Vibrational frequency scale factors for density functional theory and the polarization consistent basis sets

Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (<1000 cm^?1) and high (>1000 cm^?1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero‐point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc‐n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree‐Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05‐2X, M06‐2X), a double hybrid functional with Møller‐Plesset correlation (B2GP‐PLYP), and a dispersion corrected functional (B97‐D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc‐n, n = 1,2,3,4). A separate scale factor is recommended when the un‐polarized basis set, pc‐0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.     

Vibrational spectra and reinvestigation of the crystal structure of a polymeric copper(II)-orotate complex, [Cu(μ-HOr)(H2O)2]n: The performance of new DFT methods, M06 and M05-2X, in theoretical studies

The crystal and molecular structure of a polymeric Cu(II)-orotate complex, [Cu(μ-HOr)(H₂O)₂]_n, has been reinvestigated by single crystal X-ray diffraction. It is shown that several synergistic interactions: two axial Cu-O interactions; intramolecular and intermolecular hydrogen bonds; and π-π stacking between the uracil rings contribute to the stability of the crystal structure. The Raman and FT-IR spectra of the title complex are reported for the first time. Comprehensive theoretical studies have been performed by using three unrestricted DFT methods: B3LYP; and the recently developed M06, and M05-2X density functionals. Clear-cut assignments of all the bands in the vibrational spectra have been made on the basis of the calculated potential energy distribution, PED. The very strong Raman band at 1219 cm⁻¹ is diagnostic for the N1-deprotonation of the uracil ring and formation of the copper-nitrogen bond, in this complex. The Cu-O (carboxylate) stretching vibration is observed at 287 cm⁻¹ in the IR spectrum, while the Cu-N (U ring) stretching vibration is assigned to the strong Raman band at 263 cm⁻¹. The molecular structure and vibrational spectra (frequencies and intensities) calculated by the M06 functional method are very similar to the results obtained by the B3LYP method, but M06 performs better than B3LYP in calculations of the geometrical parameters and vibrational frequencies of the interligand O-H?O hydrogen bonding. Unfortunately, the M05-2X method seriously overestimates the strength of interligand hydrogen bond.     

Influence of the exchange‐correlation functional in all‐electron calculations of the vibrational frequencies of corundum (α‐Al2O3)

The equilibrium structural parameters, high‐ and low‐frequency dielectric tensors, Born effective charges, and Γ‐point vibrational frequencies of bulk Al₂O₃ corundum are calculated by using the periodic, ab initio program CRYSTAL, which adopts an all‐electron Gaussian‐type basis set. The effect of basis set and the performance of three different functionals, i.e., LDA, PW91, and B3LYP, are discussed. The mean absolute deviation from the measured frequencies is as small as 7 cm^?1 for both the LDA and B3LYP functionals, indicating that these functionals perform extremely well in this case. The mean absolute deviation increases to 18 cm^?1 when the PW91 functional is used. All three functionals reproduce the equilibrium geometry of corundum to a high level of accuracy, with LDA and B3LYP outperforming PW91 slightly. The comparison of the current all‐electron calculations with previous plane‐wave, pseudo‐potential calculations shows an overall similar performance. The results of isotopic substitution for both Al and O are also presented. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Scaling factors for vibrational frequencies and zero-point vibrational energies of some recently developed exchange-correlation functionals

The scaling factors for the vibrational frequencies and zero-point vibrational energies evaluated at various combinations of recently developed exchange-correlation functionals and various basis sets are reported. The exchange-correlation functionals considered are B972, B98, HCTH, OLYP, O3LYP, G96LYP, PBE0 and VSXC functionals; the basis sets employed are 3-21G, 6-31G*, 6-31G**, 6-31+G, 6-311G*, 6-311G**, 6-311G(df,p), 6-311+G(df,p), cc-pVDZ and aug-cc-pVDZ. The experimental harmonic frequencies of 122 small molecules and the zero-point vibrational energies of 39 small molecules are used to determine the scaling factors through the least-square fitting procedure. It was found that the scaling factors do not depend significantly on the basis sets considered. The vibrational frequency scaling factors evaluated by using the B98 and PBE0 functionals are recommended on the basis of smallest root mean square error. The zero-point vibrational energy scaling factors evaluated from the B972 functional with Pople's double-zeta basis set and the HCTH functional with Pople's triple-zeta basis set are recommended on the basis of smallest root mean square error.     

