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.     

A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions

We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed.     

FT-Raman and FT-IR spectra, vibrational assignments and density functional studies of 5-bromo-2-nitropyridine

The Fourier transform Raman and Fourier transform infrared spectra of 5-bromo-2-nitropyridine were recorded in the solid phase. The equilibrium geometry, natural atomic charges, harmonic vibrational frequencies, infrared intensities and Raman scattering activities were calculated by density functional B3LYP method with the 6-311++G(d,p) basis set. The scaled theoretical wavenumbers showed very good agreement with the experimental values. A detailed interpretations of the infrared and Raman spectra of 5-bromo-2-nitropyridine is reported on the basis of the calculated potential energy distribution (PED). The theoretical spectrograms for the Raman and IR spectra of the title molecule have been constructed.     

An experimental and theoretical study of molecular structure and vibrational spectra of 2-chloronicotinic acid by density functional theory and ab initio Hartree–Fock calculations

In this work, the Fourier transform Raman and Fourier transform infrared spectra of 2-chloronicotinic acid (2-CNA) are recorded in the solid phase. The molecular geometry, vibrational frequencies, infrared intensities and Raman scattering activities of 2-CNA in ground state have been calculated by using ab initio Hartree–Fock (HF) and density functional (B3LYP and B3PW91) methods with 6-31G(d) and 6-311G(d) basis sets level. On the basis of the comparison between calculated and experimental results and the comparison with related molecule, assignments of fundamental vibrational modes are examined. The optimized geometric parameters (bond lengths and bond angles) obtained by using HF show the best agreement with the experimental values of 2-CNA. Comparison of the observed fundamental vibrational frequencies of 2-CNA and calculated results by density functional (B3LYP and B3PW91) and Hartree–Fock methods indicates that B3LYP is superior to the scaled Hartree–Fock and B3PW91 approach for molecular vibrational problems.     

Experimental and theoretical studies on vibrational spectra of 4-(2-furanylmethyleneamino)antipyrine, 4-benzylideneaminoantipyrine and 4-cinnamilideneaminoantipyrine

This work deals with the IR and Raman spectroscopy of 4-(2-furanylmethyleneamino) antipyrine (FAP), 4-benzylideneaminoantipyrine (BAP) and 4-cinnamilideneaminoantipyrine (CAP) by means of experimental and quantum chemical calculations. The equilibrium geometries, harmonic frequencies, infrared intensities and Raman scattering activities were calculated by density functional B3LYP method with the 6-31G(d) basis set. The comparisons between the calculated and experimental results covering molecular structures, assignments of fundamental vibrational modes and thermodynamic properties were investigated. The optimized molecular geometries have been compared with the experimental data obtained from XRD data, which indicates that the theoretical results agree well with the corresponding experimental values. For the three compounds, comparisons and assignments of the vibrational frequencies indicate that the calculated frequencies are close to the experimental data, and the IR spectra are comparable with some slight differences, whereas the Raman spectra are different clearly and the strongest Raman scattering actives are relative tightly to the molecular conjugative moieties linked through their Schiff base imines. The thermodynamic properties (heat capacities, entropies and enthalpy changes) and their correlations with temperatures were also obtained from the harmonic frequencies of the optimized strucutres.     

A challenge for density functional theory: the XONO and XNO2 (X=F, Cl, and Br) molecules

The equilibrium geometries, harmonic frequencies, dipole moments, infrared intensities, and relative energies of the cis-XONO, trans-XONO, and XNO₂ (X=F, Cl, and Br) have been investigated using four functionals in common use in Kohn-Sham density functional theory (DFT) calculations. Two of the functionals include non-local or gradient correction terms, while the other two also incorporate some exact Hartree-Fock exchange and are labeled hybrid functionals. The quality of the results obtained from the functionals is determined by comparison to previously published high-level coupled-cluster calculations. The hybrid functionals perform better for prediction of the equilibrium geometries, where the two gradient corrected functionals yield qualitatively incorrect molecular structures for cis-FONO and cis-ClONO. None of the functionals perform well in predicting all six harmonic frequencies, showing that the correlation between equilibrium geometries and harmonic frequencies is not as strong for these DFT methods as it is for conventional wavefunction ab initio methods, such as coupled-cluster theory. Results from the various functionals generally come into better agreement with each other and also with the coupled-cluster results moving down the periodic table. Received: 12 February 1997 / Accepted: 25 March 1997     

