Proceedings - Interdisciplinary Center for Nanotoxicity

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Table 2. Calculated scale factors for C4N2H4
Conference on Current Trends in Computational Chemistry 2009
HF/6‐31G*( α=9.90·10 ‐3 )
N1 C2 C3 C4 C5 H6 H7 H8 H9 H10
N1 0.9116 0.0101 0.0101 0.0015 0.0015 0.0124 0.0053 0.0053 0.0063 0.0063
C2 0.0101 0.9037 0.0044 0.0107 0.0122 0.0015 0.0121 0.0042 0.0053 0.0061
C3 0.0101 0.0044 0.9037 0.0122 0.0107 0.0015 0.0042 0.0121 0.0061 0.0053
C4 0.0015 0.0107 0.0122 0.9037 0.0044 0.0101 0.0053 0.0061 0.0121 0.0042
C5 0.0015 0.0122 0.0107 0.0044 0.9037 0.0101 0.0061 0.0053 0.0042 0.0121
N6 0.0124 0.0015 0.0015 0.0101 0.0101 0.9116 0.0063 0.0063 0.0053 0.0053
H7 0.0053 0.0121 0.0042 0.0053 0.0061 0.0063 0.9177 0.0040 0.0021 0.0073
H8 0.0053 0.0042 0.0121 0.0061 0.0053 0.0063 0.0040 0.9177 0.0073 0.0021
C9 0.0063 0.0053 0.0061 0.0121 0.0042 0.0053 0.0021 0.0073 0.9177 0.0040
H10 0.0063 0.0061 0.0053 0.0042 0.0121 0.0053 0.0073 0.0021 0.0040 0.9177
B3LYP/6‐31G* (α=5.21·10 ‐2 )
N1 C2 C3 C4 C5 N6 H7 H8 H9 H10
N1 0.9774 0.0015 0.0015 0.0006 0.0006 0.0013 0.0018 0.0018 0.0022 0.0022
C2 0.0015 0.9748 0.0007 0.0013 0.0014 0.0006 0.0039 0.0023 0.0028 0.0016
C3 0.0015 0.0007 0.9748 0.0014 0.0013 0.0006 0.0023 0.0039 0.0016 0.0028
C4 0.0006 0.0013 0.0014 0.9748 0.0007 0.0015 0.0028 0.0016 0.0039 0.0023
C5 0.0006 0.0014 0.0013 0.0007 0.9748 0.0015 0.0016 0.0028 0.0023 0.0039
N6 0.0013 0.0006 0.0006 0.0015 0.0015 0.9774 0.0022 0.0022 0.0018 0.0018
H7 0.0018 0.0039 0.0023 0.0028 0.0016 0.0022 0.9678 0.0030 0.0022 0.0034
H8 0.0018 0.0023 0.0039 0.0016 0.0028 0.0022 0.0030 0.9678 0.0034 0.0022
C9 0.0022 0.0028 0.0016 0.0039 0.0023 0.0018 0.0022 0.0034 0.9678 0.0025
H10 0.0022 0.0016 0.0028 0.0023 0.0039 0.0018 0.0034 0.0022 0.0030 0.9678
Results show good correspondence between experimental and fitted frequencies and
closeness of the results of frequency correction with Cartesian scaling factors to the quality of
their correction by scaling force matrices in internal coordinates. Quite predictably, scale
factors for B3LYP simulations are much closer to unit matrices, and frequency fitting is
considerably better. It shows that the model of correcting theoretical vibrational frequencies by
means of scaling Cartesian force matrices is quite reasonable. Note that diagonal scale factors
for similar atoms in benzene and pyrazine molecules are close for each theoretical level. The
same is true for the pairs of bonded atoms (C, H); this shows good possibilities of transferring
scale factors for the atoms in similar environment. It is also possible to apply the procedure for
each symmetry block individually, yielding somewhat better frequency fitting, similar to what is
often done for the standard scaling approach. Small values of certain scale factors indicate the
possibility of stipulating them as fixed zero elements in minimization procedure.
Acknowledgements: This work was partly supported by RFFI grant No 08‐03‐00415‐а.
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