Harmonic vibrational frequencies: scale factors for pure, hybrid, hybrid meta, and double-hybrid functionals in conjunction with correlation consistent basis sets

Scale factors for (a) low (<1000 cm(-1)) and high harmonic vibrational frequencies, (b) thermal contributions to enthalpy and entropy, and (c) zero-point vibrational energies have been determined for five hybrid functionals (B3P86, B3PW91, PBE1PBE, BH&HLYP, MPW1K), five pure functionals (BLYP, BPW91, PBEPBE, HCTH93, and BP86), four hybrid meta functionals (M05, M05-2X, M06, and M06-2X) and one double-hybrid functional (B2GP-PLYP) in combination with the correlation consistent basis sets [cc-pVnZ and aug-cc-pVnZ, n = D(2),T(3),Q(4)]. Calculations for vibrational frequencies were carried out on 41 organic molecules and an additional set of 22 small molecules was used for the zero-point vibrational energy scale factors. Before scaling, approximately 25% of the calculated frequencies were within 3% of experimental frequencies. Upon application of the derived scale factors, nearly 90% of the calculated frequencies deviated less than 3% from the experimental frequencies for all of the functionals when the augmented correlation consistent basis sets were used.     

Evaluation of range-separated hybrid density functionals for the prediction of vibrational frequencies, infrared intensities, and Raman activities

We present an assessment of different density functionals, with emphasis on range-separated hybrids, for the prediction of fundamental and harmonic vibrational frequencies, infrared intensities, and Raman activities. Additionally, we discuss the basis set convergence of vibrational properties of H2O with long-range corrected hybrids. Our results show that B3LYP is the best functional for predicting vibrational frequencies (both fundamental and harmonic); the screened-PBE hybrid (HSE) density functional works best for infrared intensities, and the long-range corrected PBE (LC-omegaPBE), M06-HF, and M06-L density functionals are almost as good as MP2 for predicting Raman activities. We show the predicted Raman spectrum of adenine as an example of a medium-size molecule where a DFT/Sadlej pVTZ calculation is affordable and compare our results against the experimental spectrum.     

An evaluation of harmonic vibrational frequency scale factors

Scale factors for obtaining fundamental vibrational frequencies, low-frequency vibrational frequencies, zero-point vibrational energies (ZPVEs), and thermal contributions to enthalpy and entropy have been derived through a least-squares approach from harmonic frequencies determined at more than 100 levels of theory. Wave function procedures (HF, MP2, QCISD, QCISD(T), CCSD, and CCSD(T)) and a large and representative range of density functional theory (DFT) approaches (B3-LYP, BMK, EDF2, M05-2X, MPWB1K, O3-LYP, PBE, TPSS, etc.) have been examined in conjunction with basis sets such as 6-31G(d), 6-31+G(d,p), 6-31G(2df,p), 6-311+G(d,p), and 6-311+G(2df,p). The vibrational frequency scale factors were determined by a comparison of theoretical harmonic frequencies with the corresponding experimental fundamentals utilizing a standard set of 1066 individual vibrations. ZPVE scale factors were generally obtained from a comparison of the computed ZPVEs with experimental ZPVEs for a smaller standard set of 39 molecules, though the effect of expansion to a 48 molecule data set was also examined. In addition to evaluating the scale factors for a wide range of levels of theory, we have also probed the effect on scale factors of varying the percentage of incorporated exact exchange in hybrid DFT calculations using a modified B3-LYP functional. This has revealed a near-linear relationship between the magnitude of the scale factor and the proportion of exact exchange. Finally, we have investigated the effect of basis set size on HF, MP2, B3-LYP, and BMK scale factors by deriving values with basis sets ranging from 6-31G(d) up to 6-311++G(3df,3pd) as well as with basis sets in the cc-pVnZ and aug-cc-pVnZ series and with the TZV2P basis.     

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.     

What are the spectroscopic properties of HFC‐32? Answers from DFT

Although coupled cluster theory coupled to large basis sets can reach impressive accuracies for thermochemical and spectroscopic properties, it is still limited to small/medium sized molecules. Density functional theory (DFT) represents the working option for systems composed of hundreds to thousands heavy atoms. In this context, investigations are required aimed at characterizing the performances of the different density functionals (DF). This work focuses on the study of DFT performances in the prediction of spectroscopic properties, with particular attention to the vibrational problem, by focusing on the CH₂F₂ molecule as a test case. An extensive and systematic investigation is performed on several DFT model chemistries by testing their predictions of molecular constants and vibrational frequencies and intensities against CCSD(T)/aug‐cc‐pCVQZ data. B3LYP, B3PW91, B97‐1, PBE0, TPSSh, M05, M05‐2X, and B2PLYP DFs are used in conjunction with a variety of basis sets. Anharmonic frequencies are derived from the VPT2 treatment of anharmonic‐ and hybrid CCSD(T)/DFT‐force fields. A software for VPT2 computations is also presented. © 2014 Wiley Periodicals, Inc.     

