The all-Cartesian reaction plane Hamiltonian: formulation and application to the H-atom transfer in tropolone

In this work we present an all-Cartesian reaction surface approach, where the large amplitude coordinates span the so-called reaction plane, that is, the unique plane defined by the two minima and the saddle-point structure of an isomerization reaction. Orthogonal modes are treated within harmonic approximation which gives the total Hamiltonian an almost separable form that is suitable for multidimensional quantum dynamics calculations. The reaction plane Hamiltonian is constructed for the H-atom transfer in tropolone as an example for a system with an intramolecular O...H-O hydrogen bond. We find ground-state tunneling splittings of 3.5 and 0.16 cm(-1) for the normal and deuterated species, respectively. We calculated infrared-absorption spectra for a four-dimensional model focusing on the low-frequency region. Here, we identify a reaction mode which is closely connected to the tautomerization that is reflected in the increase of tunneling splitting to 18 cm(-1) upon excitation.     

Four-mode quantum calculations of resonance states in complex-forming bimolecular reactions: C- + CH3Br

The vibrational resonance states of the complexes formed in the nucleophilic bimolecular substitution (S(N)2) reaction Cl(-)+CH(3)Br-->ClCH(3)+Br(-) were calculated by means of the filter diagonalization method employing a coupled-cluster potential-energy surface and a Hamiltonian that incorporates an optical potential and is formulated in Radau coordinates for the carbon-halogen stretching modes. The four-dimensional model also includes the totally symmetric vibrations of the methyl group (C-H stretch and umbrella bend). The vast majority of bound states and many resonance states up to the first overtone of the symmetric stretching vibration in the exit channel complex have been calculated, analyzed, and assigned four quantum numbers. The resonances are classified into entrance channel, exit channel, and delocalized states. The resonance widths fluctuate over six orders of magnitude. In addition to a majority of Feshbach-type resonances there are also exceedingly long-lived shape resonances, which are associated with the entrance channel and can only decay by tunneling. The state-selective decay of the resonances was studied in detail. The linewidths of the resonances, and thus the coupling to the energetic continuum, increase with excitation in any mode. Due to the strong mixing of the many progressions in the intermolecular stretching modes of the intermediate complexes, this increase as a function of the corresponding quantum numbers is not monotonic, but exhibits pronounced fluctuations.     

Vibrational frequencies and structural determination of 1,6-dicarba-closo-hexaborane(6)

The normal mode frequencies and corresponding vibrational assignments of 1,6-dicarba-closo-hexaborane(6) are examined theoretically using the GAUSSIAN98 set of quantum chemistry codes. All normal modes were successfully assigned to one of six types of motion predicted by a group theoretical analysis (B-B stretch, B-C stretch, B-H stretch, C-H stretch, B-H bend, and C-H bend) utilizing the D(4h) symmetry of the molecule. The vibrational modes of the naturally isotopically substituted (1-(10)B, 2-(10)B 3-(10)B, and 4-(10)B) forms of 1,6-dicarba-closo-hexaborane(6) were also calculated and compared against experimental data. A complex pattern of frequency shifts and splittings is revealed.     

Six-dimensional tunneling dynamics of internal rotation in hydrogen peroxide molecule and its isotopomers

The six-dimensional torsion-vibration Hamiltonian of the H₂O₂ molecule and its H/D- and ¹⁸O/¹⁶O-isotopomers is derived. The Hamiltonian includes the kinetic energy operator, which depends on the tunneling coordinate, and the potential energy surface represented as a quartic polynomial with respect to the small-amplitude transverse coordinates. Parameters of the Hamiltonian were obtained from DFT calculations of the equilibrium geometries, eigenvectors, and eigenfrequencies of normal vibrations at the stationary points corresponding to the ground state and both the cis- and trans-transition states, carried out with the B3LYP density functional and 6-311+G(2d,p) basis set. The quantum dynamics problem is solved using the perturbative instanton approach generalized for the excited states situated above the barrier top. Vibration-tunneling spectra are calculated for the ground state and low-lying excited states with energies below 2000 cm^–1. Strong kinematic and squeezed potential couplings between the large-amplitude torsional motion and bending modes are shown to be responsible for the vibration-assisted tunneling and for the dependence of tunneling splittings on the quantum numbers of small-amplitude transverse vibrations. Mode-specific isotope effects are predicted.     

