Analytical second-order geometrical derivatives of energy for the self-consistent-charge density-functional tight-binding method

Analytical formulation of the second-order geometrical derivatives of energy for the self-consistent-charge density-functional tight-binding (SCC-DFTB) method is presented. To test its quality and numerical performance, the derived formalism has been coded and applied for calculation of harmonic vibrational frequencies for a set of 17 small and medium size molecules. For this set, the average absolute deviation from experiment is 99 cm(-1) for SCC-DFTB vs 62 cm(-1) for the M?ller-Plesset second-order perturbation theory with the cc-pVDZ basis set (MP2/cc-pVDZ) and 32 cm(-1) for the B3LYP density functional method with the same basis set (B3LYP/cc-pVDZ), while the maximal deviation is 465 cm(-1) vs 1,741 cm(-1) for MP2/cc-pVDZ and 112 cm(-1) for B3LYP/cc-pVDZ. The SCC-DFTB results are in reasonable agreement with experiments as well as with ab initio and density-functional results, and are better than other semiempirical methods. The SCC-DFTB method allows for considerable computational time saving when compared to other methods while retaining similar overall accuracy. Data for a series of conjugated polyenes show that an analytical formulation of SCC-DFTB is noticeably faster than its numerical formulation.     

Density functional theory study of vibrational spectra of acridine and phenazine

Density functional theory (DFT) calculations using Becke's exchange in conjunction with Lee-Yang-Parr's correlation functionals (BLYP), Becke's three-parameter hybrid DFT/HF method using Lee-Yang-Parr's correlation functionals (B3LYP) and ab initio Hartree-Fock (HF) method have been carried out to investigate the structure and vibrational spectra of acridine and phenazine. Structural parameters obtained by B3LYP/6-31G* geometry optimization are in good agreement with available experimental data. The raw BLYP non-CH stretching frequencies approximate the experimental results much better than the HF results with the mean absolute deviation about 16 cm(-1). The scaled B3LYP frequencies are more reliable than that of the BLYP and HF methods with the mean absolute deviation about 17 cm(-1). On the basis of the comparison between calculated and experimental results, assignments of fundamental vibrational modes are examined. Also the structure and vibrational frequencies are compared with those of anthracene, pyridine and benzene to study the similarities and differences.     

Analysis of vibrational spectra of chlorotoluene based on density function theory calculations

The conformational behavior and structural stability of chlorotoluene were investigated by utilizing ab initio calculations with 6-31G* basis set at restricted Hartree-Fock (RHF) and density function theory (DFT) levels. The vibrational frequencies of chlorotoluene were computed at the RHF and DFT levels. Complete vibrational assignments were made on the basis of normal coordinate calculations for stable conformer of the molecule. RHF results without scaled quantum mechanical (SQM) force field procedure considered are in bad agreement with experimental values. Of the five DFT methods, BLYP reproduces the observed fundamental frequencies most satisfactorily with the mean absolute deviation of the non-CH stretching modes less than 10 cm(-1). Two hybrid DFT methods are found to yield frequencies, which are generally higher than the observed fundamental frequencies. When the calculated results are compared with 'experimental' frequencies, B3LYP method is found to be slightly more accurate for C-H stretching modes. The results indicate that BLYP calculation is a very promising approach for understanding the observed spectral features.     

Structure and vibrational frequencies of 2-butanimine

The conformational behavior and structural stability of 2-butanimine were investigated by utilizing ab initio calculations with 6-311++G** basis set at HF, MP2, B3LYP and BLYP levels. The vibrational frequencies of 2-butanimine were computed. Complete vibrational assignments were made on the basis of normal coordinate calculations for stable conformer of the molecule. HF results without scaled quantum mechanical (SQM) force field procedure considered are in bad agreement with experimental values. Of the two DFT methods, BLYP reproduces the observed fundamental frequencies most satisfactorily with the mean absolute deviation of the non-CH stretching modes less than 21.3 cm(-1). The results indicate that BLYP calculation is a very promising approach for understanding the observed spectral features.     

