改进的三维分离变量表象方法计算振动光谱

The modified discrete variable representation for three-dimension (DVR3D) method was applied to the determination of the vibrational energy levels of the fundamental electronic state of H2S and H2O. The Hamiltonian was expressed in Jacobi coordinates and developed on a DVR basis for each internal coordinate. The angular coordinate used a DVR based on Legendre polynomials and the radial coordinates utilized a DVR based on sine basis functions. Successive diagonalization and truncation technique was used to reduce the size of the final Hamiltonian matrix to be diagonalized. Calculations were presented for H2S and H2O to demonstrate the accuracy of these algorithms.     

用DVR方法研究Ar-HF和Ar-DF的振转光谱

本文用离散变量表示(DVR)方法研究了Ar-HF和Ar-DF体系的振转光谱。对这两个体系的已观测到的振转能级, 用DVR方法得到的计算值与实验结果十分吻合, 误差一般小于0.1cm^-^1, 最大偏差为0.24cm^-^1对Ar-HF的(1113)态。该研究结果与Hutson等用耦合孔道法得到的计算结果基本一致, 但对(3210)振动能级和对(3002)-(3110)态的能级分裂值, 本文计算结果更接近观测值。     

Infrared spectra and ab initio calculations for the F- -(CH4)n (n = 1-8) anion clusters

Infrared spectra of mass-selected F- -(CH4)n (n = 1-8) clusters are recorded in the CH stretching region (2500-3100 cm-1). Spectra for the n = 1-3 clusters are interpreted with the aid of ab initio calculations at the MP2/6-311++G(2df 2p) level, which suggest that the CH4 ligands bind to F- by equivalent, linear hydrogen bonds. Anharmonic frequencies for CH4 and F--CH4 are determined using the vibrational self-consistent field method with second-order perturbation theory correction. The n = 1 complex is predicted to have a C3v structure with a single CH group hydrogen bonded to F-. Its spectrum exhibits a parallel band associated with a stretching vibration of the hydrogen-bonded CH group that is red-shifted by 380 cm-1 from the nu1 band of free CH4 and a perpendicular band associated with the asymmetric stretching motion of the nonbonded CH groups, slightly red-shifted from the nu3 band of free CH4. As n increases, additional vibrational bands appear as a result of Fermi resonances between the hydrogen-bonded CH stretching vibrational mode and the 2nu4 overtone and nu2+nu4 combination levels of the methane solvent molecules. For clusters with n < or = 8, it appears that the CH4 molecules are accommodated in the first solvation shell, each being attached to the F- anion by equivalent hydrogen bonds.     

Ab initio and DFT studies on vibrational spectra of some mixed carbonyl-halide complexes of ruthenium(II)

The vibrational spectra of Ru(CO)6(2+) and some of its mixed carbonyl-halide complexes, cis-Ru(CO)2X4(2-), fac-Ru(CO)3X3- and Ru(CO)5X+ (X = F, Cl, Br and I), have been systematically investigated by ab initio RHF and density functional B3LYP methods with LanL2DZ and SDD basis sets. The calculated vibrational frequencies of complexes Ru(CO)6(2+), cis-Ru(CO)2X4(2-) and fac-Ru(CO)3X3- are evaluated via comparison with the experimental values. In the infrared frequency region, the C-O stretching vibrational frequencies calculated at B3LYP level with two basis sets are in good agreement with the observed values with deviations less than 5%. In the far-infrared region, the B3LYP/SDD method achieved the best results with deviations less than 8% for Ru-X stretching and less than 2% for Ru-C stretching vibrational frequencies. The vibrational frequencies for Ru(CO)5X+ that have not been experimentally reported were predicted.     

Full-dimensional quantum calculations of vibrational spectra of six-atom molecules. I. Theory and numerical results

Two quantum mechanical Hamiltonians have been derived in orthogonal polyspherical coordinates, which can be formed by Jacobi and/or Radau vectors etc., for the study of the vibrational spectra of six-atom molecules. The Hamiltonians are expressed in an explicit Hermitian form in the spatial representation. Their matrix representations are described in both full discrete variable representation (DVR) and mixed DVR/nondirect product finite basis representation (FBR) bases. The two-layer Lanczos iteration algorithm [H.-G. Yu, J. Chem. Phys. 117, 8190 (2002)] is employed to solve the eigenvalue problem of the system. A strategy regarding how to carry out the Hamiltonian-vector products for a high-dimensional problem is discussed. By exploiting the inversion symmetry of molecules, a unitary sequential 1D matrix-vector multiplication algorithm is proposed to perform the action of the Hamiltonian on the wavefunction in a symmetrically adapted DVR or FBR basis in the azimuthal angular variables. An application to the vibrational energy levels of the molecular hydrogen trimer (H2)3 in full dimension (12D) is presented. Results show that the rigid-H2 approximation can underestimate the binding energy of the trimer by 27%. Finally, it is demonstrated that the two-layer Lanczos algorithm is also capable of computing the eigenvectors of the system with minor effort.     

