Green's Function Determination of Force Constants-H2O as Example

Treating isotopically substituted molecule as a perturbed system, Green's function for the perturbation are constructed and related to the force field of vibration. By spectral representation, Green's function is diagonalized in the normal coordinates. Then transforming back to the Cartesian coordinates, the Cartesian force constants are generated without solving the secular equation directly. The relations between the internal force constants and the Cartesian force constants ate given and complete internal force field can be obtained. The results for H₂O are discussed.     

Ab initio potential energy surfaces and nonadiabatic interactions in the H+ +NO collision system

Ab initio calculations on the H(+)+NO system have been carried out in Jacobi coordinates at the multireference configuration interaction level employing Dunning's correlation-consistent polarized valence triple zeta basis set to analyze the role of low-lying electronic excited states in influencing the collision dynamics relevant to the experimental collision energy range of 9.5-30 eV. The lowest two adiabatic potential energy surfaces, asymptotically correlating to H(+)+NO(X (2)Pi) and H((2)S)+NO(+)(X (1)Sigma(+)), have been obtained. Using ab initio procedures, the (radial) nonadiabatic couplings and the mixing angle between the lowest two electronic states (1 (2)A' and 2 (2)A') have been obtained to yield the corresponding quasidiabatic potential energy matrix. The strengths of the computed vibrational coupling matrix elements reflect a similar trend, as has been observed experimentally in the magnitudes of the state-to-state transition probability for the inelastic vibrational excitations [J. Krutein and F. Linder, J. Chem. Phys. 71, 559 (1979); F. A. Gianturco et al., J. Phys. B 14, 667 (1981)].     

The ab initio calculation of the band origin and vibrational frequencies of the Ã-X̃ system of HNCl using the non-rigid bender hamiltonian

A three-dimensional fit of ab initio MRD CI potential data has been made for the lowest two electronic states of the HNC1 molecule (X̃ ²A″ and à ²A'), and the corresponding vibrational frequencies and rotational energies have been computed using the non-rigid bender Hamiltonian. For the ground state the vibrational frequencies obtained are ν₁ = 2942 cm⁻¹, ν₂ = 1232 cm⁻¹, and ν₃ = 549 cm⁻¹, while the corresponding values for the first excited state are 3524,947 and 836 cm⁻¹ respectively. We calculate T_c(à ²A') 16200 cm⁻¹, T_o(òA') = 16400 cm⁻¹, and the Franck-Condon maximum, Ã(0,3,1)-X̃(0,0.0), is calculate at 19200 cm⁻¹(5200 Å).     

A quartic force field coordinate substitution scheme using hyperbolic sine coordinates

Quartic force fields (QFF) are currently the most cost‐effective method for the approximation of potential energy surfaces for the calculation of anharmonic vibrational energies. It is known, although, that its performance can be less than satisfactory due to limitations related to slow convergence of the series. In this article, we present a coordinate substitution scheme using a combination of Morse and sinh coordinates, well adapted for its use with cartesian normal coordinates. We derive expressions for analytical integrals for use in VSCF and VCI calculations and show that the simultaneous substitution of symmetric and antisymmetric normal coordinates by Morse and sinh coordinates, respectively, significantly improves the vibrational transition frequencies for these modes in a well‐balanced fashion. The accuracy of this substitution scheme is demonstrated by comparing one and two‐dimensional sections of substituted and unsubstituted QFF with ab initio potential energy grids, as well as with vibrational energy calculations using as test cases two well‐studied benchmark molecules: water and formaldehyde. We conclude that the coordinate substitution scheme presented constitutes a very attractive alternative to simple QFFs in the context of cartesian normal coordinates.     