Molecular structure and vibrational spectra of o-chlorotoluene, m-chlorotoluene, and p-chlorotoluene by ab initio HF and DFT calculations

In this work, experimental and theoretical study on the molecular structure and the vibrational spectra of o-chlorotoluene (OCT), m-chlorotoluene (MCT) and p-chlorotoluene (PCT) are presented. The vibrational frequencies of these compounds were obtained theoretically by ab initio HF and DFT/B3LYP calculations employing the standard 6-311++G(d,p) basis set for optimized geometries and were compared with Fourier transform infrared (FTIR) in the region of 400-4000 cm(-1) and with Raman spectra in the region of 100-4000 cm(-1). Complete vibrational assignment, analysis and correlation of the fundamental modes for these compounds have been carried out. The vibrational harmonic frequencies were scaled using scale factors, yielding a good agreement between the experimentally recorded and the theoretically calculated values.     

Assessing spin-component-scaled second-order M?ller-plesset theory using anharmonic frequencies

Four common parametrisations of spin-component-scaled second-order M?ller-Plesset (MP2) theory are benchmarked by calculating the anharmonic vibrational frequencies of a test suite consisting of eighteen diatomic and five small molecules. Of the four methods, the scaled opposite-spin MP2 (SOS-MP2), the variable-scaling opposite-spin MP2 (VOS-MP2) and the spin-component-scaled MP2 (SCS-MP2) methods perform statistically better than standard MP2 theory, while the spin-component scaled for nucleic bases MP2 (SCSN-MP2) performs worse. Vibrations of closed-shell diatomic molecules are slightly more accurately described by the SOS-MP2 method of Head-Gordon (ε(MAD) =51 cm(-1) ) than the SCS-MP2 method of Grimme (ε(MAD) =61 cm(-1)) or the size-consistent parametrisation of VOS-MP2 (ε(MAD) =54 cm(-1)). For open-shell diatomic molecules, the SOS-MP2 (ε(MAD) =83 cm(-1)) and SCS-MP2 (ε(MAD) =81 cm(-1)) methods are of similar accuracy, while VOS-MP2 is slightly better (ε(MAD) =77 cm(-1)). Since the VOS-MP2 and SOS-MP2 methods tend to have smaller deviations from experiment, and they can be made computationally more economical than the SCS-MP2 or MP2 methods, we suggest that they should be the preferred ab initio method for computing vibrational frequencies in large molecules.     

氟磺酸氯分子振动光谱的从头算研究

采用从头算HF方法以6-31G^*基组研究了对ClOSO₂F分子的几何结构、振动谐性力场和红外光谱.理论力场由Pulay的标度量子力学方法进行标度,算得的振动频率与实验值比较,平均偏差为6.0cm^-1.根据振动频率的势能分布和从头算红外光谱强度值对此分子的振动基频进行了理论归属.     

Ab initio HF, DFT and experimental (FT-IR) investigation of vibrational spectroscopy of P-N,N-dimethylaminobenzylidenemalononitrile (DBM)

The optimized geometry and vibrational frequencies of P-N,N-dimethylaminobenzylidenemalononitrile (DBM) were obtained by ab initio HF and DFT/B3LYP levels with complete relaxation in the potential energy surface using 6-31++G(d,p) and 6-311++G(d,p) basis sets. The Fourier-transform infrared (FT-IR) spectrum of DBM has been recorded in the region 4000-400 cm(-1). The harmonic vibrational frequencies were calculated and the scaled values have been compared with experimental FT-IR spectrum. The calculated frequencies are in good agreement with the experimental frequencies.     

Vibrational spectroscopy (FTIR and FTRaman) investigation using ab initio (HF) and DFT (B3LYP) calculations on the structure of 3-Bromo phenol

The FT-IR and FT-Raman spectra of 3-Bromo phenol (3-BP) molecule have been recorded using Bruker IFS 66V spectrometer in the range of 4000-100 cm(-1). The molecular geometry and vibrational frequencies in the ground state are calculated by using the ab initio Hartree-fock (HF) and DFT (B3LYP) methods with 6-31G (d, p) and 6-311G (d, p) basis sets. The computed values of frequencies are scaled using a suitable scale factor to yield good coherence with the observed values. Making use of the recorded data, the complete vibrational assignments are made and analysis of the observed fundamental bands of molecule is carried out. The geometries and normal modes of vibrations obtained from ab initio HF and B3LYP calculations are in good agreement with the experimentally observed data. The differences between the observed and scaled wave number values of most of the fundamentals are very small in DFT than HF. The inductive effect of halogen atom in the molecule has also been investigated.     

