DOI: 10.5281/zenodo.44767
title: Optimal Displacement Increment For Numerical Frequencies (Dataset)

description: 1<em>H</em>-pyrrolo[3,2-<em>h</em>]quinoline [Gorski, 2012] was optimized in ORCA v3.0.3 [Neese, 2012; http://orcaforum.cec.mpg.de] using RPBE [Perdew, 1992 and 1996] with the def2-TZVP basis sets [Weigend, 1998], and the def2-TZVP/J auxiliary bases [Weigend, 2006] for the RI approximation [Vahtras, 1992]. The nuclear Hessian, normal modes, and harmonic vibrational frequencies were then computed using analytical (ANFREQ) and numerical (NUMFREQ) methodologies.  The numerical Hessians were computed with nuclear (Cartesian) displacement increments ranging from 0.0001 Bohr to 0.1 Bohr.  The geometry optimization was conducted using the parameters of the TIGHTOPT simple input keyword; KS-SCF and CP-SCF calculations used VERYTIGHTSCF thresholds.

An analysis of the deviation of normal modes and harmonic frequencies for each numerical Hessian computation from the analytical Hessian results was presented as a single-figure presentation (SFP) at the 2016 Virtual Winterschool on Computational Chemistry (http://winterschool.cc). This SFP can be found at doi:10.5281/zenodo.44807.

For the initial OPT and ANFREQ, the following files are provided:<br>
PQ_OPT_AFQ.engrad -- Gradient data<br>
PQ_OPT_AFQ.gbw -- Wavefunction <br>
PQ_OPT_AFQ.hess -- Hessian data<br>
PQ_OPT_AFQ.out -- Computation output<br>
PQ_OPT_AFQ.trj -- Optimization trajectory (multi-frame OpenBabel XYZ)<br>
PQ_OPT_AFQ.txt -- ORCA input file<br>
PQ_OPT_AFQ.xyz -- Optimized geometry

For each following NUMFREQ, the following files are provided, where the number at the end of the filename indicates the nuclear displacement increment in Bohrs:<br>
PQ_NFQ_0.####.hess -- Hessian data<br>
PQ_NFQ_0.####.out -- Computation output<br>
PQ_NFQ_0.####.txt -- ORCA input file

Since ORCA does not report non-mass-weighted normal modes, these are provided separately for each calculation as modes_0.####.csv (modes_A.csv for the analytical Hessian.)

The dot products of each normal mode from the numerical Hessian computations with the corresponding mode in the analytical Hessian calculation (modes ordered as presented in the ORCA output) are provided in modes_dot_products.csv. The MAD of these data are plotted in the LH figure of the above-referenced SFP.

For those numerical Hessian computations with normal modes out of sequence relative to the analytical calculation, permutation matrices to bring them back in accord with the analytical Hessian modes are included as swaps_0.####.csv.

A table of the calculated vibrational frequencies for each computation, re-ordered as necessary to bring the normal modes in accord with the analytical Hessian run, is included as freqs_swapped.csv. The MAD and maximum absolute deviation of these data are plotted in the RH figure of the above-referenced SFP.
description: {"references": ["Gorski et al., J Phys Chem A 116, 11973 (2012) [doi:10.1021/jp309618b]", "Neese, WIREs Comput Mol Sci 2(1), 73 (2012) [doi:10.1002/wcms.81]", "Perdew et al., Phys Rev B 46, 6671 (1992) [doi:10.1103/PhysRevB.46.6671]", "Perdew et al., Phys Rev Lett 77, 3865 (1996) [doi:10.1103/PhysRevLett.77.3865]", "Vahtras et al., Chem Phys Lett 213(5-6), 514 (1992) [doi:10.1016/0009-2614(93)89151-7]", "Weigend et al., Chem Phys Lett 294(1-3), 143 (1998) [doi:10.1016/S0009-2614(98)00862-8]", "Weigend, Phys Chem Chem Phys 8, 1057 (2006) [doi:10.1039/B515623H]"]}