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.     

An analytical derivative procedure for the calculation of vibrational Raman optical activity spectra

We present an analytical time-dependent Hartree-Fock algorithm for the calculation of the derivatives of the electric dipole-magnetic dipole polarizability with respect to atomic Cartesian coordinates. Combined with analogous procedures to determine the derivatives of the electric dipole-electric dipole and electric dipole-electric quadrupole polarizabilities, it enables a fully analytical evaluation of the three frequency-dependent vibrational Raman optical activity (VROA) invariants within the harmonic approximation. The procedure employs traditional non-London atomic orbitals, and the gauge-origin dependence of the VROA intensities has, therefore, been assessed for the commonly used aug-cc-pVDZ and rDPS:3-21G basis sets.     

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.     

Anharmonic effects in IR, Raman, and Raman optical activity spectra of alanine and proline zwitterions

The difference spectroscopy of the Raman optical activity (ROA) provides extended information about molecular structure. However, interpretation of the spectra is based on complex and often inaccurate simulations. Previously, the authors attempted to make the calculations more robust by including the solvent and exploring the role of molecular flexibility for alanine and proline zwitterions. In the current study, they analyze the IR, Raman, and ROA spectra of these molecules with the emphasis on the force field modeling. Vibrational harmonic frequencies obtained with 25 ab initio methods are compared to experimental band positions. The role of anharmonic terms in the potential and intensity tensors is also systematically explored using the vibrational self-consistent field, vibrational configuration interaction (VCI), and degeneracy-corrected perturbation calculations. The harmonic approach appeared satisfactory for most of the lower-wavelength (200-1800 cm(-1)) vibrations. Modern generalized gradient approximation and hybrid density functionals, such as the common B3LYP method, provided a very good statistical agreement with the experiment. Although the inclusion of the anharmonic corrections still did not lead to complete agreement between the simulations and the experiment, occasional enhancements were achieved across the entire region of wave numbers. Not only the transitional frequencies of the C-H stretching modes were significantly improved but also Raman and ROA spectral profiles including N-H and C-H lower-frequency bending modes were more realistic after application of the VCI correction. A limited Boltzmann averaging for the lowest-frequency modes that could not be included directly in the anharmonic calculus provided a realistic inhomogeneous band broadening. The anharmonic parts of the intensity tensors (second dipole and polarizability derivatives) were found less important for the entire spectral profiles than the force field anharmonicities (third and fourth energy derivatives), except for a few weak combination bands which were dominated by the anharmonic tensor contributions.     

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.     

On the calculation of dipole moment and polarizability derivatives by the analytical energy gradient method: Application to the formaldehyde molecule

Following the suggestion of Komornicki and McIver we have implemented an efficient computational scheme for the evaluation of dipole moment and polarizability derivatives at the Hartree-Fock SCF level. The derivatives are obtained by utilizing the analytical gradients of the molecular energy, calculated in the presence of an external electric field, with respect to the atomic cartesian coordinates, which are differentiated numerically with respect to the field. The implementation of the method within the framework of the MOLECULE program is discussed, concentrating on such aspects as numerical accuracy, utilization of molecular symmetry and computational efficiency. As an application, the dipole moment and polarizability derivatives of the formaldehyde molecule have been calculated, yielding infrared intensities and Raman scattering activities in the double harmonic approximation. The theoretical results are compared with the available experimental data; the agreement is satisfactory given the inherent restrictions of the SCF model.     

Spectroscopic and theoretical study on peramine and some pyrrolopyrazinone compounds

The comparative analysis of IR and Raman spectra of peramine and its four derivatives in solid state was carried out. The harmonic vibrational frequencies, infrared intensities, and Raman scattering activities were calculated at density functional B3LYP methods with 6-311++G(d,p) basis set. For the predicted spectra, a potential energy distribution of normal modes was also calculated. For peramine derivatives the conjugation effect of pyrrole with pyrazinone ring was observed as a result of introduction of double bond. Moreover, ¹H NMR analysis indicated that pyrrole protons are deshielded in comparison with the pyrrolopyrazinone model ring system.     

Vibrational spectroscopic (FTIR and FT Raman) studies, first order hyperpolarizabilities and HOMO, LUMO analysis of p-toluenesulfonyl isocyanate using ab initio HF and DFT methods

The Fourier transform infrared (FTIR) and FT Raman spectra of p-toluenesulfonyl isocyanate (p-tosyl isocyanate) have been measured. The molecular geometry, vibrational frequencies, infrared intensities, Raman activities and atomic charges have been calculated by using ab initio HF and density functional theory calculation (B3LYP) with 6-311+G(d,p) basis set. Complete vibrational assignment and analysis of the fundamental modes of the compound were carried out using the observed FTIR and FT Raman data. The thermodynamic functions of the title compound were also performed with the aid of HF/6-311+G(d,p) and B3LYP/6-311+G(d,p) levels of theory. Simulated FTIR and FT Raman spectra for p-tosyl isocyanate showed good agreement with the observed spectra. The calculated HOMO and LUMO energies show that charge transfer occurs within the molecule. The dipole moment (μ), polarizability (α) and the hyperpolarizability (β) values of the investigated molecule have been computed using HF and B3LYP methods.     