Is the uniform electron gas limit important for small Ag clusters? Assessment of different density functionals for Ag(n) (n < or = 4)

Twenty-three density functional theory (DFT) methods, including the second- and the third-generation functionals, are tested in conjunction with two basis sets (LANL2DZ and SDD) for studying the properties of neutral and ionic silver clusters. We find that DFT methods incorporating the uniform electron gas limit in the correlation functional, namely, those with Perdew's correlation functionals (PW91, PBE, P86, and TPSS), Becke's B95, and the Van Voorhis-Scuseria functional VSXC, generally perform better than the other group of functionals, e.g., those incorporating the LYP correlation functional and variations of the B97 functional. Strikingly, these two groups of functionals can produce qualitatively different results for the Ag3 and Ag4 clusters. The energetic properties and vibrational frequencies of Ag(n) are also evaluated by the different functionals. The present study shows that the choice of DFT methods for heavy metals may be critical. It is found that the exact-exchange-incorporated PBE functional (PBE1PBE) is among the best for predicting the range of properties.     

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized‐gradient approximation (GGA), nonlocal correlation, meta‐GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised‐RPBE, vdW‐DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW‐DF and meta‐GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of ?2.62 and ?1.1% for the N? N stretching and Rh? H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh? H and N? N stretching modes from the bulk phonons and by solving one‐ and two‐dimensional Schrödinger equation associated with the Rh? H, Rh? N, and N? N potential energy we calculated the anharmonic correction for N? N and Rh? H stretching modes as ?31 cm^?1 and ?77 cm^?1 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. © 2014 Wiley Periodicals, Inc.     

Hydrogen bonding in the urea dimers and adenine–thymine DNA base pair: anharmonic effects in the intermolecular H-bond and intramolecular H-stretching vibrations

The equilibrium structures, binding energies, vibrational harmonic frequencies, and the anharmonic corrections for two different (cyclic and asymmetric) urea dimers and for the adenine–thymine DNA base pair system have been studied using the second-order Møller–Plesset perturbation theory (MP2) method and different density functional theory (DFT) exchange–correlation (XC) functionals (BLYP, B3LYP, PBE, HCTH407, KMLYP, and BH and HLYP) with the D95V, D95V**, and D95V++** basis sets. The widely used a posteriori Boys–Bernardi or counterpoise correction scheme for basis set superposition error (BSSE) has been included in the calculations to take into account the BSSE effects during geometry optimization (on structure), on binding energies and on the different levels of approximation used for calculating the vibrational frequencies. The results obtained with the ab initio MP2 method are compared with those calculated with different DFT XC functionals; and finally the suitability of these DFT XC functionals to describe intermolecular hydrogen bonds as well as harmonic frequencies and the anharmonic corrections is assessed and discussed.     

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     

DFT calculation and assignment of vibrational spectra of aryl and alkyl chlorophosphates

DFT calculations of vibrational spectra of chlorophosphates using wide range of basis sets and hybrid functionals were performed. Good agreement between calculated and experimental vibrational spectra was reached by the combination of non-empirical functional PBE0 with both middle and large basis sets. The frequencies of the stretching vibrations of the phosphate group calculated using semi-empirical functional B3LYP for all basis sets deviate significantly from the experimental values. The number of polarization functions on heavy atoms was shown to be a key factor for the calculation of vibrational frequencies of organophosphates. The importance of consideration of all the stable rotamers for a complete assignment of fundamental modes was shown.      

Theoretical study of the vibrational frequencies of carbon disulfide

A benchmark comparison for different computational methods and basis sets has been presented. In this study, five computational methods (Hartree–Fock (HF), MP2, B3LYP, MPW1MP91, and PBE1PBE) along with 18 basis sets have been applied to optimize the geometry of carbon disulfide (CS₂), and further calculate the vibrational frequencies of the optimized geometries. The differences between the calculated frequencies and corresponding experimental data are used to evaluate the efficiency of each combination of computational method and basis set. The comparison of frequency difference indicates that B3LYP generally gives the best prediction of frequencies for CS₂, whereas the other two density functional theory (DFT) methods, i.e., MPW1PW91 and PBE1PBE, often give parallel results. Although MP2 predicts the frequencies with accuracy almost as good as those from DFT methods, in a particular case, HF calculation outperforms MP2 as well as MPW1PW91 and PBE1PBE for prediction of the frequency of asymmetrical stretching for CS₂. © 2013 Wiley Periodicals, Inc.     