FT-IR, FT-Raman spectra and ab initio DFT vibrational analysis of p-bromophenoxyacetic acid

The Fourier transform Raman and Fourier transform infrared spectra of p-bromophenoxyacetic acid were recorded in the solid phase. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities were calculated by HF and DFT (B3LYP) method with the 6-31G(d,p) basis set. The scaled theoretical wavenumbers showed very good agreement with the experimental ones. A detailed interpretation of the infrared and Raman spectra of p-bromophenoxyacetic acid is reported on the basis of the calculated potential energy distribution. The theoretical spectrograms for the IR spectrum of the title molecule have been constructed.     

Ab initio and DFT predictions of infrared intensities and Raman activities

Relative infrared (IR) intensities and relative Raman activities have been computed for vibrations of test molecules, including from two to nine heavy atoms, using second-order Moller-Plesset perturbation theory (MP2), and three hybrid density functionals (B3LYP, M05, and M05-2X). The basis set convergence of vibrational properties is discussed. Our results demonstrate that B3LYP offers the most cost-effective choice for the prediction of molecular vibrational properties, but the predictions of another two tested hybrid functionals are very similar and in very good agreement with experimental data. MP2 shows good performance for the IR intensities, whereas the quality of prediction of the relative Raman activities should be characterized as only moderate. B3LYP calculations of the relative IR intensities using highly compact Sadlej's Z3PolX basis set retain the high accuracy of the more CPU expensive Sadlej's pVTZ and much more expensive aug-cc-pVTZ calculations. Relative Raman activities are more sensitive to basis set effects and require at least Sadlej's pVTZ to obtain quantitative results.     

FT-Raman and FT-IR spectra, ab initio and density functional studies of 3,4-dichlorobenzyl alcohol

The Fourier transform Raman and Fourier transform infrared spectra of 3,4-dichlorobenzyl alcohol were recorded in the solid phase. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities, depolarization ratios, reduced masses were calculated by HF and density functional B3LYP method with the 6-311 G** basis set. The scaled theoretical wavenumbers showed very good agreement with the experimental values. The thermodynamic functions of the title compound were also performed at HF/6-311G** and B3LYP/6-311G** levels of theory. A detailed interpretations of the infrared and Raman spectra of 3,4-dichlorobenzyl alcohol is reported. The theoretical spectrograms for FT-IR spectra of the title molecule have been constructed.     

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.     

FT-IR, FT-Raman, NMR and UV-vis spectra, vibrational assignments and DFT calculations of 4-butyl benzoic acid

The solid phase FTIR and FT-Raman spectra of 4-butyl benzoic acid (4-BBA) have been recorded in the regions 400-4000 and 50-4000cm(-1), respectively. The spectra were interpreted in terms of fundamentals modes, combination and overtone bands. The structure of the molecule was optimized and the structural characteristics were determined by density functional theory (DFT) using B3LYP method with 6-311++G(d,p) as basis set. The vibrational frequencies were calculated for monomer and dimer by DFT method and were compared with the experimental frequencies, which yield good agreement between observed and calculated frequencies. The infrared and Raman spectra were also predicted from the calculated intensities. (13)C and (1)H NMR spectra were recorded and (13)C and (1)H nuclear magnetic resonance chemical shifts of the molecule were calculated using the gauge independent atomic orbital (GIAO) method. UV-visible spectrum of the compound was recorded in the region 200-400nm and the electronic properties HOMO and LUMO energies were measured by time-dependent TD-DFT approach. The geometric parameters, energies, harmonic vibrational frequencies, IR intensities, Raman intensities, chemical shifts and absorption wavelengths were compared with the available experimental data of the molecule.     