Torsion-vibration coupling in methanol: diabatic behavior in the CH overtone region

Through a fit to methanol CH overtone data, a previously developed 4-dimensional torsion-vibration Hamiltonian is extended to high CH stretch excitation as well as to high torsional excitation. The strength of the torsion-vibration coupling is found to increase with CH stretch excitation. Systematic patterns of near degeneracy (3-, 4-, and 6-fold) are found in different regions of quantum number space. In the region of the CH fundamentals, an approximate a diabatic separation of the torsion (slow degree of freedom) from the CH stretches (fast degrees of freedom) accounts for the pattern of the energy levels and for the signs of the torsional tunneling splittings. For the higher CH overtones (v(CH) > or = 4), a diabatic representation accounts for the torsional structure obtained from the fully coupled calculation and for certain trends found in the pattern of the energy levels.     

Slit discharge IR spectroscopy of a jet-cooled cyclopropyl radical: structure and intramolecular tunneling dynamics

High-resolution infrared spectra of a jet-cooled cyclopropyl radical are reported for the first time, specifically sampling the in-phase antisymmetric CH2 stretch (nu7) vibration. In addition to yielding the first precise gas-phase structural information, the spectra reveal quantum level doubling into lower (+) and upper (-) states due to tunneling of the lone alpha-CH with respect to the CCC plane. The bands clearly reveal intensity alternation due to H atom nuclear spin statistics (6:10 and 10:6 for even:odd Ka+Kc in lower (+) and upper (-) tunneling levels, respectively) consistent with C2v symmetry of the cyclopropyl-tunneling transition state. The two ground-state-tunneling levels fit extremely well to a rigid asymmetric rotor Hamiltonian, but there is clear evidence for both local and global state mixing in the vibrationally excited nu7 tunneling levels. In particular, the upper (-) tunneling component of the nu7 state is split by anharmonic coupling with a nearly isoenergetic dark state, which thereby acquires oscillator strength via intensity sharing with this bright state. From thermal Boltzmann analysis of fractional populations, tunneling splittings for a cyclopropyl radical are estimated to be 3.2 +/- 0.3 cm(-1) and 4.9 +/- 0.3 cm(-1) in the ground and nu7-excited states, respectively. This analysis indicates ground-state stereoracemization of the alpha-CH radical center to be a very fast process [k approximately 2.0(4) x 10(11) s(-1)], with the increase in the tunneling rate upon CH2 in-phase asymmetric stretch excitation consistent with ab initio predictions of equilibrium vs transition-state zero-point energies. Modeling of the ground-state-tunneling splittings with high level ab initio 1D potentials indicates an improved V0 = 1115 +/- 35 cm(-1) barrier height for alpha-CH inversion through the cyclopropyl CCC plane.     

Vibrational predissociation in the HCl dimer

We present results of a combined theoretical and experimental study on the vibrational predissociation of the HCl dimer. On the theoretical side, photodissociation linewidths and product-state distributions for monomer stretch excited states with total angular momentum J=0 were computed, using the Fermi golden rule approximation. The resonances investigated include excitation of the hydrogen bond donor and acceptor stretches, as well as combinations of one of these modes with the intermolecular stretch and geared bend modes, for both even and odd permutation symmetry. Line strengths for the transitions from the J=1, K=0 ground state to excited states with J=0 were computed using quasibound states. On the experimental side, the photofragment angular distribution method was employed to obtain complete final-state distributions for the monomer stretch excited states. Three different transitions were probed, all starting from the lower tunneling component of the ground state: the (R)Q(0)(1) transition for excitation of the acceptor stretch and the (Q)R(0)(0) transition and unresolved (R)Q(0) branch for the donor stretch excitation. We find that, in contrast to the HF dimer, the excited-state alignment of the HCl dimer, resulting from excitation using a polarized laser beam, is completely lost on the time scale of the dissociation. The agreement between theory and experiment for the product-state distributions and line strengths is reasonable. The computed lifetimes are 1-2 orders of magnitude too small, which is attributed to a deficiency in the potential energy surface.     