Conformational equilibrium study of calix[4]tetrolarenes using Density Functional Theory (DFT) and Molecular Dynamics simulations

The present work deals with the theoretical study of conformational equilibrium of calix[4]tetrolarenes (1,2,3 trimethoxy substituted calix[4]arene) in gaseous and solvation phases. A total of 64 calculations (four conformations at eight level of theories) were performed using Density Functional Theory (DFT) functionals viz. wB97XD, B97D, B3LYP, CAM-B3LYP with diffused (6–31 + G(d)) and non-diffused basis sets (6-31G(d)). It has been found that the conformational profile of calix[4]tetrolarene changes from cone to 1,3-Alternate upon incorporating – OMe group. The B97D and wB97XD functionals gave the most accurate result having rmsd value ~0.73Å followed by B3LYP and CAM-B3LYP > 0.78Å. Furthermore, NBO calculations demonstrated that reduction in charges at lower rim oxygens reduces the chances of hydrogen bonding. Moreover, global reactivity parameters and molecular dynamics also complement the observed trend. Owing to the methoxy substitutions, anion binding study of these new molecules indicates towards the promising capability to bind Cl^? and F^? ions.     

Density functional studies of AnF6 (An=U,Np, and Pu) and UF6−nCln (n=1–6) using hybrid functionals: geometries and vibrational frequencies

We have compared the performance of widely used hybrid functionals for calculating the bond lengths and harmonic vibrational frequencies of AnF₆ (An=U, Np, and Pu) and UF_6?nCl_n (n=1–6) molecules using “small‐core” relativistic effective core potentials and extended basis sets. The calculated spectroscopic constants compare favorably with experimental data for the bond lengths (average error ≤ 0.01 Å) and vibrational frequencies (average error ≤ 7 cm^?1) of the AnF₆ molecules. The experimental vibrational frequencies of the stretching modes were available for most of the UF_6?nCl_n (n=1–6) molecules. The calculated vibrational frequencies are in good agreement with the experimental data to within 4.6 cm^?1 and 7.6 cm^?1 for selected Becke1 and Lee, Yang, Parr (B1LYP), and Becke3 and Perdew, Wang (B3PW91) functionals, respectively. We conclude that one can predict reliable geometries and vibrational frequencies for the unknown related systems using hybrid density functional calculations with the RECPs. The geometries and vibrational frequencies of the UF_6?nCl_n (n=1–6) molecules that have not been determined experimentally are also presented and discussed. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 2010–2017, 2001     

An evaluation of scaling factors for multiparameter scaling procedures based on DFT force fields

An extended database of scaling factors for calculating fundamental frequencies within multiparameter scaled quantum mechanical (SQM) force field, and effective scaling frequency factor (ESFF) methods, based on various DFT force fields is reported. Twenty-six density functionals have been examined in conjunction with various Pople's and Dunning's basis sets of VDZ and VTZ quality. The calculations were based on a standard training set of 30 molecules proposed by Baker et al., for which 660 vibrational modes were assigned. Six functionals turned out to be particularly well-suited to the calculations oriented toward determination of scaled frequencies. They are B3LYP, B3PW91, B97, B97-1, B97-2, and O3LYP; they are all capable of providing reasonable scaled frequencies even for the small, 6-31G* basis set (rms <15 cm(-1)). Correlations between the quality of the scaled frequencies and the basis set quality as well as the accuracy of the predicted molecular geometry were investigated. The 6-311+G** basis set turned out to be preferable. In addition, correlation between the rms values in the scaled frequencies and the errors in the predicted geometric parameters was found. Both 11- and 9-parameter scaling frames are compared. It is shown that 9-parameter scaling is preferable in the middle range of the vibrational spectrum (500-2500 cm(-1)), provided it was based on high-quality force fields. Finally, statistical uncertainties of the calculated scaling factors are reported.     