Insights into the structures, energetics, and vibrations of aqua-rubidium(I) complexes: ab initio study

We have carried out ab initio and density functional theory calculations of hydrated rubidium cations. The calculations involve a detailed evaluation of the structures, thermodynamic properties, and IR spectra of several plausible conformers of Rb+ (H2O)(n=1-8) clusters. An extensive search was made to find out the most stable conformers. Since the water-water interactions are important in hydrated Rb+ complexes, we investigated the vibrational frequency shifts of the OH stretching modes depending on the number of water molecules and the presence/absence of outer-shell water molecules. The predicted harmonic and anharmonic vibrational frequencies of the aqua-Rb+ clusters reflect the H-bonding signature, and would be used in experimental identification of the hydrated structures of Rb+ cation.     

Discrete variable approaches to tetratomic molecules: part II: application to H2O2 and H2CO

We have carried out large-scale calculations for accurate vibrational energy levels of formaldehyde and hydrogen peroxide. The discrete variable representations of the radial and angular coordinates are employed together with the contraction scheme resulting from several diagonalization/truncation steps. The global potential energy surface due to Carter et al. [J. Mol. Spectrosc. 90 (1997) 729] is used for H2CO and due to Koput et al. [J. Phys. Chem. A 102 (1998) 6325] for H2O2. For both molecules, the calculated vibrational energy levels are characterized by combining vibrationally averaged geometries and expectation values of rotational constants with several adiabatic projection schemes for automatic quantum number assignments. The energy levels of H2CO involving the excited v2 and v3 vibrations appear as resonances beyond the zero-order picture consisting of uncoupled 3D stretching and 2D bending modes. The torsional energy levels of H2O2 are studied in great detail and different energy patterns occurring below and above the cis barrier are discussed. Our full dimensional calculations for H2O2 have shown that the OH triad levels, 2vOH, are symmetry adapted local mode states.     

Ab initio determination of molecular geometries and vibrational frequencies of CX3 COOH (X=H, F, Cl, Br)

Using Gaussian 03 Revision C.02 version of the quantum chemical program ab initio and DFT computations have been carried out at the rhf/6-31+g*, b3lyp/6-31+g*, b3lyp/6-31++g** and b3lyp/6-311++g** levels to compute optimized geometries, harmonic vibrational frequencies along with intensities in IR and Raman spectra and atomic charges for the acetic (ethanoic) acid and its 1,1,1-tri-halo (fluoro, chloro and bromo) derivatives. The optimized molecular structures for all the four molecules are found to possess Cs point group symmetry. The symmetric stretching mode is found to have lowest magnitude of the three CX3 stretching modes for all the four molecules, whereas the symmetric deformation mode is found to have the lowest magnitude for EA and TFEA and the highest magnitude for TCEA and TBEA. The parallel rocking mode of the CX3 group is found to have lower magnitude than the perpendicular rocking mode for EA and TFEA where reverse is found for TCEA and TBEA. The modes of the COOH group are substituent sensitive except the OH stretching mode. Moreover, the maximum effect is found for the TFEA molecule. The CF3 group is found to have the characteristic frequencies as 235-505, 787, 1150-1190 and 1400 cm(-1) which are due to the modes delta s(CF3), nu s(CF3), nu as(CF3) and nu(C-CF3), respectively.     

Degeneracy in discrete variable representations: general considerations and application to the multiconfigurational time-dependent Hartree approach

Problems appear in discrete variable representations (DVRs) based on general basis sets when the coordinate matrix has degenerate eigenvalues. Then the DVR is not uniquely defined. This paper shows that this problem can be caused by symmetry. Taking the symmetry into account when constructing the DVR solves the problem. The symmetry effect can be particularly important for the time-dependent DVR used in multiconfigurational time-dependent Hartree calculations employing the correlation DVR (CDVR) approach. Problems reported previously for the initial-state selected treatment of the H+H(2) reaction can be attributed to this symmetry effect. They can be solved by using a symmetry-adapted approach to construct the time-dependent DVR. Thus, the present paper shows that the CDVR scheme can be employed also in initial-state selected scattering calculations if the symmetry of the system is properly taken into account in the construction of the time-dependent DVR.     

