Calculation Of Vibrational Spectra Research Articles

A theory of vibrations of solid solutions with inclusion of the cluster effects: Non-self-consistent and self-consistent approximations

A theory of vibrational spectra of solid solutions proposed by the author has been developed, in which a cluster of n cells statistically filled with impurity atoms is used as a phonon scattering unit. The calculation of vibrational spectra of a disordered linear chain in the generalized non-self-consistent approximation has demonstrated a strong dependence of the spectrum on the number n. For n = 6, the calculated spectrum is in an excellent agreement with the result of the computer experiment performed by Dean for a chain of 8000 atoms. The maximum number of impurities in the cluster to be considered depends on the magnitude of the initial damping (in real crystals, it is damping due to anharmonicity). The spectrum has also been calculated in the generalized self-consistent approximation. This calculation gives a smeared structureless curve, which absolutely does not agree either with the theoretical calculation in the non-self-consistent approximation or with the results obtained by Dean. This means that the generalized self-consistent approximation overestimates the weight of the incoherent scattering processes, which leads to averaging of the phases. The spectrum of a three-dimensional solid solution is calculated using a simple model of the crystal.

Vibrational Raman Spectra from the Self-Consistent Charge Density Functional Tight Binding Method via Classical Time-Correlation Functions

The Self-Consistent Charge Density Functional Tight Binding (SCC-DFTB) method has been extended for the calculation of vibrational Raman spectra employing the Fourier Transform of Time-Correlation Function (FTTCF) formalism. As Witek and co-workers have already shown for a set of various organic molecules, the minimal basis SCC-DFTB approach performs surprisingly good in terms of polarizability calculations. Therefore, we were encouraged to use this electronic structure method for the purpose of Raman spectra calculations via FTTCF. The molecular polarizability was accessed via second order numeric derivatives of the SCC-DFTB energy with respect to the components of an external electric field “on-the-fly” during a molecular dynamics (MD) simulation. The finite electric field approach delivers Raman spectra that are in overall good agreement for most of 10 small organic model compounds examined in the gas phase compared to a standard Normal Mode Analysis (NMA) approach at the same (SCC-DFTB) and at a higher level of theory (BLYP aug-cc-pVTZ). With the use of reparametrized SCC-DFTB repulsive potentials, a distinct improvement of the Raman spectra from the SCC-DFTB/FTTCF protocol of conjugated hydrocarbons has been observed. Further QM/MM test calculations of l-phenylalanine in aqueous solution revealed larger deviations concerning vibrational frequencies and relative intensities for several stretching and bending modes in the benzene ring as compared to experimental results. Our SCC-DFTB/FTTCF approach was also tested against a hybrid method, in which polarizability calculations at the B3YLP 6-31G(d) level were performed on a trajectory at the SCC-DFTB level. We found that our SCC-DFTB/FTTCF protocol is not only much more efficient but in terms of the resulting Raman spectra also of similar accuracy compared to the hybrid approach. In our opinion, the more accurately calculated polarizabilities at the B3YLP 6-31G(d) level cannot compensate for the usually insufficient sampling of phase space when employing high level QM methods in a FTTCF framework.

A vibrational spectroscopic investigation of rhodanine and its derivatives in the solid state

AbstractRaman and infrared spectra are reported for rhodanine, 3‐aminorhodanine and 3‐methylrhodanine in the solid state. Comparisons of the spectra of non‐deuterated/deuterated species facilitate discrimination of the bands associated with NH, NH2, CH2 and CH3 vibrations. DFT calculations of structures and vibrational spectra of isolated gas‐phase molecules, at the B3‐LYP/cc‐pVTZ and B3‐PW91/cc‐pVTZ level, enable normal coordinate analyses in terms of potential energy distributions for each vibrational normal mode. The cis amide I mode of rhodanine is associated with bands at ∼1713 and 1779 cm−1, whereas a Raman and IR band at ∼1457 cm−1 is assigned to the amide II mode. The thioamide II and III modes of rhodanine, 3‐aminorhodanine and 3‐methylrhodanine are observed at 1176 and 1066/1078; 1158 and 1044; 1107 and 984 cm−1 in the Raman and at 1187 and 1083; 1179 and 1074; 1116 and 983 cm−1 in the IR spectra, respectively. Copyright © 2010 John Wiley & Sons, Ltd.