Oscillator strengths of the bands of the B̃2 A′1—X̃2 A″2 system of CD3 and a spectroscopic measurement of the recombination rate comparison with CH3

Absolute CD₃ concentrations were measured in the flash photolysis of d₆-HgMe₂. An oscillator strength of (0.99 ± 0.10) × 10^?2 was recorded for the 0O band of the B?—X? system, and a recombination rate coefficient of (4.9 ± 0.4) × 10^?11 cm³ molecule^?1 s^?1 was derived. It is suggested that the probability of recombination per collision is virtually the same as for the CH₃ radical.Some new bands of the B?—X? system have been discovered and tentatively assigned: from a study of the temperature dependence of the intensity of the 47300 cm^?1 transition, Herzberg's scheme ‘b’ has been established for the vibrational assignment.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

Theoretical and experimental study on metal(II) halide complexes of 1,3-bis(4-pyridyl)propane

We report the results of detailed experimental and theoretical studies on the molecular structure and vibrational spectra of metal(II) halide complexes of 1,3-bis(4-pyridyl)propane [M(N₂C₁₃H₁₄)X₂, where M represents Zn or Hg, and X represents Cl, Br, or I]. The FT–infrared spectra (FT-IR) and FT-Raman spectra of the metal complexes of the 1,3-bis(4-pyridyl)propane molecule in the powder form were recorded between the 400–4000 and 5–3500 cm^?1 regions, respectively. The molecular geometry and vibrational frequencies of the metal complexes of 1,3-bis(4-pyridyl)propane in the ground state were calculated using density functional theory (B3LYP functional) with LANL2DZ and SDD as basis sets. The total energy distributions (TED) among the symmetry coordinates of the normal modes were computed for the low-energy structure of the molecules. Complete vibrational assignments based on the calculated TED values are given.     

Vibrational assignment of the spectral data and thermodynamic properties of 2-chloro-4-fluorobenzophenone using DFT quantum chemical calculations

The FT-Raman (3500-100 cm⁻¹) and FT-IR (4000-450 cm⁻¹) spectra of 2-chloro-4-fluorobenzophenone were recorded in the solid phase. Density functional theory calculations with B3LYP/6-31G (d, p) basis set was used to determine the ground state molecular geometries (bond lengths and bond angles), harmonic vibrational frequencies, infrared intensities and Raman activities of this compound. Potential energy distributions (PEDs) and normal modes, for the spectral data computed at B3LYP/6-31G (d, p) level, have also been obtained from force-field calculations. The wavenumbers found after scaling of the force field showed very good agreement with the experimentally determined values. A comparison of the theoretical spectra and experimental FT-IR and FT-Raman spectra of the title molecule has been made and full vibrational assignments of the observed spectra have been proposed. On the basis of vibrational analyses, the thermodynamic properties of title compound at different temperatures have been calculated.     

HF and DFT studies and vibrational spectra of 1,2-bis(2-pyridyl)ethylene and its zinc (II) halide complexes

Ab initio restricted Hartree–Fock and density function theory calculations using BLYP, B3LYP and B3PW91 functionals were carried out to study molecular structure and vibrational spectrum of 1,2-bis(2-pyridyl)ethylene (which is abbreviated as bpe). Comparison of calculated and experimental results indicates the density functional B3LYP and BLYP/6-311G* methods are more accurate in predicting fundamental vibrational frequencies than the scaled other approaches. On the basis of calculated results, assignment of fundamental vibrational modes of bpe was proposed. Complexes of the type Zn(bpe)X₂ [where X = Cl, Br, I] have been studied in the 4000–400 cm⁻¹ region, and assignments of all the observed bands were made. The analysis of the infrared spectra indicates that there is some structure-spectra correlations.     

用GGA密度泛函及其长程、色散校正方法计算各类氢键的结合能

应用广义梯度近似(GGA) (PW91和PBE)、含动能密度的广义梯度近似(meta-GGA) (M06-L)、杂化泛函(hyper-GGA)(M06-2X、X3LYP和B3LYP)及其长程校正泛函LC-DFT(CAM-B3LYP、LC-ωPBE和ωB97X)和色散校正密度泛函(DFT-D)(ωB97X-D和B97-D),用多种基函数对15种不同强度的传统氢键和非传统氢键体系的结合能进行了系统的计算与分析.并与高精度的CCSD(T)/aug-cc-pVQZ结果比较发现:在上述各类泛函中,对于氢键结合能的计算M06-2X和ωB97X-D泛函较为精确与可靠,且没有必要使用过大的基函数,6-311++G(2d,2p)或aug-cc-pVDZ水平的基组就已足够,各类泛函所计算结合能的基组重叠误差(BSSE)均较小,除ωB97X和ωB97X-D外,其它9种泛函不经BSSE校正也能得到同样甚至更准确的结果.     