Vibrational analysis of cyclo(d-Ala-l-Ala) in two crystalline forms. Effect of structure on peptide group and CH modes

Cyclo(d-Ala-l-Ala) has been found by X-ray diffraction to crystallize in two forms with different hydrogen bond patterns and strengths and different conformations of the C^αH^αC^βH₃ group. We have done a comprehensive analysis of the Raman and i.r. spectra of both forms and their N-deuterated derivatives. Spectra were taken of oriented single crystals, polycrystalline powders, and aqueous solutions, allowing a virtually complete vibrational assignment. Systematic, distinct differences were observed in the modes of the CONH group and in the CH stretching and bending modes. These spectral differences have been correlated with the different molecular and crystal structures. In particular, the width and sub-band structure of the NH stretch mode and the splittings of the CO stretch are shown to be related to the hydrogen bond pattern, and the NH bend modes are found to be relatively as sensitive to the hydrogen bond strength as is the NH stretch. The differences in the CH^α bend modes show that both conformations exist in solution. Ab initio molecular orbital calculations have been done to understand the frequency shifts of the NH and CH^α stretch modes in the two forms. Normal mode calculations were also done.     

Simulation of inversion motion and N-H stretching overtone spectra of aniline

A curvilinear internal coordinate Hamiltonian is used to simulate the N-H stretching overtone spectra and the associated inversion splittings in aniline. A simple local mode type model is applied to the N-H stretching and H-N-H bending modes. Geometric algebra is employed to derive the kinetic energy operator for the large amplitude inversion motion. Electronic structure calculations at the Moller-Plesset second order perturbation theory and correlation consistent aug-cc-pVTZ basis set level are used to obtain model parameters, some of which have been optimized with the least-squares method using experimental vibrational term values as data. The observed N-H stretching overtone vibrational levels and the inversional tunneling splittings are well reproduced with our approach.     

Ground and asymmetric CO-stretch excited state tunneling splittings in the formic acid dimer

There has been some controversy concerning the assignment of measured tunneling splittings for the formic acid dimer in the vibrational ground state and the asymmetric CO-stretching excited state. The discussion is intimately related to the question whether the fundamental excitation of the CO-vibration promotes or hinders tunneling. Here we will address this issue on the basis of a five-dimensional reaction space Hamiltonian which includes three large amplitude coordinates as well as two harmonic modes whose linear superposition reproduces the asymmetric CO-vibrational mode. Within density functional theory using the B3LYP functional together with a 6-311++G(3df,3pd) basis set we obtain a ground state tunneling splitting which is about 2.4 larger than the one for the CO-stretching excited state.     

Vibrational frequencies and structure of B4Cl4: an ab intio quantum chemical study

The normal mode frequencies and corresponding vibrational assignments of B4Cl4 are examined theoretically using the Gaussian 98 set of quantum chemistry codes. All normal modes were successfully assigned to one of three types of motion predicted by a group theoretical analysis (B-B stretch, B-Cl stretch, B-Cl bend) utilizing the Td symmetry of the molecule. The vibrational modes of the naturally isotopically substituted (1-(10)B, 2-(10)B, 3-(10)B and 4-(10)B) forms of B4Cl4 were also calculated and compared against experimental data. A complex pattern of frequency shifts and splittings is revealed.     

Iterative diagonalization in the state-averaged multi-configurational time-dependent Hartree approach: excited state tunneling splittings in malonaldehyde

An iterative block Lanczos-type diagonalization scheme utilizing the state-averaged multi-configurational time-dependent Hartree (MCTDH) approach is introduced. Combining propagation in real and imaginary time and using a set of initial seed wavefunctions corresponding to excitations via the different components of the dipole moment vector, the scheme can favorably be used to selectively compute vibrational states which show high intensities in vibrational absorption spectra. Tunneling splitted vibrational states in double well systems can be described particularly efficient employing an increased set of seed wavefunctions which includes symmetric and anti-symmetric wavefunctions simultaneously. The new approach is used to study the tunneling splittings of the vibrationally excited states of malonaldehyde. Full-dimensional multi-layer MCTDH calculations are performed and results for the tunneling splittings of several excited vibrational states can be obtained. The calculated tunneling splittings agree reasonably well with available experimental data. Order of magnitude differences between tunneling splittings of different vibrationally excited states are found and interpreted.     