Resonance Raman spectra of uracil based on Kramers-Kronig relations using time-dependent density functional calculations and multireference perturbation theory

The use of time-dependent density functional calculations for the optimization of excited-state structures and the subsequent calculation of resonance Raman intensities within the transform-theory framework is compared to calculations of Hartree-Fock/configuration interaction singles-type (CIS). The transform theory of resonance Raman scattering is based on Kramers-Kronig relations between polarizability tensor components and the optical absorption. Stationary points for the two lowest excited singlet states of uracil are optimized and characterized by means of numerical differentiation of analytical excited-state gradients. It is shown that the effect of electron correlation leads to substantial modifications of the relative intensities. Calculations of vibrational frequencies for ground and excited states are carried out, which show that the neglect of Duschinsky mixing and the assumption of equal wave numbers for ground and excited state are not in all cases good approximations. We also compare the transform-theory resonance Raman intensities with those obtained within a simple approximation from excited-state gradients at the ground-state equilibrium position, and find that they are in qualitative agreement in the case of CIS, but show some important differences in calculations based on density functional theory. Since the results from CIS calculations are in better agreement with experiment, we also present approximate resonance Raman spectra obtained using excited-state gradients from multireference perturbation theory calculations, which confirm the CIS gradients.     

Structure and vibrational spectra of dinitromethane and trinitromethane

The molecular geometries of dinitromethane and trinitromethane were optimized and their harmonic force fields were calculated by the DFT/B3LYP method. The force fields obtained made it possible to interpret reliably the vibrational spectra of dinitromethane, trinitromethane and a number of isotopomers of trinitromethane. Some general conclusions on geometry and vibrational spectra of the molecules under study are made. The hybrid density functional method used is shown to predict the reliable structural parameters and vibrational frequencies for polynitromethanes.     

Encapsulation effect of π-conjugated quaterthiophene on the radial breathing and tangential modes of semiconducting and metallic single-walled carbon nanotubes

We developed a hybrid approach, combining the density functional theory, molecular mechanics, bond polarizability model and the spectral moment's method to compute the nonresonant Raman spectra of a single quaterthiophene (4T) molecule encapsulated into a single-walled carbon nanotube (metallic or semiconducting). We reported the optimal tube diameter allowing the 4T encapsulation. The influence of the encapsulation on the Raman modes of the 4T molecule and those of the nanotube (radial breathing modes and tangential modes) are analyzed. An eventual charge transfer between the 4T oligomer and the nanotube is discussed.     

The frequency-dependent dipole polarizability of the mercury dimer from four-component relativistic density-functional theory

The frequency-dependent dipole polarizability of Hg(2) is calculated using response theory within four-component relativistic density-functional theory [using the local-density approximation (LDA) and the hybrid functional B3LYP] including corrections for the basis-set superposition error. The anisotropic component of the polarizability tensor agrees well with the values obtained from collision-induced Raman spectroscopy carried out at a wavelength of 488 nm. The values obtained from the two density functionals agree closely with the experimentally derived anisotropy component of the dipole polarizability, despite their rather large differences in the dimer potential-energy curves (LDA is strongly overbinding while B3LYP is purely repulsive). The first two refractivity virial coefficients for the generalized Clausius-Mossotti function are derived.     

A characterization study on 2,6-dimethyl-4-nitropyridine N-oxide by density functional theory calculations

This study deals with the identification of a title compound, 2,6-dimethyl-4-nitropyridine N-oxide by means of theoretical calculations. The optimized molecular structures, vibrational frequencies, corresponding vibrational assignments, thermodynamic properties and atomic charges of the title compound in the ground state were evaluated using density functional theory (DFT) with the standard B3LYP/6-311G(d,p) method and basis set combination for the first time. Theoretical vibrational spectra were interpreted with the aid of normal coordinate analysis based on scaled density functional force field. The results show that the optimized geometric parameters (bond lengths and bond angles) and vibrational frequencies were observed to be in good agreement with the available experimental results. Based on the results of comparison between experimental results and theoretical data, the chosen calculation level is powerful approach for understanding the molecular structures and vibrational spectra of the 2,6-dimethyl-4-nitropyridine N-oxide. Moreover, we not only simulated frontier molecular orbitals (FMO) and molecular electrostatic potential (MEP) but also determined the transition state and energy band gap. Based on the investigations, the title compound is found to be useful to bond metallically and interact intermolecularly. Infrared intensities and Raman activities were also reported.     