Millimeter wave spectrum of CaO

The pure rotational spectrum of diatomic calcium oxide, CaO, in the X ¹Σ⁺ state, has been observed in the millimeter wave region. Measurements in the ground and first excited vibrational states yield the following spectroscopic constants:- Y₀₁ ? 3/4 Y₂₁ (≈ B_e ? 3/4 γ_c) = 13324.3578(32) MHz, Y₁₁ + 2Y₂₁ (≈ ? α_e + 2γ_e) = ?99.3110(28)MHz and Y₀₂ (≈ ? D_e) = ?19.623(33) kHz.     

Equilibrium structure and vibrational frequencies of the O4 molecule

SCF closed shell calculations were performed to determine the equilibrium structure and vibrational frequencies of the O₄ molecule by means of Payne's method and with the help of the molecule's symmetry coordinates. The equilibrium geometry corresponds to symmetry group D_2d with R = 1.505 Å and h = 0.094 Å. The vibrational frequencies are: ν₅(E) = 885.5 cm^?1, ν₃(B₁) = 1051.9 cm^?1, ν₁(A₁) = 1018.3 cm^?1, ν₄(B₂) = 880.3 cm^?1. The second vibrational coordinate (A₁) corresponds to a double-well potential. The first vibrational levels were calculated by a variational method.     

The transformation of inhomogeneously broadened spectra due to frequency migration

The motion-induced transformation of static spectra has been calculated for multipole and exchange interactions of randomly distributed centres. The non-monotonic dependence of the spectrum width on the modulation rate has been obtained under the assumption that the motion results in the Markoffian modulation of frequency. The difference in shape of experimental Raman spectra [J. Schoederet al., Mol. Phys.34, 1501 (1977); J. chem. Phys.66, 3215 (1977)], can be attributed to the fact that the spectra are motion-broadened in the former case and motion-narrowed in the latter case.     

Vibrational calculations in formaldehyde: the CH stretch system

An alternative procedure for the calculation of highly excited vibrational levels in S0 formaldehyde was developed to apply to larger molecules. It is based on a new set of symmetrized vibrational valence coordinates. The fully symmetrized vibrational kinetic energy operator is derived in these coordinates using the Handy expression [Molec. Phys. 61, 207 (1987)]. The potential energy surface is expressed as a fully symmetrized quartic expansion in the coordinates. We have performed ab initio electronic computations using GAMESS to obtain all force constants of the S0 formaldehyde quartic force field. Our large scale vibrational calculations are based on a fully symmetrized vibrational basis set, in product form. The vibrational levels are calculated one by one using an artificial intelligence search/selection procedure and subsequent Lanczos iteration, providing access to extremely high vibrational energies. In this work special attention has been given to the CH stretch system by calculating the energies up to the fifth CH stretch overtone at ∼16000 cm⁻¹, but the method has also been tested on two highly excited combination levels including other lower frequency modes.      

Variational calculations on the vibrational level structure of S0 HDCO

We perform converged high precision variational calculations to determine the frequencies of the vibrational levels in S₀ HDCO, extending up to 5000 cm^?1 of vibrational excitation energy. For these calculations we use our specific vibrational method (recently employed for studies on H₂CO and D₂CO), consisting of a combination of a search/selection algorithm and a Lanczos iteration procedure and based on the Martin, Lee, Taylor potential energy surface for formaldehyde. The calculated level structure is compared to the recently measured frequencies by Ellsworth et al. in order to improve their assignments and further clarify the vibrational mixing pattern and vibrational resonances in HDCO that are very different from the other more symmetric formaldehyde species H₂CO and D₂CO studied recently.     