Stereomutation tunneling switching dynamics and parity violation in chlorineperoxide Cl-O-O-Cl

In a search for efficient spectroscopic avenues toward experiments on molecular parity violation, we investigate the stereomutation tunneling processes in the axially chiral chlorine isotopomers of Cl2O2 by the quasi-adiabatic channel reaction path Hamiltonian (RPH) approach and the corresponding parity violating potentials by means of quantum chemical calculations including our recently developed Multiconfiguration linear response (MC-LR) approach to electroweak quantum chemistry. The calculated ground-state torsional tunneling splittings for all isotopomers of Cl2O2 are much smaller than the parity violating energy differences Delta(pv)E between the enantiomers of these molecules and therefore parity violation is predicted to dominate the quantum dynamics of stereomutation at low energies. We also compare these with torsional ground-state tunneling splittings and parity violating energy differences of the whole series of axially chiral HXYH(+) isotopomers (with X, Y= Cl(+), O, S, Se, Te). A comparison with our previous results for the homologous molecule Cl2S2 shows that for Cl2O2 a spectroscopic high-resolution analysis should be easier and the energy region of large tunneling splittings should be more easily accessible by IR excitation. We thus propose a scheme using "tunneling switching" with vibrational excitation in order to carry out the measurement of time-dependent parity violation in superposition states of initially well-defined parity. We discuss the advantages and drawbacks of such an experiment that can be carried out entirely in the IR spectral range (for Cl2O2 or related molecules).     

Exchange interactions between dimers of chromium(III). A cluster approach

Exchange interactions in dimers, tetramers and octamers of chromium(III) are treated with an effective Hamiltonian of the Heisenberg-Dirac-vanVleck (HDvV) type. Energies and wave functions of the cluster states are computed. The results of interdimer interactions are: (i) energy splittings and (ii) a contamination of the cluster ground state with excited configurations. The results are used for a qualitative rationalisation of the observed low-temperature properties of Cs₃Cr₂Cl₉.     

Jet cooled spectroscopy of H2DO+: Barrier heights and isotope-dependent tunneling dynamics from H3O+ to D3O+

The first high resolution spectroscopic data for jet cooled H2DO+ are reported, specifically via infrared laser direct absorption in the OH stretching region with a slit supersonic jet discharge source. Transitions sampling upper (0-) and lower (0+) tunneling states for both symmetric (nu1+ <-- 0+, nu1- <-- 0-, and nu1- <-- 0+) and antisymmetric (nu3+ <-- 0+ and nu3- <-- 0-) OH stretching bands are observed, where +/- refers to wave function reflection symmetry with respect to the planar umbrella mode transition state. The spectra can be well fitted to a Watson asymmetric top Hamiltonian, revealing band origins and rotational constants for benchmark comparison with high-level ab initio theory. Of particular importance are detection and assignment of the relatively weak band (nu1- <-- 0+) that crosses the inversion tunneling gap, which is optically forbidden in H3O+ or D3O+, but weakly allowed in H2DO+ by lowering of the tunneling transition state symmetry from D(3h) to C(2v). In conjunction with other H2DO+ bands, this permits determination of the tunneling splittings to within spectroscopic precision for each of the ground [40.518(10) cm(-1)], nu1 = 1 [32.666(6) cm(-1)], and nu3 = 1 [25.399(11) cm(-1)] states. A one-dimensional zero-point energy corrected potential along the tunneling coordinate is constructed from high-level ab initio CCSD(T) calculations (AVnZ, n = 3,4,5) and extrapolated to the complete basis set limit to extract tunneling splittings via a vibrationally adiabatic treatment. Perturbative scaling of the potential to match splittings for all four isotopomers permits an experimental estimate of DeltaV0 = 652.9(6) cm(-1) for the tunneling barrier, in good agreement with full six-dimensional ab initio results of Rajamaki, Miani, and Halonen (RMH) [J. Chem. Phys. 118, 10929 (2003)]. (DeltaV0 (RMH) = 650 cm(-1)). The 30%-50% decrease in tunneling splitting observed upon nu1 and nu3 vibrational excitations arises from an increase in OH stretch frequencies at the planar transition state, highlighting the transition between sp2 and sp3 hybridizations of the OHD bonds as a function of inversion bending angle.     