Structure and vibrational spectra of H+(HF)n (n=2–9) clusters: An ab initio study

The morphological development of the hydrogen bond network in the protonated hydrogen fluoride clusters, H(+)(HF)(n) (n=2-9), is investigated in detail by ab initio methods. We find a dominance of the linear morphology, which is energetically well separated from the other minimum energy morphologies of the clusters. The geometry for these clusters shows a pattern due to the cooperativity effect prevalent in the hydrogen bonds, as a result of the difference in electronegativities of hydrogen and fluorine atom in the HF molecule. The variations in the covalent HF and hydrogen bond distances in the clusters are in turn reflected in the vibrational spectra. Distinct HF stretching modes for the linear and ring with tail structures were identified. We have discussed the signature peaks for the two possible ion-core morphologies present in the clusters. The highly corrosive nature of HF makes it difficult to study using experiments. We, thus, believe that our structure and vibrational spectra calculations would be useful in understanding the key features in these systems.

Synthesis, characterization and supramolecular synthons in crystals of new derivatives of 10-oxa-4-azatricyclo[5.2.1.02,6]dec-8-ene-3,5-dione

In the study of supramolecular synthons formed by the imide group, four polycyclic imides (2–5) with unsubstituted NH group have been synthesized. The parent compound (1), obtained previously, and its derivatives 2–5 have been characterized by an elemental analysis, FTIR, 1H NMR, 13C NMR and X-ray crystallography methods. The differences in supramolecular structure were discussed on the basis of the X-ray analysis and the solid-state IR spectra. Selected theoretical calculations of vibrational spectra and binding energies confirm the observations that follow from experiment. In particular, the observed splittings of bands corresponding to CO stretching vibrations in the solid-state IR spectra of 1, 2 and 5 are well predicted by quantum chemical calculations.The molecules 1–5, having chiral centers, crystallize in centrosymmetric space groups as racemic compounds. In the solid state the association motifs of the imide fragments seem to be related to the structure (molecular shape and substituents) of the interacting molecules. The strongest interactions are the Nimide–H…Oimide/epoxy hydrogen bonds. They stabilize cyclic dimers (1,2), infinite chains (3,5) and other patterns (4) in crystal architecture. Additionally, in the crystals electrostatic interactions involving CO groups are observed; they form parallel (1) and anti-parallel (3,4) motifs.

Calculation of vibrational spectra by an algebraic approach: Applications to Copper Tetramesityl Porphyrin and its Cation radicals

Using the Lie algebraic model, Hamiltonian vibrational frequencies of Copper Tetramesityl Porphyrin and its Cation radicals are calculated for 64 vibrational bands.

Experimental and theoretical studies on corals. I. Toward understanding the origin of color in precious red corals from Raman and IR spectroscopies and DFT calculations

AbstractAn attempt to explain the origin of the vivid red color in precious pink and red corals was undertaken. Raman and IR spectroscopies were applied to characterize white, pink and red corals. The position of the Raman signal near 1500 cm−1 of some corals and pearls was associated by several authors with the presence of the mixture of all‐trans‐polyenic pigments, containing 6–16 conjugated CC bonds or β‐carotenoids. This hypothesis was examined theoretically by performing extensive B3LYP‐DFT calculations of vibrational spectra of the model polyenic compounds. The B3LYP/6‐311++G** predicted positions of the dominating Raman mode depend on the number of CC units (Cn parameter) and can be accurately predicted for larger systems from a simple nonlinear fit. The DFT‐predicted Raman activities of these modes are extremely sensitive to Cn, and sharply increase with the number of double bonds. This implies a presence of only—two to three polyenes differing slightly in the number of CC units as the source of color in pink and red corals. Copyright © 2009 John Wiley & Sons, Ltd.