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

The infrared, the Fourier transform infrared and Fourier transform Raman spectra of p-chlorobenzoic acid (p-CBA) has been recorded in the region 4000-600 cm(-1), 4000-400 cm(-1) and 4000-100 cm(-1), respectively. The optimized geometry, frequency and intensity of the vibrational bands of p-CBA were obtained by the ab initio HF and DFT (B3LYP) methods with complete relaxation in the potential energy surface using 6-311+G(d,p) basis set. The harmonic-vibrational frequencies were calculated and the scaled values have been compared with experimental FT-IR and FT-Raman spectra. The observed and the calculated frequencies are found to be in good agreement. The experimental spectra also coincide satisfactorily with those of theoretically constructed bar type spectrograms.     

Ab initio studies on vibrational spectra of XSO_2NCO (X=F,Cl):harmonic force fields and frequency assignments

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Vibrational spectral analysis and first hyperpolarizability studies of 1-bromonaphthalene based on ab initio and DFT methods

In this work, the experimental and theoretical vibrational spectra of 1-bromonaphthalene (1-BN) were studied. FTIR and FT Raman spectra were recorded in the region 4000-400 cm(-1) and 3500-50 cm(-1), respectively. The structural and spectroscopic data of the molecule in the ground state were calculated by using ab initio Hartree-Fock and density functional method (B3LYP) with the 6-311++G(d,p) basis set. The vibrational frequencies were calculated and scaled values were compared with experimental FTIR and FT Raman spectra. The observed and calculated frequencies are found to be in good agreement. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method. The optimized geometric parameters were calculated. The predicted first hyperpolarizability also shows that the molecule might have a reasonably good nonlinear optical (NLO) behaviour. The calculated HOMO-LUMO energy gap reveals that charge transfer occurs within the molecule.     

Vibrational spectroscopy investigation using ab initio and density functional theory analysis on the structure of 2-amino-4,6-dimethoxypyrimidine

The FTIR and FT-Raman spectra of 2-amino-4,6-dimethoxypyrimidine (2A46DMP) has been recorded in the region 4000-400 cm(-1) and 3500-100 cm(-1), respectively. The optimized geometry, frequency and intensity of the vibrational bands of 2A46DMP were obtained by the ab initio and DFT levels of theory with complete relaxation in the potential energy surface using 6-31G(d,p) and 6-311G(d,p) basis sets. The harmonic vibrational frequencies were calculated and the scaled values have been compared with experimental FTIR and FT-Raman spectra. The observed and the calculated frequencies are found to be in good agreement. The experimental spectra also coincide satisfactorily with those of theoretically constructed bar type spectrograms.     

Spectroscopic analysis of 2-(2,3-dihydro-1,5-dimethyl-3-oxo-2-phenyl-1H-pyrazol-4-ylimino)-2-(4-nitro-phenyl) acetonitrile

The optimized geometry and vibrational frequencies of 2-(2,3-dihydro-1,5-dimethyl-3-oxo-2-phenyl-1H-pyrazol-4-ylimino)-2-(4-nitro-phenyl) acetonitrile (DOPNA) were obtained by ab initio DFT/B3LYP level with complete relaxation in the potential energy surface using 6-31G and 6-311G basis sets. The Fourier-transform infrared (FT-IR) spectrum of DOPNA has been recorded in the region 4000-400 cm(-1). The harmonic vibrational frequencies were calculated and the scaled values have been compared with experimental FT-IR spectrum. The calculated frequencies are in comparable agreement with the experimental frequencies. The calculated energy span between the HOMO and the LUMO of DOPNA is 2.94 and 2.87eV by B3LYP/6-31G and B3LYP/6-311G, respectively.     