Rotational spectrum of BiBr

The microwave absorption spectra of Bi⁷⁹Br and Bi⁸¹Br have been measured in the 65–100 GHz region. Frequencies of rotational transitions (υ,J + 1) ← (υ,J) in the 0⁺ electronic ground state with J = 26,27 and 35–39, and in the vibrational state υ = 0–11 can be fitted to the expression: ν = 2[Y₀₁ + Y₁₁(υ + $\text{1}\text{2}$) + Y₂₁(υ + $\text{1}\text{2}$)²] (J + 1) + 4Y₀₂(J + 1)³. The results for the Dunham coefficients are: Y₀₁ = 1295.5609(12) MHz, Y₁₁ = ?3.97809(18) MHz, Y₂₁ = 2.303(18) kHz, Y₀₂ = ?220.26(45) Hz for Bi⁷⁹Br, and: Y₀₁ = 1272.3406(12) MHz, Y₁₁ = ?3.87164(16) MHz, Y₂₁ = 2.225(14) kHz, Y₀₂ = ?212.31(45) Hz for Bi⁸¹Br. From these results we have deduced the value for the equilibrium distance r_e, for the potential constants a₀ and a₁, and for the vibrational constants ω_e and ω_eχ_e. The molecular constants of BiBr are almost the same as of TIBr, the situation found also for BiI and TII.     

Potential energy distributions and normal coordinates of methyl,methyl-d3 and partially deuterated methyl chloride,bromide and iodide

The potential energy distributions and normal coordinates (L^?1 matrices) for twelve methyl halides, CH₃X, CH₂DX, CD₂HX and CD₃X (X = Cl, Br, I) have been calculated from known structural data. General harmonic force fields for methyl chloride, bromide and iodide previously determined from the most complete available isotopic frequency, Coriolis and centrifugal distortion data were used. The vibrational modes of these molecules are compared and discussed.     

Relevance of π-Backbonding for the Reactivity of Electrophilic Anions [B12X11]− (X=F,Cl, Br,I, CN)

Electrophilic anions of type [B₁₂X₁₁]⁻ posses a vacant positive boron binding site within the anion. In a comparatitve experimental and theoretical study, the reactivity of [B₁₂X₁₁]⁻ with X=F, Cl, Br, I, CN is characterized towards different nucleophiles: (i) noble gases (NGs) as σ-donors and (ii) CO/N₂ as σ-donor-π-acceptors. Temperature-dependent formation of [B₁₂X₁₁NG]⁻ indicates the enthalpy order (X=CN)>(X=Cl)≈(X=Br)>(X=I)≈(X=F) almost independent of the NG in good agreement with calculated trends. The observed order is explained by an interplay of the electron deficiency of the vacant boron site in [B₁₂X₁₁]⁻ and steric effects. The binding of CO and N₂ to [B₁₂X₁₁]⁻ is significantly stronger. The B3LYP 0 K attachment enthapies follow the order (X=F)>(X=CN)>(X=Cl)>(X=Br)>(X=I), in contrast to the NG series. The bonding motifs of [B₁₂X₁₁CO]⁻ and [B₁₂X₁₁N₂]⁻ were characterized using cryogenic ion trap vibrational spectroscopy by focusing on the CO and N₂ stretching frequencies and , respectively. Observed shifts of and are explained by an interplay between electrostatic effects (blue shift), due to the positive partial charge, and by π-backdonation (red shift). Energy decomposition analysis and analysis of natural orbitals for chemical valence support all conclusions based on the experimental results. This establishes a rational understanding of [B₁₂X₁₁]⁻ reactivety dependent on the substituent X and provides first systematic data on π-backdonation from delocalized σ-electron systems of closo-borate anions.     

A reassignment of the vibrational fundamentals of sulfuryl chloride fluoride

Low temperature Raman spectroscopy has led to a significant revision in the assignment of the vibrational fundamentals of sulfuryl chloride fluoride (SO₂FCl). The fundamentals in cm⁻¹ are: (a′) 1230, 826, 632, 503, 422, 295; (a″) 1469, 476, 303. All are from gas-phase i.r. spectra except 295 cm⁻¹, which is from the liquid-phase Raman spectrum. The revised assignments are consistent with the predictions of Pfeiffer's normal coordinate calculations [Z. phys. chem., Leipzig 240, 380 (1969)].     