Direct calculations of vibrational absorption and circular dichroism spectra of alanine dipeptide analog in water: Quantum mechanical/molecular mechanical molecular dynamics simulations

The vibrational absorption (IR) and vibrational circular dichroism (VCD) spectra of alanine dipeptide analog in water are directly calculated by Fourier transforming the time correlation functions of the electric and magnetic dipole moments, which are calculated using the dynamic partial charges and trajectory of the peptide generated from the quantum mechanical/molecular mechanical molecular dynamics simulations. The alanine dipeptide analog is treated at the Hartree-Fock level with 3-21G, 4-31G, 6-31G, and 6-31G(*) basis sets and the solvent H(2)O is modeled with the TIP3P water. The atomic partial charges are obtained from the Lowdin population analysis, which gives consistent IR spectral profiles irrespective of the basis sets used. The simulated VCD spectrum by a polyproline II(P(II))-dominant trajectory is compatible with the previous experimental results of the polyproline peptides, where the amide I and II VCD bands are negative couplets with a weak positive peak to the high frequency region. The sampling efficiency of the P(II) conformer is much lower than the other ones at all basis levels used. The simulated VCD spectrum of alpha-helix averaged over five trajectories has the reverse sign pattern compared to the P(II) spectrum and is found to be consistent with the previously observed spectral features of alpha-helical polypeptides. The sign patterns of the beta-strand VCD spectrum are qualitatively similar to the experimental spectra of beta-sheet rich proteins. The VCD spectra obtained from the trajectories containing several extended conformers such as beta and P(II) are not clearly distinguishable from the beta-strand-dominant spectra. It is interesting that the P(II) and the coil VCD spectra coincide in sign pattern and relative intensity for all amide modes. This demonstrates that the negative couplet structures of the amide I and II VCD spectra do not necessarily prove the dominance of either P(II) or coil conformation. We anticipate that the present method can be used to directly simulate the IR and VCD spectra of structurally heterogeneous biomolecules in condensed phases.

Quantum chemical analysis of the structure and spectroscopic properties of aryl vinyl ethers

A series of aromatic vinyl ethers and some compounds close to them in structure are studied by DFT (B3LYP/6-311+G(2d,p)) and MP2(full)/6-311+G(2d,p) methods. Measurements of Raman spectra are also used. The calculation of vibrational spectra of aryl vinyl ether (AVE) isomers shows that stretching vibrations ν(C=C) are most conformation sensitive. The calculated value of I(C=C) for vinyl phenyl ether more than twice exceeds the corresponding value for vinyl methyl ether. The calculated and experimental values of I(C=C) are consistent with the hypothesis about the presence of a common conjugated π-system in the molecules of substituted AVEs. Here the bridging oxygen atom provides the π,p,π-interaction.

Vibrational, electronic, and vibronic excitations of polarC60F18molecules: Experimental and theoretical study

Polarized optical conductivity spectra in the IR and visible range and variable-temperature photoluminescence spectra of the ${\text{C}}_{60}{\text{F}}_{18}$ single crystals in the 4--300 K temperature range are reported. Density-functional theory (DFT) calculations of vibrational spectra and time-dependent DFT calculations of the excitation energies of the ${\text{C}}_{60}{\text{F}}_{18}$ molecule are performed to interpret experimentally observed phenomena. Orientation of the ${C}_{3v}$-symmetric ${\text{C}}_{60}{\text{F}}_{18}$ molecules in the single crystal is revealed by comparison of the experimental polarized IR spectra and vibrational DFT calculations. ${A}_{2}$ symmetry is assigned to the lowest energy singlet excited state of ${\text{C}}_{60}{\text{F}}_{18}$, and hence pure electronic ${S}_{0}\ensuremath{\rightarrow}{S}_{1}$ excitation is found to be dipole forbidden. Fine vibronic structure found at low temperature is interpreted in terms of Herzberg-Teller and Franck-Condon mechanisms. Considerable similarity with vibronic spectra of ${\text{C}}_{60}$ is found and explained by presumable localization of the lowest energy electronic excitation of ${\text{C}}_{60}{\text{F}}_{18}$ on the fullerenelike part of the molecule.