Quantum chemical calculation of vibrational spectra of large molecules--Raman and IR spectra for Buckminsterfullerene

In this work we demonstrate how different modern quantum chemical methods can be efficiently combined and applied for the calculation of the vibrational modes and spectra of large molecules. We are aiming at harmonic force fields, and infrared as well as Raman intensities within the double harmonic approximation, because consideration of higher order terms is only feasible for small molecules. In particular, density functional methods have evolved to a powerful quantum chemical tool for the determination of the electronic structure of molecules in the last decade. Underlying theoretical concepts for the calculation of intensities are reviewed, emphasizing necessary approximations and formal aspects of the introduced quantities, which are often not explicated in detail in elementary treatments of this topic. It is shown how complex quantum chemistry program packages can be interfaced to new programs in order to calculate IR and Raman spectra. The advantages of numerical differentiation of analytical gradients, dipole moments, and static, as well as dynamic polarizabilities, are pointed out. We carefully investigate the influence of the basis set size on polarizabilities and their spatial derivatives. This leads us to the construction of a hybrid basis set, which is equally well suited for the calculation of vibrational frequencies and Raman intensities. The efficiency is demonstrated for the highly symmetric C(60), for which we present the first all-electron density functional calculation of its Raman spectrum.     

FTIR and FT-Raman spectra, assignments, ab initio HF and DFT analysis of xanthine

The molecular vibrations of xanthine were investigated in polycrystalline sample, at room temperature by Fourier transform infrared (FTIR) and FT-Raman spectroscopies. The spectra of the molecule have been recorded in the regions 4000-50 cm(-1) and 3500-100 cm(-1), respectively. Theoretical information on the optimized geometry, harmonic vibrational frequencies, infrared and Raman intensities were obtained by means of ab initio Hartree-Fock (HF) and density functional theory (DFT) gradient calculations with complete relaxation in the potential energy surface using 6-311++G(d,p) basis set. The vibrational frequencies which were determined experimentally from the spectral data are compared with those obtained theoretically from ab initio and DFT calculations. A close agreement was achieved between the observed and calculated frequencies by refinement of the scale factors. The infrared and Raman spectra were also predicted from the calculated intensities. Thermodynamic properties like entropy, heat capacity, zero point energy have been calculated for the molecule. Unambiguous vibrational assignment of all the fundamentals was made using the potential energy distribution (PED).     

Lagrangian approach to molecular vibrational Raman intensities using time-dependent hybrid density functional theory

The authors propose a new route to vibrational Raman intensities based on analytical derivatives of a fully variational polarizability Lagrangian. The Lagrangian is constructed to recover the negative frequency-dependent polarizability of time-dependent Hartree-Fock or adiabatic (hybrid) density functional theory at its stationary point. By virtue of the variational principle, first-order polarizability derivatives can be computed without using derivative molecular orbital coefficients. As a result, the intensities of all Raman-active modes within the double harmonic approximation are obtained at approximately the same cost as the frequency-dependent polarizability itself. This corresponds to a reduction of the scaling of computational expense by one power of the system size compared to a force constant calculation and to previous implementations. Since the Raman intensity calculation is independent of the harmonic force constant calculation more, computationally demanding density functionals or basis sets may be used to compute the polarizability gradient without much affecting the total time required to compute a Raman spectrum. As illustrated for fullerene C60, the present approach considerably extends the domain of molecular vibrational Raman calculations at the (hybrid) density functional level. The accuracy of absolute and relative Raman intensities of benzene obtained using the PBE0 hybrid functional is assessed by comparison with experiment.     