Normal coordinate analysis and thermodynamic functions of niobium and tantalum pentahalides

Normal coordinate treatment of NbX₅ and TaX₅ (X = F, Cl, Br) in the Urey-Bradley force fields was performed using published vibrational frequencies. The analysis was carried out with Wilson's FG formalism and the force constants were evaluated by a computer program based on the least-squares-fit method. Normal coordinates, potential energy distributions and thermodynamic functions were also determined. The results support the reported assignments of the fundamental frequencies of the pentachlorides and the pentabromides, and suggest that the pentafluoride assignments are incorrect.     

Vibrational spectra and normal coordinate analysis for cis-diamminetetrachloroplatinum

The normal coordinate analysis of cis-diamminetetrachloroplatinum has been carried out by using a modified Urey—Bradley force field. According to the molecular structure, 45 internal coordinates were established and 33 theoretical vibrational frequencies were calculated. Due to considering the interaction between non-neighbouring stretching vibrations and between bending vibrations and introducing an appropriate set of internal coordinates in the course of calculation, the calculated frequencies agree well with the observed values, with an average difference 3.61 cm⁻¹ between them. The rationality and the reliability of the results are discussed and the questionable empirical assignment of ν(PtCl) in the literature is corrected.     

Normal coordinate analysis of trans-stilbene and tolane

The vibrational frequencies and modes of trans-stilbene and tolane have been calculated using a simplified overlay valence force field previously developed for a series of smaller conjugated molecules. The force constants have been directly transferred assuming that the large molecules can be regarded as weakly coupled systems. Several unexpected changes in frequencies and modes on isotopic substitution are discussed, the most interesting ones occurring in the Raman spectrum of α,α′-¹³C substituted trans-stilbene. On the basis of the calculations many revisions in the assignments have been made. The rms frequency deviations are 8.0 cm⁻¹ and 6.9 cm⁻¹ for trans-stilbene and tolane, respectively.     

Far infrared spectra of mono- and bisphthalocyanine derivatives

The far infrared spectra of a series of unsubstituted monophthalocyanine (Pc) and di-Pc derivatives and some of the corresponding tetra-tert-butyl substituted Pc molecules are reported. The infrared data were recorded between 100 and 4.50 cm⁻¹. The vibrational assignment of metal-nitrogen stretching frequencies is discussed. The far infrared data for tert-butyl Pc derivatives and a group of C_4ν Pc complexes are presented here for the first time.     

Scaled Quantum Mechanical Force Fields for the Isoelectronic Molecules CF3X (X = SiH3, PH2, SH,Cl )

The vibrational properties of the CF₃X (X = SiH₃, PH₂, SH, Cl) series of molecules were studied by means of density functional theory (DFT) techniques. After obtaining the optimized geometrical parameters and conformations, the frequencies corresponding to the normal modes of vibration and the associated force constants were calculated. The original force fields in Cartesian coordinates were transformed to local symmetry coordinates and subsequently scaled to reproduce the experimental frequencies. Some trends observed in the experimental data could be explained on the basis of the calculated atomic charges.     

The adaptive hierarchical expansion of the kinetic energy operator

The hierarchical expansion of the kinetic energy (HEKE) operator in curvilinear coordinates presented recently (Strobusch and Scheurer, J. Chem. Phys. 2011a, 135, 124102; Strobusch and Scheurer, J. Chem. Phys. 2011b, 135, 144101) relies on a many‐body expansion of the metric tensor. It is shown how this expansion can be adapted to a specific system. An analytic formula is derived, which yields an estimate of the impact of a certain expansion term on the spectrum. In combination with the hierarchical structure of the many‐body expansion and interpolation techniques, the memory consumption and evaluation time of the HEKE operator as well as the computational costs for subsequent vibrational self‐consistent field and vibrational configuration interaction calculations are reduced significantly, which is demonstrated by studies on two small test systems H₂O₂ and formaldehyde (H₂CO). © 2013 Wiley Periodicals, Inc.