Infrared photodissociation spectroscopy of Na(NH3)n clusters: probing the solvent coordination

The first mass-selective vibrational spectra have been recorded for Na(NH3)n clusters. Infrared spectra have been obtained for n = 3-8 in the N-H stretching region. The spectroscopic work has been supported by ab initio calculations carried out at both the DFT(B3LYP) and MP2 levels, using a 6-311++G(d,p) basis set. The calculations reveal that the lowest energy isomer for n or= 7 is indicative of molecules entering a second solvation shell, i.e., the inner solvation shell around the sodium atom can accommodate a maximum of six NH3 molecules.     

四原子分子振转相互作用的Lie代数方法

利用Lie代数方法研究了四原子分子振转相互作用，在代数框架内首次给出四 原子分子振转相互作用的张量算子非对角矩阵元的表达式，利用这些表达式对线型 四原子分子HCCF振转相互作用的l-doubling进行了计算。     

Car-Parrinello molecular dynamics simulation of Fe 3+ (aq)

The optimized geometry and energetic properties of Fe(D2O)n 3+ clusters, with n = 4 and 6, have been studied with density-functional theory calculations and the BLYP functional, and the hydration of a single Fe 3+ ion in a periodic box with 32 water molecules at room temperature has been studied with Car-Parrinello molecular dynamics and the same functional. We have compared the results from the CPMD simulation with classical MD simulations, using a flexible SPC-based water model and the same number of water molecules, to evaluate the relative strengths and weaknesses of the two MD methods. The classical MD simulations and the CPMD simulations both give Fe-water distances in good agreement with experiment, but for the intramolecular vibrations, the classical MD yields considerably better absolute frequencies and ion-induced frequency shifts. On the other hand, the CPMD method performs considerably better than the classical MD in describing the intramolecular geometry of the water molecule in the first hydration shell and the average first shell...second shell hydrogen-bond distance. Differences between the two methods are also found with respect to the second-shell water orientations. The effect of the small box size (32 vs 512 water molecules) was evaluated by comparing results from classical simulations using different box sizes; non-negligible effects are found for the ion-water distance and the tilt angles of the water molecules in the second hydration shell and for the O-D stretching vibrational frequencies of the water molecules in the first hydration shell.     

Using MD snapshots in ab initio and DFT calculations: OH vibrations in the first hydration shell around Li+(aq)

The average OH stretching vibrational frequency for the water molecules in the first hydration shell around a Li(+) ion in a dilute aqueous solution was calculated by a hybrid molecular dynamics + quantum-mechanical ("MD + QM") approach. Using geometry configurations from a series of snapshots from an MD simulation, the anharmonic, uncoupled OH stretching frequencies were calculated for 100 first-shell OH oscillators at the B3LYP and HF/6-31G(d,p) levels of theory, explicitly including the first shell and the relevant second shell water molecules into charge-embedded supermolecular QM calculations. Infrared intensity-weighting of the density-of-states (DOS) distributions by means of the squared dipole moment derivatives (which vary by a factor of 20 over the OH stretching frequency band at the B3LYP level), changes the downshift from approximately -205 to -275 cm(-1) at the B3LYP level. Explicit inclusion of relevant third-shell water molecules in the supermolecular cluster leads to a further downshift by approximately -30 cm(-1). Our final estimated average downshift is approximately -305 cm(-1). The experimental value lies somewhere in the range between -290 and -420 cm(-1). Also, the absolute nu(OH) frequency is well reproduced in our calculations. "In-liquid" instantaneous correlation curves between nu(OH) and various typical H-bond strength parameters such as R(O...O), R(H...O), the intramolecular OH bond length, and the IR intensity are presented. Some of these correlations are robust and persist also for the rather distorted instantaneous geometries in the liquid; others are less so.     

Deeply bound cold caesium molecules formed after 0(-)(g) resonant coupling

Translationally cold caesium molecules are created by photoassociation below the 6s + 6p(1/2) excited state and selectively detected by resonance enhanced two photon ionization (RE2PI). A series of excited vibrational levels belonging to the 0(-)(g) symmetry is identified. The regular progression of the vibrational spacings and of the rotational constants of the 0(-)(g) (6s + 6p(1/2)) levels is strongly altered in two energy domains. These deviations are interpreted in terms of resonant coupling with deeply bound energy levels of two upper 0(-)(g) states dissociating into the 6s + 6p(3/2) and 6s + 5d(3/2) asymptotes. A theoretical model is proposed to explain the coupling and a quantum defect analysis of the perturbed level position is performed. Moreover, the resonant coupling changes dramatically the spontaneous decay products of the photoexcited molecules, strongly enhancing the decay into deeply bound levels of the a(3)Σ(+)(u) triplet state and of the X(1)Σ(+)(g) ground state. These results may be relevant when conceiving population transferring schemes in cold molecule systems.     

