displacement vectors. Experimental values (Ref. 18) are given in parentheses.

Image of FIG. 2.
FIG. 2.

Flow chart of the procedure for calculating vibrational frequencies using the VSCF method in internal coordinates. VSCF-diagonal stands for anharmonic frequencies calculated without coupling, while VSCF-PT2 stands for anharmonic coupled vibrational frequencies calculated using a second order perturbation theory correction.

Image of FIG. 3.
FIG. 3.

CCSD(T)/cc-pVTZ in Cartesian coordinates (dotted line) and internal coordinates (solid line). (a) H1–O2 bond distance is plotted against O4–N3–O2–H1 torsion angle at the VSCF points along the torsion mode ; (b) H1–O2 bond distance is plotted against the N3–O2–H1 angle at the VSCF points along the bending mode .

Image of FIG. 4.
FIG. 4.

CCSD(T)/cc-pVDZ in Cartesian coordinates (dotted line) and internal coordinates (solid line). (a) the H5–O2 bond distance is plotted against the H5–O2–N1–O3 torsion angle at the VSCF points along torsion mode . (b) the H5–O2 bond distance is plotted against the H5–O2–N1 bending angle on the VSCF points along bending mode .

Image of FIG. 5.
FIG. 5.

Total errors obtained as a difference between calculated and experimental vibrational frequencies.

Image of FIG. 6.
FIG. 6.

Coarse-grained parallelization of PES calculations in the VSCF method.

Image of FIG. 7.
FIG. 7.

Speed up curve for parallelized VSCF at the MP2 level of theory with the cc-pVDZ basis set carried out on molecule. The dashed line with data point represented as triangles is the theoretical curve that follows linear speed up. The actual speed up is represented by the solid line with circles as data points. Beneath each point in parentheses are given the number of points per each group that needed to be calculated, followed up by the timings in minutes.

Tables

Generic image for table
Table I.

MP2 and CCSD diagonal frequencies with the cc-pVDZ (ccd), cc-pVTZ (cct), and cc-pVQZ (ccq) basis sets. The amplitude maps onto the energy level , see text. Increasing the value of amp corresponds to a larger spacing of the PES points along the normal mode.

Generic image for table
Table II.

, MP2 and CCSD calculations with the cc-pVDZ (ccd), cc-pVTZ (cct), and cc-pVQZ (ccq) basis sets. The actual values of harmonic (harm), scaled harmonic [harm(scal)], anharmonic in Cartesian coordinates [anhr(cart)], anharmonic in internals using two bonds and the angle [anhr(int)2ba], anharmonic in internals using three bonds [anhr(int)3b], and experimental (Refs. 27 and 28) (exp) values are given.

Generic image for table
Table III.

Experimental frequencies (Refs. 27 and 28) and the errors between calculated and experimental frequencies for . Calculations were performed at MP2 and CCSD levels of theory with the cc-pVDZ (ccd), cc-pVTZ (cct), and cc-pVQZ (ccq) basis sets. The following frequencies were calculated: harmonic (harm), scaled harmonic [harm(scal)], anharmonic in Cartesian coordinates [anhr(cart)], and anharmonic in internal coordinates [anhr(int)].

Generic image for table
Table IV.

Experimental frequencies (Ref. 19) and the errors between calculated and experimental frequencies for . Calculations were performed with PM2 and CCSD(T) using the cc-pVDZ (ccd), and cc-pVTZ (cct) basis sets. The following frequencies were calculated: harmonic (harm), scaled harmonic [harm(scal)], anharmonic in Cartesian coordinates [anhr(cart)], and anharmonic in internal coordinates [anhr(int)].

Generic image for table
Table V.

Calculated anharmonic vibrational frequencies for and at CCSD(T) with the cc-pVDZ basis set. Frequencies were calculated without coupling (diag) or with coupling but only using VSCF level without a PT2 correction (vscf). Depending on the type of coordinates in which the PES was created, diag(cart) and vscf(cart) correspond to Cartesian coordinates, while diag(int) and vscf(int) correspond to internal coordinates. Difference between diag(cart) and vscf(cart) is labeled as diff(cart), while difference in diag(int) and vscf(int) is labeled as diff(int). Difference between diag(cart) and diag(int) is given as diff(diag).

Generic image for table
Table VI.

Experimental frequencies (Ref. 19) and the errors between calculated and experimental frequencies for . Calculations were performed with MP2 and CCSD(T) and the cc-pVDZ (ccd), and cc-pVTZ (cct) basis sets. The following frequencies were calculated: harmonic (harm), scaled harmonic (harm(scal)), anharmonic in Cartesian coordinates [anhr(cart)], and anharmonic in internal coordinates [anhr(int)].

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/content/aip/journal/jcp/129/16/10.1063/1.2987712
2008-10-24
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Predicting accurate vibrational frequencies for highly anharmonic systems
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/16/10.1063/1.2987712
10.1063/1.2987712
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