Vibrational spectra density function theory

Kesyczynski, J. Goodman, L., Kwiatkowski, J. S., 1997, Density Functional Theory and Post-Hartree-Fock Studies on Molecular Structure and Harmonic Vibrational Spectrum of Formaldehyde , Theor. Chem. Acc., 97, 195. 

Martin, J. M. L., El-Yazal, J., Francois, J.-P, 1996, Structure and Vibrational Spectrum of Some Polycyclic Aromatic Compounds Studied by Density Functional Theory. 1. Naphtalene, Azolene, Phenanthrene, and Anthracene , J. Phys. Chem., 100, 15358. 

The vibrational spectrum of 13 is nicely reproduced by quantum chemical calculations at the CCSD(T) level of theory," whereas density functional theory (DFT) shows a variable performance for 13 depending on the functional employed." This caution holds especially for the distance between the radical... 

M. Plazanet, N. Fukushima, M.R. Johnson, A.J. Horsewill, H.P. Trommsdorff (2001). J. Chem. Phys., 115, 3241-3248 The vibrational spectrum of crystalline benzoic acid Inelastic neutron scattering and density functional theory calculations. H.B. Burgi S.C. Capelli (2000). Acta Cryst., A56 403-412. Dynamics of molecules in crystals from multi-temperature anisotropic displacement parameters. I Theory. 

H.G. Schimmel, M.R. Johnson, G.J. Kearley, A.J. Ramirez-Cuesta, J. Huot F.M. Mulder (2004). Materials Science and Engineering B-Solid State Materials for Advanced Technology, 108, 38-41. The vibrational spectrum of magnesium hydride from inelastic neutron scattering and density functional theory. 

Femtosecond photoelectron spectroscopy was employed to study the excitation of trons-stilbene above the isomerization reaction barrier [82]. Apart from the contribution, evidence of a second electronic state was found on the basis of two different transients measured across the photoelectron spectrum. Time-dependent density functional theory calculations on So, Si, S2, and Do, tt ether with simulations of the electron energy distribution, supported the experimental findings for selective photoelectron energies of the So, Si,... electronic states. The photoelectron spectra of trans-stilbene following the excitation with 266 nm laser pulses consisting of a pronounced three-peak structure were subjected to a substantia] broadening, due to the large number of closely spaced vibrational states involved in the excitation scheme. 

Calaminici, P., Koster, A. M., Carrington, T., Roy, P. N., Russo, N., Salahub, D. R. (2001). V3 Structure and vibrations from density functional theory, Franck-Condon factors, and the pulsed-field ionization zero-electron-kinetic energy spectrum. Journal of Chemical Physics, 114, 4036. 

Circular dichroism (CD) can be observed in the vibrational transitions of chiral molecules vibrational circular dichroism (VCD). An example of a VCD spectrum is shown in Figure 1, together with the corresponding unpolarized absorption spectrum. The sample is a 0.6 M solution of (lR,4jR)-(-i-)-cam-phor in CCI4. Here, we discuss the theoretical analysis of VCD spectra. The current state-of-the-art is illustrated in Figure 1, where VCD and absorption spectra of camphor, predicted within the harmonic approximation (HA) using ab initio density functional theory (DFT), are shown. 

An illustration of the importance of the tautomeric form for base-pairing properties can be found in the case of GC base-pairing. There are about 50 ways to form GC base pairs by hydrogen bonding. The one structure that is prevalent in DNA (the Watson-Crick structure) has a subpicosecond excited-state lifetime, evidenced by a broad UV spectrum, while other structural arrangements of the same base-pair have sharp spectra, consistent with much longer excited-state lifetimes [75]. Figure 7.9 the shows IR-UV spectra for three structural isomers of GC base pairs. The stick spectra are density functional theory (DFT) calculated vibrational frequencies for the structures shown in the insets. Structure A is the Watson-Crick structure, while structure C is almost the same structure but with the cytosine... 

Model calculations were performed on the VAMP [24], DMOL [25, 26], and CASTEP [27] modules of the Materials Studio program package from Accelrys. Full geometry optimizations and vibrational frequency analyses were carried out in all electron approximation using in DMOL the BLYP [28, 29] functional in conjunction with the double-numeric-basis set with polarization functions (DNP) and the IR models were calculated from the Hessians [30], In CASTEP the gradient-corrected (GGA) PBE [31] functional was selected for the density functional theory (DFT) computations with norm conserving and not spin polarized approach [32], In the semi-empirical VAMP method we used the PM3 parameterization [33] from the modified neglect of diatomic differential overlap (NDDO) model to obtain the Hessians for vibrational spectrum models [30],... 

HaU and coworkers used density functional theory calculations to assign the inelastic neutron scattering derived vibrational spectrum of the elongated dihydrogen complex, (Tp )Rh(H)2(/ -H2) [66], They conclude that the H-H distance derived from neutron diffraction for the (Tp )Rh(H)2( / -H2) complex may in fact correspond to the average of the H-H distances of the tetrahydride and bis-hydride/// -H2 species. 

The Einstein theory is simple. The normal vibrations of a crystal span a wide spectrum. It would be wise to introduce a spectral density function g(v), such that... 

At T 0 the sharp lines corresponding to the harmonic modes are broadened by anharmonic effects until, at high temperature, the simple relationship between vibrational density of states and dynamical matrix is lost. In this regime, and especially for large aggregates, MD is the most suitable tool to compute the vibrational spectrum. Standard linear response theory within classical statistical mechanics shows that the spectrum f(co) is given by the Fourier transform of the velocity-velocity autocorrelation function... 

In this work 2 was a sphere of radius R and the nucleus was placed at the center of the sphere. This reduced the problem to that of the radial function only. In 1911, H. Weyl solved some vibrational problems [3], which now may be interpreted as describing the structure of the highly excited part of the spectrum of a free particle in a bounded region 2 with Dirichlet boundary conditions. Weyl s famous asymptotic formulae for the density of states in a region of large volume, that depends on the volume but not on the form of the region 2 (see e.g. Sect. VI.4. in [4], or Sect. XIII.15 in [5]), are usually used in physical chemistry when the partition function is calculated for translational motion of an ideal gas. Nowadays the next term in this asymptotic expression is usually studied in the theory of chaos (see e.g. Sect. 7.2 of [6]). 

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