DFT, FT-Raman, and FT-IR investigations of 1-cyclopropylpiperazine

FT-IR and FT-Raman spectra of 1-cyclopropylpiperazine (1cppp) are experimentally examined in the range 4000-200 cm^?1. The optimized geometric parameters, conformational equilibria, normal mode frequencies and corresponding vibrational assignments of 1cppp C₇H₁₄N₂ are theoretically examined by means of B3LYP hybrid density functional theory (DFT) with the 6–31++G(d,p) basis set. Based on the potential energy distribution (PED) reliable vibrational assignments are made and the thermodynamics functions, highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) of 1cppp are predicted. Calculations are performed for four different conformations in two point groups of 1cppp in the gas phase. A comparison between the experimental and theoretical results indicates that the B3LYP method is able to provide satisfactory results for the prediction of vibrational frequencies, structural parameters, and assignments. Furthermore, the C _s (equatorial-equatorial) point group is found as the most stable conformer of 1cppp.     

Energy-transfer reactions between He(2 3S) and Ne(3P0.2) metastable atoms and PN radicals

Energy-transfer reactions between He(2 ³S) and Ne(³P_0.2) metastable atoms and PN radicals have been investigated by emission spectroscopy. Thirteen new PN⁺ (B ¹Σ⁺ ?X ²Σ⁺) emission bands were found in addition to eight previously identified bands in the range 305–395 nm. From these observed band-head wavelengths, the following molecular constants were obtained for the X and B states of PN⁺ : PN⁺ (X): ω_c = 1306 ± 3 cm^?1, ω_cx_c = 7.9 ± 0.7 cm^?1, PN^? (B): T_c = 31354 ± 6 cm^?1, ω_c = 719 ± 3 cm^?1, ω_cx_c = 1.6 ± 0.7 cm^?1. The PN⁺ (B) state vibrational population was estimated from the emission intensities and the calculated Morse Franck—Condon (FC) factors for the PN⁺ (B–X) transition. Both the results obtained by He(2 ³S) and Ne(³P_0.2) Penning ionization shifted to lower vibrational levels in comparison with the calculated FC factors for vertical PN(X) → PN⁺ (B) ionization. Besides PN⁺ (B–X) emission, unidentified bands were observed in the 231–236 nm region in the helium afterglow, probably originating from PN or PN^?.     

DFT, FT-Raman and FT-IR investigations of 5-methoxysalicylic acid

FT-IR and FT-Raman spectra of 5-methoxysalicylic acid (5MeOSA) have been experimentally reported in the region of 4000–10 cm⁻¹ and 4000–50 cm⁻¹, respectively. The optimized geometric parameters, conformational equilibria, normal mode frequencies and corresponding vibrational assignments of 5MeOSA (C₈H₈O₄) are theoretically examined by means of B3LYP hybrid density functional theory (DFT) method together with 6-31++G(d,p) basis set. Furthermore, reliable vibrational assignments have made on the basis of potential energy distribution (PED) calculated and the thermodynamics functions, highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) of 5MeOSA have been predicted. Calculations are employed for different conformations of 5MeOSA, both in gas phase and in solution. Solvent effects are investigated using chloroform and dimethylsulfoxide. All results indicate that B3LYP method is able to provide satisfactory results for predicting vibrational frequencies and the structural parameters, vibrational frequencies and assignments, IR and Raman intensities of 5MeOSA are solvent dependent.     

Improvement of scale factors for harmonic vibrational frequency calculations using new polarization functions

Density functional calculations were carried to improve the calculated CO vibrational frequencies for transition metal carbonyls. Two types of density functionals were studied, hybrid and generalized‐gradient methods. Using the simplex optimization method, new polarization functions for C and O atoms were obtained. With these new optimized functions, new scaling factors were obtained. The results reveal that, with the new polarization functions, the agreement between the calculated and the experimental values improves considerably. In general, the new scaling factors are very close to unit, with standard uncertainties close to ±0.006 cm^?1. The use of the new polarization functions allows more precise calculations of the transition metal carbonyl CO vibrational frequencies. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008