Uncontracted core Pople basis sets in vibrational frequency calculations

Abstract

The effects that uncontracting the core 1s basis functions in the Pople basis sets have on the calculation of harmonic vibrational frequencies, scaling factors, and anharmonic frequencies are examined for a selection of hybrid and meta‐hybrid density functional theory methods across a wide range of molecules. Median improvements of around half a wavenumber indicate that uncontracting the core functions provides modest improvements for harmonic calculations. The importance of these core functions is found to increase when using meta‐hybrid or anharmonic methods. The core functions are also found to be particularly important for several types of vibrational coordinate, including some carbonyl and carbon‐nitrogen stretching modes, where interaction between the uncontracted 1s functions and triple‐ζ 2s functions appear to play a significant role. Extra core functions are also particularly important for anharmonic second‐order perturbation theory calculations involving alkyne molecule bending modes, where individual transitions can change by as much as 230 wavenumbers.

Benchmarking DFT-D Dispersion Corrections for Anharmonic Vibrational Frequencies and Harmonic Scaling Factors

“…To assess the effects that DFT-D dispersion corrections have on anharmonic frequency shifts, it is important to first look at the changes that these corrections introduce into the harmonic vibrations. The incorporation of anharmonicity through the use of linear scaling factors has also proven to be an effective correction to the harmonic approximation for a wide variety of molecular systems. ,− The commonly used F1 molecular test set has therefore been used both to examine the magnitude of the harmonic frequency shifts due to dispersion effects and also to conduct a systematic study of the scaling factors appropriate for the range of DFT-D methods studied.…”

“…However, the average differences between the dispersion corrected and uncorrected 2MR anharmonic frequencies (Δ2MR) are either smaller, or not much larger, than the differences between the corrected and uncorrected harmonic frequencies (Δ0MR) shown in Table . To better quantify the impact that the dispersion corrections have on the diagonal and mode-coupling aspects of the anaharmonicity, these differences, termed Δ diag and Δ cpl , are defined by and where ν is a fundamental transition frequency in wavenumbers, the superscripts “Disp” and “B3LYP” denote the use of the B3LYP functional either with or without an empirical dispersion correction, respectively, while the nMR subscripts denote the truncation level of the anharmonic force field. The differences between these two types of anharmonic shift show that the effect dispersion corrections have on the mode-coupling terms is more significant than the Δ2MR values would suggest.…”

“…32 The anharmonic frequency calculations were compared to fundamentals from a reduced variation of the F1 set, termed the modified anharmonic F1 set (Table 1). 33 These modifications were chosen to reduce the number of molecules and modes to a more computationally manageable number, with focus on reducing the number of "floppy" molecules, that is, molecules that are not semirigid, as well as molecules containing molecular rotors or high symmetry axes which are known to cause problems matching with experiment under certain conditions. 31 The following low-frequency modes have also been removed for consistency across the anharmonic methods tested: ClF 3 , modes 1−2; ClSN, mode 1; NCl 2 F, mode 1; Cl 2 O, mode 1; SOCl 2 , modes 1−2; SCl 2 , mode 1; SOCl 2 , modes 1−2; SCl 2 , mode 1; S 2 F 2 , modes 1−3; COCl 2 , mode 1; CSCl 2 , modes 1−2; C 2 Cl 2 , modes 1−4; C 2 N 2 , modes 1−2; trans-CHClCHCl, modes 1−2; cis-CHClCHCl, mode 1; CH 2 CCl 2 , mode 1; cis-CHFCHF, mode 1; OCHCHO, mode 1; CH 2 CCHCl, mode 1; CH 2 CHCHO, mode 1; HCCCCH, modes 1−2; CH 2 CHCHCH 2 , modes 1−2.…”

Excited-State Vibrational Frequencies: Restricted Virtual Space Time-Dependent Density Functional Theory

“…Previous studies have looked at the effects of reducing the excitation space within TDDFT for other properties and have found that removing excitations from occupied core donor orbitals could also be an effective way of reducing the calculation size without introducing significant errors. , However, one recent study found that core basis functions can be important for describing vibrational frequencies in the ground state . The effects that removing the core orbitals has on the S 1 -calculated vibrational frequencies have therefore been tested for these molecules as well, by removing either one or both of the core orbitals in each molecule, as shown in Tables – .…”

“…31,32 However, one recent study found that core basis functions can be important for describing vibrational frequencies in the ground state. 46 The effects that removing the core orbitals has on the S 1 -calculated vibrational frequencies have therefore been tested for these molecules as well, by removing either one or both of the core orbitals in each molecule, as shown in Tables 4−8. In the case of ethene, the core orbitals are not localized onto one specific carbon atom but rather involve in-phase (ip) and out-of-phase (oop) combinations of the C(1s) atomic orbitals shown in Figure 7.…”