The confirmation of accurate combination of functional and basis set for transition‐metal dimers: Fe2, Co2, Ni2, Ru2, Rh2, Pd2, Os2, Ir2, and Pt2

Eight kinds of density functionals named B3LYP, PBE1PBE, B1B95, BLYP, BP86, G96PW91, mPWPW91, and SVWN along with two different valence basis sets (LANL2DZ and CEP‐121g) are employed to study the transition‐metal dimers for the elements of group VIII. By comparing the equilibrium bond distances, vibrational frequencies, and dissociation energies of the ground state of these dimers with the available experimental values and theoretical data, we show that the “pure” DFT methods (G96PW91, BLYP, and BP86) with great‐gradient approximation always give better results relative to the hybrid HF/DFT schemes (B3LYP, PBE1PBE, and B1B95). The striking case found by us is that the G96PW91 functional, which is not tested in previous systemic studies, always predicts the dissociation energy to be well. The Ru₂ and Os₂ dimers are sensitive to not only the functionals employed but also the valence basis sets adopted. The natural bond orbital population is analyzed, and the molecular orbitals of the unpaired electrons are determined. Furthermore, our results indicate that the s and d orbitals of these dimers always hybridize with each other except for Rh₂ and Pt₂ molecules. And by analyzing the electron configuration of the bonding atom, the dissociation limit of the ground state is obtained. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Theoretical study on infrared vibrational spectra of boric-acid in gas-phase using density functional methods

Density functional theory (DFT) methods with various exchange-correlation functionals such as SVWN, BVWN, BVWN5, BLYP, B1LYP, B3LYP, B3PW91, and BH and H are employed in a theoretical study of molecular boric-acid in gas-phase. In the calculations, the split valence 6-311++G** and 6-31G* basis sets were used. The geometry, zero-point vibrational energies (ZPVEs), and harmonic infrared vibrational (IR) frequencies are predicted. The calculated C_3h-symmetry geometrical parameters are compared with Hartree–Fock (HF) calculation results and experimental data. IR frequencies predicted by the BLYP, B3LYP, and B3PW91 calculations are in good agreement with experimental data. The frequency calculations presented here also suggest that the C_3h-symmetrical structure corresponds to a minimum in the potential energy surface, but neither is D_3h- or C₃-symmetrical structure.     

Conventional strain energies of azetidine and phosphetane: Can density functional theory yield reliable results?

The conventional strain energies for azetidine and phosphetane are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero‐point vibrational energies are computed for all pertinent molecular systems using self‐consistent field theory, second‐order perturbation theory, and density functional theory and using the correlation consistent basis sets cc‐pVDZ, cc‐pVTZ, and cc‐pVQZ. Single point fourth‐order perturbation theory, CCSD, and CCSD(T) calculations using the cc‐pVTZ and the cc‐pVQZ basis sets are computed using the MP2/cc‐pVTZ and MP2/cc‐pVQZ optimized geometries, respectively, to ascertain the contribution of higher order correlation effects and to determine if the quadruple‐zeta valence basis set is needed when higher order correlation is included. In the density functional theory study, eight different functionals are used including B3LYP, wB97XD, and M06‐2X to determine if any functional can yield results similar to those obtained at the CCSD(T) level. © 2012 Wiley Periodicals, Inc.     

TD-CI simulation of the electronic optical response of molecules in intense fields II: comparison of DFT functionals and EOM-CCSD

Time-dependent configuration interaction (TD-CI) simulations can be used to simulate molecules in intense laser fields. TD-CI calculations use the excitation energies and transition dipoles calculated in the absence of a field. The EOM-CCSD method provides a good estimate of the field-free excited states but is rather expensive. Linear-response time-dependent density functional theory (TD-DFT) is an inexpensive alternative for computing the field-free excitation energies and transition dipoles needed for TD-CI simulations. Linear-response TD-DFT calculations were carried out with standard functionals (B3LYP, BH&HLYP, HSE2PBE (HSE03), BLYP, PBE, PW91, and TPSS) and long-range corrected functionals (LC-ωPBE, ωB97XD, CAM-B3LYP, LC-BLYP, LC-PBE, LC-PW91, and LC-TPSS). These calculations used the 6-31G(d,p) basis set augmented with three sets of diffuse sp functions on each heavy atom. Butadiene was employed as a test case, and 500 excited states were calculated with each functional. Standard functionals yield average excitation energies that are significantly lower than the EOM-CC, while long-range corrected functionals tend to produce average excitation energies slightly higher. Long-range corrected functionals also yield transition dipoles that are somewhat larger than EOM-CC on average. The TD-CI simulations were carried out with a three-cycle Gaussian pulse (ω = 0.06 au, 760 nm) with intensities up to 1.26 × 10(14) W cm(-2) directed along the vector connecting the end carbons. The nonlinear response as indicated by the residual populations of the excited states after the pulse is far too large with standard functionals, primarily because the excitation energies are too low. The LC-ωPBE, LC-PBE, LC-PW91, and LC-TPSS long-range corrected functionals produce responses comparable to EOM-CC.     