Calculation and analysis of vibrational spectra of adenine–thymine, guanine–cytosine, and adenine–uracil complementary pairs in the condensed state

We have calculated the frequencies of the normal vibrations of the complementary nucleic acid base pairs adenine–thymine, guanine–cytosine, adenine–uracil, corresponding to the Watson–Crick structure, and the adenine–uracil pair, corresponding to the Hoogsteen structure, in condensed states and we interpret the spectra. We determine the contributions of hydrogen bonds to the vibrational modes of the complementary pairs. We have analyzed the nature of the relative displacements of the nucleic acid bases as integral molecular units along the hydrogen bonds. We show the role of hydrogen bonds in tautomeric interconversions of complementary nucleic acid base pairs.

Density functional theory calculations of vibrational spectra of rhodium oxide clusters

Predicted infrared vibrational spectra of low-energy isomers of rhodium cluster oxides, Rh6Om+(m=1–4), are presented, based on structures calculated using density functional theory. The oxygen stretching frequencies are found to be characteristic of the oxygen binding mode. These simulated spectra provide a guide to future experimental measurements of the infrared multi-photon dissociation spectra, enabling assignment of the binding sites of oxygen atoms on the cluster. In favourable cases these calculations suggest that a determination of the underlying metal framework structure is possible.

Photoinduced oxidation of triphenylphosphine isolated in a low-temperature oxygen matrix

Photooxidation reactions of triphenylphosphine (Ph 3P) monomers isolated in matrices of solid oxygen at 10 K were characterized by means of infrared spectroscopy. Upon UV ( λ > 280 nm) irradiation of O 2 matrices, ca. 90% of Ph 3P was converted to triphenylphosphine oxide (Ph 3P O), with concomitant formation of ozone. In the competing photoreaction, ca. 10% of Ph 3P was converted to diphenyl-phenyl-phosphinate, Ph 2(Ph−O−)P O. The interpretation was assisted by theoretical [DFT(B3LYP)/6-31G(d, p)] calculations of vibrational spectra, as well as by comparison with the experimental vibrational data from separate experiments in which monomeric Ph 3P and Ph 3P O were isolated in argon and oxygen matrices at 10 K.

Geometry Optimizations and Vibrational Spectra of Large Molecules from a Generalized Energy-Based Fragmentation Approach

The generalized energy-based fragmentation (GEBF) approach (Li, W.; Li, S.; Jiang, Y. J. Phys. Chem. A 2007, 111, 2193) is extended for geometry optimizations and vibrational spectra calculations of general large molecules or clusters. In this approach, the total energy and its derivatives, and some molecular properties, of a target system are obtained from conventional calculations on a series of subsystems derived from the target system. Each subsystem is electronically embedded in the background point charges generated by all other atoms outside the subsystem so that the long-range interactions and polarization effects between remote fragments are approximately taken into account. The approach computationally scales linearly with the system size and can be easily implemented for large-scale parallelization. By comparing the results from the conventional and GEBF calculations for several test molecules including a polypeptide and a water cluster, we demonstrate that the GEBF approach is able to provide quite reliable predictions for molecular geometries, vibrational frequencies, and thermochemistry data and satisfactory descriptions for vibrational intensities, for general molecules with polar or charged groups.

