Harmonic frequency scaling factors for Hartree-Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2 with the Sadlej pVTZ electric property basis set

Scaling factors for obtaining fundamental vibrational frequencies from harmonic frequencies calculated at six of the most commonly used levels of theory have been determined from regression analysis for the polarized-valence triple-zeta (pVTZ) Sadlej electric property basis set. The Sadlej harmonic frequency scaling factors for first- and second-row molecules were derived from a comparison of a total of 900 individual vibrations for 111 molecules with available experimental frequencies. Overall, the best performers were the hybrid density functional theory (DFT) methods, Becke's three-parameter exchange functional with the Lee–Yang–Parr fit for the correlation functional (B3-LYP) and Becke's three-parameter exchange functional with Perdew and Wang's gradient-corrected correlation functional (B3-PW91). The uniform scaling factors for use with the Sadlej pVTZ basis set are 0.9066, 0.9946, 1.0047, 0.9726, 0.9674 and 0.9649 for Hartree–Fock, the Slater–Dirac exchange functional with the Vosko–Wilk–Nusair fit for the correlation functional (S-VWN), Becke's gradient-corrected exchange functional with the Lee–Yang–Parr fit for the correlation functional (B-LYP), B3-LYP, B3-PW91 and second-order M?ller–Plesset theory with frozen core (MP2(fc)), respectively. In addition to uniform frequency scaling factors, dual scaling factors were determined to improve the agreement between computed and observed frequencies. The scaling factors for the wavenumber regions below 1800 cm⁻¹ and above 1800 cm⁻¹ are 0.8981 and 0.9097, 1.0216 and 0.9857, 1.0352 and 0.9948, 0.9927 and 0.9659, 0.9873 and 0.9607, 0.9844 and 0.9584 for Hartree–Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2(fc), respectively. Hybrid DFT methods along with the Sadlej pVTZ basis set provides reliable theoretical vibrational spectra in a cost-effective manner. Received: 22 May 2000 / Accepted: 30 August 2000 / Published online: 28 February 2001     

Density functional theory study of the FT-IR spectra of phthalimide and N-bromophthalimide

Fourier transform infrared (FT-IR) spectra of phthalimide and N-bromophthalimide have been recorded in the range of 4000-400 cm-1. With the hope of providing more and effective information on the fundamental vibrations, a normal coordinate analysis has been performed on phthalimide and N-bromophthalimide, by assuming C2v symmetry. Density functional theory (DFT)-Beck3-Lee-Yang-Parr (B3LYP) levels with 6-31G* and 6-311+G** basis sets have been employed in quantum chemical analysis. The computational frequencies are in good agreement with the observed results. The theoretical spectra obtained along with intensity data agree well with the observed spectra.     

Analysis of vibrational spectra of 2 and 3-methylpiperidine based on density functional theory calculations

The experimental and theoretical vibrational spectra of 2 and 3-methylpiperidine (abbreviated as 2-MP and 3-MP) were studied. The FT-Infrared spectra of 2-MP and 3-MP molecules were recorded in the liquid phase. The structural and spectroscopic analysis of the title molecules were made by using density functional harmonic calculations. For the title molecules, only one form was found most stable structure by using B3LYP level with the 6-311G (d,p) basis set. Selected experimental bands were assigned and characterized based on the scaled theoretical wave numbers by their total energy distribution (TED).     

Adsorption and dissociation of methanol on Au(1 1 1) surface: A first-principles periodic density functional study

The adsorption and dissociation of methanol on Au(111) surface were studied using the first-principles calculations based on density functional theory (DFT) with the generalized gradient approximation (GGA). Adsorption energies, geometric structures, Mulliken charges population, and vibrational frequencies of the various intermediates were computed from full-geometry optimization with a three-layer slab model. The most stable adsorption modes of the species, i.e. CH₃OH, CH₃O, and HCHO were considered in calculation. The possible decomposition pathways were investigated with transition state search methods. The results indicate that methoxyl radical is likely the decomposition intermediate.     

A DFT analysis of the vibrational spectra of nitrobenzene

Raman and FTIR, spectra of nitrobenzene, nb, and its isotopomers, nb-¹⁵N, nb-¹³C₆ and nb-d₅, were obtained and the fundamental vibrational modes assigned with the aid of a B3LYP/6-311+G** calculation, without the need for scaling of the force constants. The changes in vibrational coupling between the nitro and benzene groups upon certain isotopic substitutions are well modelled by the calculation, which is able to reproduce the isotopic shifts in frequencies for the nitro vibrations, as well as changes in IR intensities.     