Analysis of the infrared and Raman spectra of phenylacetic acid and mandelic (2-hydroxy-2-phenylacetic) acid

The structural stability of phenylacetic acid and mandelic acid was investigated by the DFT-B3LYP and the ab initio MP2 calculations with the 6-311G** basis set. The two molecules were predicted at the DFT and MP2 levels of calculation to have the non-planar (Np) forms as their lowest energy structures. The observed spectral intensities of the acids were consistent with the Np conformation being the predominant form at room temperature. The vibrational wavenumbers were computed at the B3LYP level of theory and tentative vibrational assignments were provided on the basis of combined theoretical and experimental infrared and Raman data of the molecules. The sharpness of the methylenic O-H stretching mode in the IR spectrum of mandelic acid suggests the absence of intermolecular dimerization in the acid which is supported by the observation of no splitting of its CO stretching mode.     

IR spectroscopic investigation of cis-(CH(3))(2)Au(O,O'-acac) and cis-(CD(3))(2)Au(O,O'-acac)

The IR spectrum of cis-(CH(3))(2)Au(O,O'-acac) has been reassigned by comparing frequencies for cis-(CH(3))(2)Au(O,O'-acac) and cis-(CD(3))(2)Au(O,O'-acac), and by analysis of the DFT-calculated normal modes and their frequencies for the isolated molecules. The vibrational intensity in the C-H stretching region arises almost entirely from the cis-(CH(3))(2)Au fragment, while the methyl deformation intensity is largely of acetylacetonato ligand origin. A low frequency mode in the C-H stretching region is the first overtone of the delta(a)(CH(3)) mode of cis-(CH(3))(2)Au. The Au-C stretching modes are affected by deuteration of the cis-(CH(3))(2)Au fragment, while the Au-O stretching modes are not.     

High level ab initio study of the structure and vibrational spectra of HO(2)NO(2)

A high-level ab initio study has been performed on the conformational structure and vibrational spectra of HO(2)NO(2). Calculations carried out with coupled-cluster methods using a series of Pople and Dunning basis sets reveal that there is a significant basis set dependence on the predicted ab initio structure. Higher angular momentum basis sets are shown to be necessary in order to bring the calculated structure into agreement with experimental rotational constants. Harmonic vibrational frequencies of HO(2)NO(2) are computed at the CCSD(T)/aug-cc-pVTZ level of theory while the corresponding vibrational anharmonicities are calculated at the MP2/cc-pVTZ level. In addition, the absorption cross sections of OH stretching overtones in HO(2)NO(2) are calculated using a dipole function computed at the QCISD level of theory and found to be in good agreement with the available experimental data.     

New scale factors for harmonic vibrational frequencies using the B3LYP density functional method with the triple-zeta basis set 6-311+G(d,p)

We have calculated optimal frequency scaling factors for the B3LYP/ 6-311+G(d,p) method for fundamental vibrational frequencies on the basis of a set of 125 molecules. Using the new scaling factor, the vibrational frequencies calculated with the triple-zeta basis set 6-311+G(d,p) give significantly better accuracy than those calculated with the double-zeta 6-31G(d) basis set. Scale factors were also determined for low-frequency vibrations using the molecular set of 125 molecules and for zero-point energies using a smaller set of 40 molecules. We have studied the effect on the calculated vibrational frequencies for various combinations of diffuse and polarization functions added to the triple-zeta 6-311G basis set. The 6-311+G(d,p) basis set is found to give almost converged frequencies for most molecules, and we conclude that our optimum scaling factors are valid for the basis sets 6-311G(d,p) to 6-311++G(3df,3pd). The new scale factors are 0.9679 for vibrational frequencies, 1.0100 for low-frequency vibrations, and 0.9877 for zero-point vibrational energies.     

Theoretical studies on vibrational spectra of some mixed carbonyl-halide complexes of Osmium(II)

The vibrational spectra of Os(CO)(6)(2+) and some of its mixed carbonyl-halide complexes, cis-Os(CO)(2)X(4)(2-), fac-Os(CO)(3)X(3)(-) and Os(CO)(5)X(+) (X=F, Cl, Br and I), have been systematically investigated by ab initio RHF and density functional B3LYP methods with LanL2DZ and SDD basis sets. The calculated vibrational frequencies of complexes Os(CO)(6)(2+), cis-Os(CO)(2)X(4)(2-) and fac-Os(CO)(3)X(3)(-) are evaluated via comparison with the experimental values. In infrared frequency region, the C-O stretching vibrational frequencies calculated at B3LYP level with two basis sets are in good agreement with the observed values with deviations less than 5%. In the far-infrared region, the B3LYP/SDD method achieved the best results with deviations less than 9% for Os-X stretching and less than 8% for Os-C stretching vibrational frequencies. The vibrational frequencies for Os(CO)(5)X(+) that have not been experimentally reported were predicted.