Molecular structure and vibrational raman and infrared spectra of bromochlorofluoromethane and its silicon and germanium analogs: quantum-mechanical DFT and MP2 calculations

DFT(B3LYP) and MP2 calculations with the 6-311G(2d, 2p)-type basis set have been carried out for the prediction of molecular parameters (bond distances, bond angles, rotational constants, and dipole moments) and vibrational Raman and infrared spectra (harmonic wavenumbers, absolute intensities, Raman scattering activities, and depolarization ratios) of bromochlorofluoromethane (HCBrCIF) and its silicon and germanium analogs (HSiBrClF and HGeBrCIF). The predicted geometry and vibrational Raman and infrared spectra of HCBrClF agree well with the available experimental data for this molecule and their deuterated derivatives. This agreement allows one to believe that the predicted molecular parameters and vibrational spectra of HSiBrClF, HGeBrClF, and their deuterated derivatives will guide their future experimental studies.     

Analytical derivative techniques for TDDFT excited-state properties: Theory and application

We review our recent work on the methodology development of the excited-state properties for the molecules in vacuum and liquid solution.The general algorithms of analytical energy derivatives for the specific properties such as the first and second geometrical derivatives and IR/Raman intensities are demonstrated in the framework of the time-dependent density functional theory(TDDFT).The performance of the analytical approaches on the calculation of excited-state energy Hessian has also been shown.It is found that the analytical approaches are superior to the finite-difference method on the computational accuracy and efficiency.The computational cost for a TDDFT excited-state Hessian calculation is only 2–3 times as that for the DFT ground-state Hessian calculation.With the low computational complexity of the developed analytical approaches,it becomes feasible to realize the large-scale numerical calculations on the excited-state vibrational frequencies,vibrational spectroscopies and the electronic-structure parameters which enter the spectrum calculations of electronic absorption and emission,and resonance Raman spectroscopies for medium-to large-sized systems.     

Structure and vibrational spectra of the salts of mononitroalkanes

The molecular geometries of the anions of nitromethane and 2-nitropropane were optimised and their harmonic force fields were calculated by the RHF/6-311G(d,p), MP2/6-311G(d,p) and B3LYP/6-311G(d,p) methods. The force fields obtained made it possible to reliably interpret the IR and Raman spectra of the Na⁺ salt of nitromethane, d₂-nitromethane and 2-nitropropane. The assignment proposed significantly improves the interpretation of vibrational spectra known so far. Some general conclusions on geometry and vibrational spectra of the salts of mononitroalkanes studied are made. The hybrid density functional method used (B3LYP) is shown to be in better agreement with experimental data available than the Hartree–Fock methods.     

Accurate theoretical IR and Raman spectrum of Al2O2 and Al2O3 molecules

The accurate harmonic vibration frequencies together with the infrared (IR) and Raman intensities of the most stable conformers of Al₂O₂ and Al₂O₃ molecules have been calculated by the density functional theory (DFT) method with B3LYP exchange–correlation potential and using a set of the augmented correlated consistent basis sets up to quintuple order. The anharmonic vibration frequencies of the non-linear Al₂O₂ molecule have also been calculated. The obtained equilibrium geometrical parameters, harmonic and anharmonic vibration frequencies along with the IR and Raman intensities good converge to their limits with increasing the size of the used basis set. A comparison of the calculated harmonic and anharmonic vibrational frequencies with the available experimental ones points out that the small differences between the calculated harmonic and experimental frequencies can be further substantially reduced when calculations of the anharmonic vibrational frequencies will be available for all types of molecular geometries.     

Experimental and theoretical studies on the identification of p-biphenyloxycarbonylphenyl acrylate

This study presents the identification of a title compound, p-biphenyloxycarbonylphenyl acrylate by means of experimental and theoretical evidences. The spectroscopic properties of the compound were experimentally investigated by Fourier transformation-infrared spectra (in the region 400-4000 cm(-1)) and nuclear magnetic resonance (NMR) chemical shifts (with a frequency of 400 MHz). Moreover, the optimized molecular structures, vibrational frequencies including infrared intensities and Raman activities, corresponding vibrational spectra interpreted with the aid of normal coordinate analysis based on scaled density functional force field, thermodynamic properties, atomic charges and ultraviolet-visible (UV-vis) spectra were analyzed utilizing ab initio Hartree-Fock (HF) and Density Functional Theory (B3LYP) methods at 6-31G(d,p) calculation level. It was found that the vibrational frequencies and chemical shifts obtained were shown to have a good agreement with available experimental results. We not only simulated frontier molecular orbitals (FMO) and molecular electrostatic potential (MEP) but also evaluated the transition state and energy band gap clearly.     

First-principles DFT study of the structural, electronic and vibrational properties of azidopentazole

In this Letter we report a density functional all-electron calculation of the structural and electronic properties of the polynitrogen high-energy molecule, azidopentazole (N₈). We have also performed a vibrational analysis to determine the IR and Raman spectra. Our calculated geometrical properties and vibrational frequencies are in good agreement with previous ab initio and density functional calculations. The weaker IR modes show a different relative ordering than previously reported. We also report calculated Raman intensities for azidopentazole.