New approach for the correction of Ab initio molecular force fields in cartesian coordinates

AbstractThis paper presents a scaling technique applicable to molecular force constants in Cartesian coordinates. In the course of spectroscopic and structural research, it is a common practice to achieve better correspondence between measured and calculated vibrational frequencies of a molecule by appropriate scaling of the force constant matrices obtained by quantum chemical methods. However, the existing scaling procedure requires introduction of the complete system of internal coordinates, which may be tedious and time‐consuming for complex molecules. Scaling scheme suggested in this paper is applied directly to Cartesian force constant matrices and thus does not require introduction of the internal coordinates. Practical implementation of the proposed approach is illustrated with the examples of simple molecules. The scheme allows imposing special constraints on the determined Cartesian scale factors, which may be used for obtaining scale factors possessing transferability properties. These properties are very important for vibrational spectra calculations of related compounds, especially for large biological molecules, associates and nanostructures. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Correlation between Raman and X-ray crystallography data of (Pro-Pro-Gly) 10

Model biopolymers are powerful tools to guide the interpretation of physical properties in complex systems. (Pro-Pro-Gly) 10, (PPG) 10, is a collagen-model peptide, whose structure is known at high resolution. Herein, Raman microscopy data of (PPG) 10 powders and single crystals are reported. The spectra interpretation leads to an accurate assignment of three well-resolved amide bands corresponding to the three peptide bonds (PP, PG and GP) present in the (PPG) 10 structure. These data together with the availability of torsional angles φ and ψ derived from the high-resolution crystal structure, provide the opportunity to test the validity of theoretical equations for the calculation of non-canonical amide III bands and represent a reference for theoretical calculations of vibrational spectra and for polyproline II detection in complex proteins. Spectroscopic data do not support the indication of two distinct and equally populated up and down conformations of the pyrrolidine rings observed in the (PPG) 10 crystal structure.

DFT calculations of vibrational spectra and nonlinear optical properties for MgO nanotube clusters

The IR and Raman spectra, nonlinear optical properties of MgO nanotube clusters are studied by density-functional theory at B3LYP/6-31G(d) level. The IR spectra are match closely to those in the corresponding MgO cluster and bulk materials. The strongest peaks of the IR spectra are located in the range from 650 to 750 cm −1. The Raman spectra are very sensitive to structural variations in MgO clusters, and redshift of vibrational frequency is observed in Raman spectra as increasing cluster length. The motion of the strongest peaks in spectra is discussed. The total dipole moment and the first hyperpolarizabilities oscillate between zero and a constant when the layer is grown for the layer dependence of symmetry in MgO nanotube clusters.

First-principles calculation of vibrational Raman spectra of tetrahedral amorphous carbon

The nonresonant vibrational Raman spectra of tetrahedral amorphous carbon are calculated from first principles. The structural model was generated using Car–Parinello molecular dynamics, the vibrational modes are determined using the linear response approach and Raman tensors are calculated using the finite electric field method. Our theoretical visible and reduced Raman spectra show an overall good agreement with experimental spectra, and better than previous calculated results. The analysis in terms of atomic vibrations shows that the Raman spectrum mainly comes from sp 2 contribution, G peak is due to the stretching vibration of any pair of sp 2 atoms and only a small sp 3 contribution can be noticed. The differences between peak intensities of reduced theoretical and experimental results mainly come from defects and the high sp 3 content in our simulated structure.

Theoretical study on the structures, isomerization and stability of SiC3H isomers

The calculations of the geometry optimizations, energies, dipole moments, vibrational spectra, rotational constants, and isomerization of doublet SiC3H species were performed using density functional theory and ab initio methods. Four types of isomers, a total of 18 minima, connected by 16 interconversion transition states, were located on the potential energy surface (PES) at the B3LYP/6-311G (d, p) level. More accurate energies were obtained at the CCSD(T)/6-311G(2df, 2p), and G3(MP2) levels. With the highest isomerization barrier, the lowest lying structure, linear A1 possesses the largest kinetic stability. Besides, the isomerization barriers of A2, A4, C2, F1, F4 and F5 are over 10 kcal/mol, and these isomers are also considered to be higher kinetically stable. Other isomers cannot be kinetically stabilized with considerably low isomerization barriers. Investigation on the bonding properties and the computations of vibrational spectra, dipole moments, and rotational constants for SiC3H isomers are helpful for understanding their structures and also valuable for their detections in the interstellar space and laboratory.

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.