FTIR and FT Raman, molecular geometry, vibrational assignments, ab initio and density functional theory calculations for 1,5-methylnaphthalene

The FTIR and FT Raman vibrational spectra of 1,5-methylnaphthalene (1,5-MN) have been recorded using Brunker IFS 66 V Spectrometer in the range 3600-10 cm(-1) in the solid phase. A detailed vibrational spectral analysis has been carried out and assignments of the observed fundamental bands have been proposed on the basis of peak positions and relative intensities. The Optimized molecular geometry, harmonic frequencies, electronic polarizability, atomic charges, dipole moment, rotational constants and several thermodynamic parameters in the ground state were calculated using ab initio Hartree Fock (HF) and density functional B3LYP methods (DFT) with 6-311++ G(d) basis set. With the help of different scaling factors, the observed vibrational wavenumbers in FTIR and FT Raman spectra were analyzed and assigned to different normal modes of the molecule. Most of the modes have wavenumbers in the expected range. The results of the calculations were applied to simulated infrared and Raman spectra of the title compound which showed excellent agreement with the observed spectra.     

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.     

Comparison of experimental and ab initio HF and DFT vibrational spectra of benzimidazole

In this work, we will report a combined experimental and theoretical study on molecular and vibrational structure of benzimidazole. The laser Raman and Fourier transform infrared spectra of benzimidazole were recorded in the solid phase. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities, Raman scattering activities, depolarization ratios and reduced masses were calculated by HF and density functional B3LYP method with the 6-311G(d,p) basis set. The scaled theoretical wavenumbers showed very good agreement with the experimental values. The thermodynamic functions of the title compound were also performed at HF/6-31G(d,p)/6-311G(d,p) and B3LYP/6-31G(d,p)/6-311G(d,p) levels of theory. A detailed interpretations of the infrared and Raman spectra of benzimidazole is reported. The theoretical spectrograms for FT-IR spectra of the title molecule have been constructed.     

Vibrational spectroscopy investigation using ab initio and density functional theory analysis on the structure of 5-amino-o-cresol

The Fourier transform Raman and Fourier transform infrared spectra of 5-amino-o-cresol (5AOC) were recorded in the solid phase. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities were calculated by HF and density functional B3LYP method with the 6-311G(d,p) basis set. The scaled theoretical wavenumbers showed very good agreement with the experimental values. The thermodynamic functions of the title compound were also performed at HF/6-311G(d,p) and B3LYP/6-311G(d,p) levels of theory. A detailed interpretation of the infrared and Raman spectra of 5-amino-o-cresol is reported. The theoretical spectrograms for FT-IR spectra of the title molecule have been constructed.     

Vibrational spectrum, ab initio calculations, conformational stabilities and assignment of fundamentals of the Ci conformer of 1,4-dichlorobutane

The infrared and Raman spectrum of 1,4-dichlorobutane is reported in solid, liquid and gas. Ab initio calculations for the nine stable or metastable conformers of 1,4-dichlorobutane are reported for Moller-Ploessett second order electron correlation and B3LYP density functionals with a variety of basis sets, using approximations as high as 6-311+g(2d, 2p). Normal coordinate calculations were conducted for the nine conformers and the results used to provide assignments for some of the observed infrared and Raman bands. An attempt to use the assignments together with the ab initio intensities or Raman activities to investigate the composition of the liquid at room temperature proved modestly successful, and suggested that the populations are altered from those expected in the gas phase by interactions of the permanent electric dipole moments with the dipolar plasma in which the conformers are immersed in the liquid. A substantial disagreement between the Moeller-Ploessett and density functional results is reported, and the calculation of intensities and activities is insufficiently accurate to allow detailed interpretation of the spectrum of the room temperature liquid. A complete assignment of fundamentals is given for the conformer of Ci symmetry, and one Raman and one infrared band is identified with the C2h conformer. All the other infrared and Raman bands in the liquid or the gas are composites of several contributors.