Fundamental vibrational frequencies and dominant resonances in methylamine isotopologues by ab initio and density functional theory methods

Ab initio and density functional theory (DFT) calculations were performed for obtaining fundamental vibrational frequencies of methylamine, CH3NH2, and its deuterated variants CH3ND2, CD3NH2, and CD3ND2. The calculations were carried out using the CCSD(T) coupled cluster approximation with cc-pVTZ and cc-pVQZ basis sets, and by the DFT method with the semiempirical hybrid functional B97-1 with polarization consistent pc-2 and pc-3 basis sets. Reasonable performance of the DFT harmonic and ab initio harmonic calculations was found, which improved considerably upon combination of the harmonic fundamental frequencies with anharmonic corrections from the smaller, pc-2, basis. The computed anharmonic fundamental frequencies of methylamine isotopologues agree very well with the experimental values and represent a useful tool for assignment and analysis of the dominant resonances.     

The performance of different density functional methods in the calculation of molecular structures and vibrational spectra of platinum(II) antitumor drugs: cisplatin and carboplatin

A comparison of eight density functional models for predicting the molecular structures, vibrational frequencies, infrared intensities, and Raman scattering activities of platinum(II) antitumor drugs, cisplatin and carboplatin, is reported. Methods examined include the pure density functional protocols (G96LYP, G96PW91, modified mPWPW and original PW91PW91), one‐parameter hybrid approaches (mPW1PW and mPW1LYP), and three‐parameter hybrid models (B3LYP and B3PW91), as well as the HF and MP2 levels of theory. Different effective core potentials (ECPs) and several basis sets are considered. The theoretical results are discussed and compared with the experimental data. It is remarkable that the mPW1PW protocol introduced by Adamo and Barone [J Chem Phys 1998, 108, 664], is clearly superior to all the remaining density functional methods (including B3LYP). The geometry and vibrational frequencies of cisplatin and carboplatin calculated with the mPW1PW method, and the ECP of Hay and Wadt (LanL2DZ basis set) are in better agreement with experiment than those obtained with the MP2 method. The use of more elaborated ECP and the enlargements of basis sets do not significantly improve the results. A clear‐cut assignments of the platinum‐ligand vibrations in cisplatin and carboplatin are presented. It is concluded that mPW1PW is the new reliable method, which can be used in predicting molecular structures and vibrational spectra of large coordination compounds containing platinum(II). © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 901–912, 2001     

Anharmonic analysis of the vibrational spectrum of ketene by density functional theory using second-order perturbative approach

The paper reports main results of a comprehensive study of the vibrational spectrum of ketene computed using second-order perturbation theory treatment based on quartic, cubic and semidiagonal quartic force constants. Two different models--a homogeneous model using the same density functionals and basis functions for the harmonic calculations and anharmonic corrections, and a hybrid model in which the two parts of the calculation are conducted using different density functionals and basis sets--have been employed in the present calculations. Different DFT and CCSD methods and DZ and TZ extended basis sets involving diffuse and polarization functions have been used to calculate optimized and vibrationally averaged geometrical parameters, the harmonic and anharmonic vibrational frequencies and the spectroscopic constants such as anharmonicity constants, rotational constants, rotation-vibration coupling constants, Nielsen's centrifugal distortion constants and Coriolis coupling constants. Homogeneous model is found to be superior to the hybrid model in several respects. Difficulties in the hybrid model may arise due to one of the following reasons: (a) the basic requirement that the geometry optimization and frequency calculations must be done at the same level of theory to have valid frequencies is not met in the hybrid model; (b) the molecular structure gets reoptimized at the low level for anharmonic corrections; (c) in addition, the perturbation could also diverge for the above reasons, particularly for the very low, very anharmonic terms where the harmonic approximation is not close enough to make the perturbation work.