DFT and ab initio quantum chemical studies on p-cyanobenzoic acid

The Fourier transform infrared (FTIR) and FT-Raman spectra of p-cyanobenzoic acid (CBA) have been recorded in the range 4000-400 and 4000-100 cm(-1), respectively. The complete vibrational assignment and analysis of the fundamental modes of the compound were carried out using the observed FTIR and FT-Raman data. The vibrational frequencies determined experimentally were compared with theoretical wavenumbers obtained from ab initio HF and DFT-B3LYP gradient calculations employing 6-31G**, 6-311++G** and cc-pVTZ basis sets for the optimised geometry of the compound. The geometry and normal modes of vibration obtained from the HF and DFT methods are in good agreement with the experimental data. The normal coordinate analysis was also carried out with ab initio force fields utilising Wilson's FG matrix method. The interactions of cyano and carboxylic acid groups with the skeletal vibrational modes were investigated.     

Vibrational spectroscopy investigation using ab initio and density functional theory analysis on the structure of 3,4-dimethylbenzaldehyde

The FT-IR and FT-Raman spectra of 3,4-dimethylbenzaldehyde (3,4-DMB) has been recorded in the region 4000-400 and 3500-100 cm(-1), respectively. The optimized geometry, frequency and intensity of the vibrational bands of 3,4-DMB were obtained by the ab initio and DFT levels of theory with complete relaxation in the potential energy surface using 6-311G(d,p) basis set. The harmonic vibrational frequencies were calculated and the scaled values have been compared with experimental FT-IR and FT-Raman spectra. The observed and the calculated frequencies are found to be in good agreement. The experimental spectra also coincide satisfactorily with those of theoretically constructed bar type spectrograms.     

FTIR, FT-Raman spectra and ab initio DFT vibrational analysis of 2,4-dichloro-6-nitrophenol

The FTIR and FT-Raman spectra of 2,4-dichloro-6-nitrophenol (2,4-DC6NP) has been recorded in the region 4000-400 cm(-1) and 3500-100 cm(-1), respectively. The optimized geometry, frequency and intensity of the vibrational bands of (2,4-DC6NP) were obtained by the ab initio and DFT levels of theory with complete relaxation in the potential energy surface using 6-31G(d,p) and 6-311+G(d,p) basis sets. The harmonic vibrational frequencies were calculated and the scaled values have been compared with experimental FTIR and FT-Raman spectra. The observed and the calculated frequencies are found to be in good agreement. The experimental spectra also coincide satisfactorily with those of theoretically constructed bar type spectrograms.     

Vibrational and electronic investigations, thermodynamic parameters, HOMO and LUMO analysis on crotonaldehyde by ab initio and DFT methods

The energy, geometrical parameters and vibrational wavenumbers of crotonaldehyde were calculated by using ab initio and B3LYP with 6-31G(d,p) and 6-311G(d,p) basis sets. The FT-IR and FT-Raman spectra for liquid state crotonaldehyde have been recorded in the region 3400-400 cm(-1) and 3400-100 cm(-1), respectively and compared with the theoretical spectrographs constructed from the scaled harmonic vibrational frequencies calculated at HF and DFT levels. The difference between the observed and scaled wavenumber values of most of the fundamentals is very small. Detailed interpretations on vibrational modes have been made on the observed and theoretical spectra and PED for each mode was also reported more precisely. HOMO and LUMO energy levels are constructed and the corresponding theoretical frontier energy gaps are calculated to realise the charge transfer occurring in the molecule. The thermodynamic properties of the title compound have been calculated at different temperatures and the results reveals the standard heat capacities (C(0)(p)), standard entropies (S(0)) and standard enthalpy changes (ΔH(0)) increases with rise in temperature.     

Approximating coupled cluster level vibrational frequencies with composite methods

An extensive study of the harmonic frequencies of a large set of small polyatomic closed-shell molecules computed at both single level ab initio and composite approximations is presented here. Using various combinations of basis sets, composite methods are capable of predicting single level ab initio CCSD(T) harmonic frequencies to within 5 cm(-1) on average, which suggests a computationally affordable means of obtaining highly accurate vibrational frequencies compared to the CCSD(T) level. A general approach for calculating the composite level equilibrium geometries and harmonic frequencies for polyatomic systems that uses the Collin's method of interpolating potential energy surfaces is also described here. This approach is further tested on tetrafluoromethane, and an estimation of the potential CPU time savings that may be obtained is also presented. It is envisaged that the findings here will enable theoretical studies of fundamental frequencies and energetics of significantly larger molecular systems.