变分过渡态理论对H＋H2及其同位素选态反应的研究

将选态速度常数的计算推广到任意指定反应物、过渡态的振动激发态.用此法计算了H+H_2(v)及其同位素经不同振动激发过渡态时的速度常数,发现弯曲振动模激发所得结果与实验值更符合,并且在给定能量下,过渡态的弯曲振动模激发比其对称伸缩模激发更有利于反应进行.     

A reaction surface Hamiltonian study of malonaldehyde

We report calculations using a reaction surface Hamiltonian for which the vibrations of a molecule are represented by 3N-8 normal coordinates, Q, and two large amplitude motions, s(1) and s(2). The exact form of the kinetic energy operator is derived in these coordinates. The potential surface is first represented as a quadratic in Q, the coefficients of which depend upon the values of s(1),s(2) and then extended to include up to Q(6) diagonal anharmonic terms. The vibrational energy levels are evaluated by solving the variational secular equations, using a basis of products of Hermite polynomials and appropriate functions of s(1),s(2). Our selected example is malonaldehyde (N=9) and we choose as surface parameters two OH distances of the migrating H in the internal hydrogen transfer. The reaction surface Hamiltonian is ideally suited to the study of the kind of tunneling dynamics present in malonaldehyde. Our results are in good agreement with previous calculations of the zero point tunneling splitting and in general agreement with observed data. Interpretation of our two-dimensional reaction surface states suggests that the OH stretching fundamental is incorrectly assigned in the infrared spectrum. This mode appears at a much lower frequency in our calculations due to substantial transition state character.     

Exciton dissociation at donor-acceptor polymer heterojunctions: quantum nonadiabatic dynamics and effective-mode analysis

The quantum-dynamical mechanism of photoinduced subpicosecond exciton dissociation and the concomitant formation of a charge-separated state at a semiconducting polymer heterojunction is elucidated. The analysis is based upon a two-state vibronic coupling Hamiltonian including an explicit 24-mode representation of a phonon bath comprising high-frequency (C==C stretch) and low-frequency (torsional) modes. The initial relaxation behavior is characterized by coherent oscillations, along with the decay through an extended nonadiabatic coupling region. This region is located in the vicinity of a conical intersection hypersurface. A central ingredient of the analysis is a novel effective mode representation, which highlights the role of the low-frequency modes in the nonadiabatic dynamics. Quantum dynamical simulations were carried out using the multiconfiguration time-dependent Hartree method.     

Vibrational frequencies and structural determination of diethynyldimethylsilane

The normal mode frequencies and corresponding vibrational assignments of diethynyldimethylsilane are examined theoretically using the Gaussian 98 set of quantum chemistry codes. Each of the vibrational modes was assigned to one of nine types of motion predicted by a group theoretical analysis (Si-C stretch, C[triple bond]C stretch, C-H stretch, C[triple bond]C-H bend, Si-C[triple bond]C bend, C-Si-C bend, H-C-H bend, CH3 wag, and CH3 twist) utilizing the C3v symmetry of the molecule. A set of uniform scaling factors was derived for each type of motion. Predicted infrared and Raman intensities are reported.     

Probing intermolecular couplings in liquid water with two-dimensional infrared photon echo spectroscopy

Two-dimensional infrared photon echo and pump probe studies of the OH stretch vibration provide a sensitive probe of the correlations and couplings in the hydrogen bond network of liquid water. The nonlinear response is simulated using numerical integration of the Schrodinger equation with a Hamiltonian constructed to explicitly treat intermolecular coupling and nonadiabatic effects in the highly disordered singly and doubly excited vibrational exciton manifolds. The simulated two-dimensional spectra are in close agreement with our recent experimental results. The high sensitivity of the OH stretch vibration to the bath dynamics is found to arise from intramolecular mixing between states in the two-dimensional anharmonic OH stretch potential. Surprisingly small intermolecular couplings reproduce the experimentally observed intermolecular energy transfer times.