The electronic structures and spectra of nonbenzenoid aromatic hydrocarbons containing the cyclopropenyl ring

The ground-state electronic properties and electronic spectra of triafulvene, I, triafulvalene, II, calicene, III, heptatriafulvalene, IV, benzocalicene, V, and dibenzocalicene, VI, have been studied by the semiempirical SCF CI LCAO--MO method which allows for bond order-bond length correlation at each iteration. The dependence of the resonance integral on bond length is scrutinized by trying to reproduce the properties of the ground and excited states in a series of reference compounds. For the bonds in the cyclopropenyl ring a new bond order-bond length relationship is proposed which allows for the fact that their components are bent. The calculated dipole moment and bond lengths of III and the predicted electronic spectra of III, V, and VI are in good agreement with the available experimental data.

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Zusammenfassung Grundzustand und Elektronenspektren von Triafulven, Triafulvalen, Calicen, Heptatriafulvalen, Benzocalicen und Dibenzocalicen wurden mittels eines semiempirischen SCF-Verfahrens mit Korrelation zwischen Bindungsordnung und -länge untersucht. Die Abhängigkeit des Resonanzintegrals von der Bindungslänge wurde bestimmt, indem Grund- und angeregte Zustände einer Reihe von Bezugssubstanzen zur Justierung herangezogen wurden. Für die Bindungen im Cyclopropylenring wird eine neue Beziehung zwischen Bindungsordnung und -länge vorgeschlagen, die den verzerrten -Komponenten Rechnung trägt. Die berechneten Dipolmomente und Bindungslängen von Calicen und die Spektren aller drei Calicene stimmen befriedigend mit dem Experiment überein.

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Résumé La méthode SCF-CI-LCAO--MO avec variation de la longueur de liaison en fonction de l'indice de liaison à chaque itération, a été utilisée pour l'étude des propriétés électroniques de l'état fondamental et du spectre des composés suivants: I triafulvène, II triafulvalène, III calicène, IV heptatriafulvalène, V benzocalicène, VI dibenzocalicène. La dépendance à la longueur de liaison de l'intégrale de résonance est sondée par ajustement à l'expérience de propriétés moléculaires. Pour le cyclopropylène une nouvelle relation entre longueur et indice de liaison est proposée pour tenir compte de ce que les composantes sont courbes. Le moment dipolaire et les longueurs de liaison de III et les spectres électroniques de III, V et VI sont prévus en bon accord avec les données expérimentales disponibles.

     

The molecular structure and infrared and Raman spectra of SCCCS

The structure, rotational constants, and vibrational spectra of SCCCS have been predicted by ab initio and density functional quantum mechanical methods. Basis sets ranging in size from double-ζ plus polarization (DZP) to triple-ζ plus double polarization, augmented with f functions (TZ2Pf) were employed. Our theoretical results are in agreement with experiments for both the geometrical structure and most of the fundamental frequencies that have been observed. An exception occurs for the SCC bending frequency υ₅, for which the 1966 and 1972 assignments of Bates and Smith appear superior to the 1966 Smith and Leroi Raman assignment, accepted in the definitive recent studies of Holland and Winnewisser. We present results for four isotopomers of SCCCS that have not yet been observed in the laboratory.     

Density functional theory study of vibrational spectra. 8. Assignment of fundamental vibrational modes of 9,10-anthraquinone and 9,10-anthraquinone-d8

Density functional theory (using Becke's exchange and Lee-Yang-Parr's correlation functionals (BLYP)) and ab initio Hartree-Fock calculations were carried out in order to investigate the molecular structure and vibrational spectra of 9,10-anthraquinone and its perdeuterated analog. The calculated structural and spectral features are in good agreement with the available experimental results. Most of the BLYP/6-31G* non-CH(D) stretching frequencies are slightly lower than reliable experimental assignments; the mean absolute deviation is about 14 cm⁻¹. On the basis of agreement between calculated and experimental results, assignments of the fundamental vibrational modes were examined and some reassignments were proposed. The calculated results can serve as a guide for a future experimental search for the missing fundamentals of the target molecules.     

Vibrational computations beyond the harmonic approximation: performances of the B3LYP density functional for semirigid molecules

The performances of the B3LYP density functional in the computation of harmonic and anharmonic frequencies were tested using 14 standard basis sets of double and triple zeta quality for a set of semirigid molecules containing from 4 to 12 atoms. The quality of the results is assessed by comparison with the most reliable computations available in the literature. The study reveals that the relatively cheap 6-31+G(d,p) basis set performs a very good job for harmonic frequency calculations and that B3LYP anharmonicities are in close agreement with the reference values irrespective of the basis set used. On these grounds "hybrid force fields" are proposed to achieve the best compromise between computer time and quality of the results.     

