Table 1
Frequency-range-specific scaling factors for the PAHs in Figure 1.
| PAH | ![]() |
![]() |
B3LYP Max.r.e. | ![]() |
D3 Max.r.e. |
|---|---|---|---|---|---|
| In | 0.9563 a | 0.9834 | 0.0132 | 0.9852 | 0.0269 |
| 0.9523 b | 0.9677 | 0.0124 | 0.9675 | 0.0151 | |
| 0.9595 c | 0.9612 | 0.0025 | 0.9614 | 0.0023 | |
| Iyl | 0.9563 | 0.9830 | 0.0099 | 0.9838 | 0.0093 |
| 0.9523 | 0.9665 | 0.0074 | 0.9664 | 0.0114 | |
| 0.9595 | 0.9621 | 0.0026 | 0.9627 | 0.0028 | |
| An | 0.9794 | 0.9815 | 0.0109 | 0.9807 | 0.0190 |
| 0.9691 | 0.9734 | 0.0103 | 0.9711 | 0.0114 | |
| 0.9597 | 0.9603 | 0.0001 | 0.9610 | 0.0003 | |
| Tn | 0.9563 | 0.9830 | 0.0103 | 0.9818 | 0.0118 |
| 0.9523 | 0.9677 | 0.0120 | 0.9679 | 0.0037 | |
| 0.9595 | 0.9608 | 0.0012 | 0.9614 | 0.0009 | |
| Pn | 0.9563 | 0.9854 | 0.0402 | 0.9848 | 0.0500 |
| 0.9523 | 0.9676 | 0.0102 | 0.9648 | 0.0113 | |
| 0.9595 | 0.9612 | 0.0013 | 0.9618 | 0.0010 | |
Notes. The scaling factors from the AMES PAH database (
) are compared to those from this work: 6-31+G(d)/B3LYP
and 6-31+G(d)/B3LYP+GD3 (
). The maximum relative errors (Max.r.e) of the scaled frequencies are also included for both
and
. The specific frequency (or wavelength) range of harmonic frequencies for each scaling factor in this work
is according to the standard range set proposed by Zapata Trujillo & McKemmish (2022a,b). The wavelength ranges are highlighted for indene (In) as an example: (a)> 10 μm, (b)5–10 μm, (c)<5 μm. Max.r.e was computed using wavelength units.
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![$\[\mathrm{SF}_{3}^{\mathrm{AMES}}\]$](/articles/aa/full_html/2025/12/aa54031-25/aa54031-25-eq6.png)
![$\[\mathrm{SF}_{3}^{\text {B3LYP}}\]$](/articles/aa/full_html/2025/12/aa54031-25/aa54031-25-eq7.png)
![$\[\mathrm{SF}_{3}^{\mathrm{D} 3}\]$](/articles/aa/full_html/2025/12/aa54031-25/aa54031-25-eq8.png)