A theoretical investigation on the geometry and vibrational spectra of 10,10,2,6,5-pentamethyl-1-hydroxychroman: a model of alpha-tocopherol

In the present study, density functional theory calculations with the combined Becke's three-parameter exchange functional in combination with the Lee, Yang, and Parr correlation functional (B3LYP) exchange-correlation energy functions were performed by using the 6-311G** basis set to study the structure and vibrational spectra of 10,10,2,6,5-pentamethyl-1-hydroxychroman (a model of alpha-tocopherol). The fully optimized geometry of the molecule was found to be very consistent with the X-ray crystal structure. The predicted vibrational frequencies made it possible to give a reliable assignment of the IR spectrum of the molecule according to the potential energy distributions (PEDs).     

Basis set effects on the stability of the Cl2O3 isomers using B3P86 and B3LYP methods of density functional theory

Four Cl₂O₃ isomers have been calculated using density functional theory with B3P86 and B3LYP functionals and various basis sets. The energy hypersurfaces of Cl₂O₃ are very flat and the relative energies of the isomers which have hypervalent characters such as ClOCl(O)O and ClClO₃ are strongly dependent on the basis sets. The stability for Cl₂O₃ isomers are in the order of (1)ClOOOCl(C_s), (2)ClOOOCl(C₂), (3)ClClO₃ and (4)ClOCl(O)O with ClOCl(O)O being most stable. We suggest that at least the cc-pV6Z(-ghi) basis set for Cl and the cc-pVTZ basis set for O are required to obtain reliable relative stabilities of Cl₂O₃ isomers with hypervalent characters.     

OH stretch IR spectra of (H2O)3 and benzene-(H2O)3

The OH stretch IR spectrum of (H₂O)₃ is significantly altered upon complexation of the cluster with a benzene molecule. Theoretical calculations show that the differences in the OH stretch spectra of (H₂O)₃ and benzene-(H₂O)₃ are primarily due to mode localization induced by the benzene molecule. Received: 27 January 1997 / Accepted: 28 January 1997     

The vibrational frequencies of CaO2, ScO2, and TiO2: a comparison of theoretical methods

The vibrational frequencies of several states of␣CaO₂, ScO₂, and TiO₂ are computed using density functional theory (DFT), the Hartree-Fock approach, second-order M?ller-Plesset perturbation theory (MP2), and the complete-active-space self-consistent-field theory. Three different functionals are used in the DFT calculations, including two hybrid functionals. The coupled cluster singles and doubles approach including the effect of connected triples, determined using perturbation theory, is applied to selected states. The Becke-Perdew 86 functional appears to be the most cost-effective method of choice, although even this functional does not perform well for one state of CaO₂. The MP2 approach is significantly inferior to the DFT approaches. Received: 3 September 1997 / Accepted: 8 December 1997     

Molecular structure, vibrational spectra and NBO analysis of phenylisothiocyanate by density functional method

The molecular geometry, vibrational frequencies and NBO analysis of phenylisothiocyanate (PITC) in the ground state have been calculated by using density functional theory calculation (B3LYP) with 6-311++G(d,p) basis set. The optimized geometrical parameters obtained by DFT calculations are in good agreement with experimental values. Comparison of the observed fundamental vibrational frequencies of the PITC and calculated result by density functional theory (B3LYP) indicates B3LYP is superior for molecular vibrational problems. The entropy of the title compound was also performed at HF/B3LYP/6-311++G(d,p) levels of theory. Natural bond orbital (NBO) analysis of title molecule is also carried out. A detailed interpretation of the IR and Raman spectra of PITC is reported on the basis of the calculated potential energy distribution (PED). The theoretical spectrogram for IR spectrum of the title molecule has been constructed.     

Density functional theory study of vibrational spectra, and assignment of fundamental vibrational modes of 1-bromo 4-fluoronaphthalene

The FTIR and FT-Raman spectra of 1-bromo 4-fluoronaphthalene have been recorded in the regions 4000-100cm(-1) and 3500-100cm(-1), respectively. The spectra were interpreted with the aid of normal coordinate analysis based on DFT (density functional theory) using standard B3LYP/6-311+G** basis set combination for the most optimized geometry. Normal coordinate calculations performed with the DFT force field and subsequently corrected by a recommended set of scale factors, yielded fairly good agreement between observed and calculated frequencies. On the basis of the comparison between calculated and experimental results, assignments of fundamental modes were examined.     

Molecular structure and vibrational spectra of indole and 5-aminoindole by density functional theory and ab initio Hartree–Fock calculations

The molecular geometry and vibrational frequencies of indole and 5-aminoindole in the ground state have been calculated by using the Hartree–Fock and density functional method with 6-311++G(d,p) basis set. The optimized geometrical parameters obtained by DFT calculations are in good agreement with the experimental values. Comparison of the observed fundamental vibrational frequencies of indole and 5-aminoindole with the calculated results by density functional and Hartree–Fock methods indicates that B3LYP is superior to the scaled Hartree–Fock approach for molecular vibrational problems. The theoretical spectrograms for FT-IR spectrum of 5-aminoindole have been constructed.     

Ab initio and DFT studies of the molecular structures and vibrational spectra of succinonitrile

The Molecular structure, conformational stability and vibrational frequencies of succinonitrile NCCH2CH2CN have been investigated with ab initio and density functional theory (DFT) methods implementing the standard 6-311++G* basis set. The potential energy surfaces (PES) have been explored at DFT-B3LYP, HF and MP2 levels of theory. In agreements with previous experimental results, the molecule was predicted to exist in equilibrium mixture of trans and gauche conforms with the trans form being slightly lower in energy. The vibrational frequencies and the corresponding vibrational assignments of succinonitrile in both C2h and C2 symmetry were examined theoretically and the calculated Infrared and Raman spectra of the molecule were plotted. Observed frequencies for normal modes were compared with those calculated from normal mode coordinate analysis carried out on the basis of ab initio and DFT force fields using the standard 6-311++G* basis set of the theoretical optimized geometry. Theoretical IR intensities and Raman activities are reported.     

A theoretical study of the structure and vibrations of 2,4,6-trinitrotolune

Theoretical calculations of the structure, internal rotations and vibrations of 2,4,6-trinitrotolune, TNT, in the gas phase were performed at the B3LYP/6-31G* and B3LYP/6-311+G** levels of theory. Two genuine energy minimum structures were found. In both structures the 4-nitro group is planar to the phenyl ring, while the 2,6-nitro groups are slightly out of plane with the phenyl ring due to steric interaction with the methyl group. The two structures are related by internal rotations of the methyl and 2, or 6-nitro group. The lowest energy route for interconversion between them is a concerted motion of the methyl group and 2 or 6 nitro group in a ‘cog wheel’ type of mechanism. The geometry of the low energy structure A is closest to that observed in the crystal structures of TNT, where all three nitro groups are out of plane with the phenyl ring. FTIR and Raman spectra of solid TNT and ¹³C, ¹⁵N enriched TNT are presented and assigned with the help of the B3LYP/6-311+G** calculations on A. The lower level B3LYP/6-31G* calculation fails to predict the correct vibrational coupling between the nitro and phenyl groups. The B3LYP/6-311+G** calculation gives a good prediction of the nitro vibrations and the isotopic shifts observed for TNT isotopomers.     

Argon-matrix-isolation Raman spectra and density functional study of 1,3-butadiene conformers

s-trans, s-cis and gauche conformers of 1,3-butadiene have been studied using density functional theory and the coupled-cluster method using double substitutions (CCD). Matrix isolation Raman and IR data for the minor conformer were obtained and are used in combination with the theoretical results to resolve earlier ambiguities in vibrational assignments. Based on high-quality Hessians, new harmonic stretching force constants are reported for the carbon backbone of s-trans-1,3-butadiene. For the minor conformer the best unscaled root mean square error of the calculated frequencies for the s-cis and gauche geometries are 17.5 cm⁻¹ and 7.4 cm⁻¹, respectively, primarily due to a better agreement of the gauche results for the vibrations at 983 cm⁻¹, 596 cm⁻¹ and 470 cm⁻¹ which depend strongly on the torsional angle. Although this points towards the gauche form rather than the s-cis form, the calculated transition dipole moment directions at the CCD/6-311G(d,p) level confirm the earlier conclusion that the minor conformer has C _{2 v} symmetry in the matrix. It is concluded that either the better agreement between the frequencies calculated for the gauche form and the observed values is coincidental, or that the molecule is indeed nonplanar in the matrix and tunnels very rapidly between the two mirror-image forms (or its lowest vibrational level lies above the barrier). Received: 1 July 1998 / Accepted: 26 October 1998 / Published online: 15 February 1999     

Approximation of the molecular electrostatic potential in a gaussian density functional method

The recently developed Asymptotic Density Model (ADM) [6, 9] is here implemented in the density functional framework using the program deMon-KS [13]. While the original implementation divided the atoms into a core shell and a valence shell, the present version allows for an arbitrary number of shells making it therefore more flexible and, as shown with benzene, potentially more accurate. Moreover, since this method is derived through Poisson's equation, an expression for the electronic charge density is also obtained. However, the present discussion will restrict itself to the electrostatic potential. Finally, even though this method requires parametrization, it is shown that the parameters obtained for homonuclear diatomic species, and used as is in molecular calculations, yield satisfactory results. Indeed, the ADM reproduces almost all basic features of the MEP for all molecules presented here, (water, ammonia, ethylene, acetylene, hydrogen cyanide, carbon monoxide, benzene, nitrous acid). Received: 5 July 1996 / Accepted: 12 November, 1996