Intramolecular proton transfer in malonaldehyde: accurate multilayer multi-configurational time-dependent Hartree calculations

Full-dimensional (multilayer) multi-configurational time-dependent Hartree calculations studying the intramolecular proton transfer in malonaldehyde based on a recent potential energy surface (PES) [Wang et al., J. Chem. Phys. 128, 224314 (2008)] are presented. The most accurate calculations yield a ground state tunneling splitting of 23.8 cm(-1) and a zero point energy of 14,678 cm(-1). Extensive convergence tests indicate an error margin of the quantum dynamics calculations for the tunneling splitting of about 0.2 cm(-1). These results are to be compared with the experimental value of the tunneling splitting of 21.58 cm(-1) and results of Monte Carlo calculations of Wang et al. on the same PES which yielded a zero point energy of 14,677.9 cm(-1) with statistical errors of 2-3 cm(-1) and a tunneling splitting of 21.6 cm(-1). The present data includes contributions resulting from the vibrational angular momenta to the tunneling splitting and the zero point energy of 0.2 cm(-1) and 2.4 cm(-1), respectively, which have been computed using a perturbative approach.     

Automatic generation of potential energy and property surfaces of polyatomic molecules in normal coordinates

A procedure for the automatic construction of Born-Oppenheimer (BO) potential energy and molecular property surfaces in rectilinear normal coordinates is presented and its suitability and accuracy when combined with vibrational structure calculations are assessed. The procedure relies on a hierarchical n-mode representation of the BO potential energy or molecular property surface, where the n-mode term of the sequence of potentials/molecular properties includes only the couplings between n or less vibrational degrees of freedom. Each n-mode cut of the energy/molecular property surface is first evaluated in a grid of points with ab initio electronic structure methods. The ab initio data are then spline interpolated and a subsequent polynomial fitting provides an analytical semiglobal representation for use in vibrational structure programs. The implementation of the procedure is outlined and the accuracy of the method is tested on water and difluoromethane. Strategies for improving the proposed algorithm are also discussed.     

S0 ring-puckering potential energy function for coumaran

With the aid of a reported inversion splitting value, the far-infrared spectrum resulting from the ring-puckering vibration of coumaran has been reassigned and the one-dimensional potential energy function has been determined. The barrier to planarity is 155 +/- 4 cm(-1) and the dihedral angle is 25 degrees . These results agree well with the millimeter wave spectra values of 152 cm(-1) and 23 degrees , which utilized different data and a different type of potential function for the calculations. The MP2/cc-pvtz ab initio values of 238 cm(-1) and 26.5 degrees agree more poorly. If the benzene ring is assumed to remain rigid, the calculated barrier drops to 204 cm(-1). The puckering potential functions for the ring-flapping and ring-twisting vibrationally excited states were also determined and the barriers were found to be 149 and 156 cm(-1), respectively.     

The ground state tunneling splitting and the zero point energy of malonaldehyde: a quantum Monte Carlo determination

Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7+/-0.3 cm-1 is obtained, and the vibrational ground state energy is found to be 15 122+/-4 cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21+/-0.09 cm-1 and the vibrational ground state energy to 14 385+/-2 cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.     

Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface

Quantum calculations of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcalmol, in excellent agreement with the reported ab initio value. Model one-dimensional and "exact" full-dimensional calculations of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calculated using the unbiased "fixed-node" diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm(-1) in Cartesian coordinates and 22.6 cm(-1) in normal coordinates, with an uncertainty of 2-3 cm(-1). This splitting is also calculated based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calculation gives a tunneling splitting of 21-22 cm(-1). The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm(-1). These calculated tunneling splittings agree with each other to within less than the standard uncertainties obtained with the DMC method used, which are between 2 and 3 cm(-1), and agree well with the experimental values of 21.6 and 2.9 cm(-1) for the H and D transfer, respectively.     

Trajectory-guided configuration interaction simulations of multidimensional quantum dynamics

We propose an approach to modelling multidimensional quantum systems which uses direct-dynamics trajectories to guide wavefunction propagation. First, trajectory simulations are used to generate a sample of dynamically relevant configurations on the potential energy surface (PES). Second, the sampled configurations are used to construct an n-mode representation of the PES using a greedy algorithm. Finally, the time-dependent Schr?dinger equation is solved using a configuration interaction expansion of the wavefunction, with individual basis functions derived directly from the 1-mode contributions to the n-mode PES. This approach is successfully demonstrated by application to a 20-dimensional benchmark problem describing tunnelling in the presence of coupled degrees of freedom.     

A new potential energy surface and predicted infrared spectra of He-CO2: dependence on the antisymmetric stretch of CO2

A new potential energy surface involving the antisymmetric Q(3) normal mode of CO(2) for the He-CO(2) van der Waals complex is constructed at the coupled-cluster singles and doubles with noniterative inclusion of connected triple [CCSD(T)] level with augmented correlation-consistent quadruple-zeta (aug-cc-pVQZ) basis set plus bond functions. Two vibrationally adiabatic potentials with CO(2) at both the ground and the first excited vibrational states are generated from the integration of the three-dimensional potential over the Q(3) coordinate. The potential has a T-shaped global minimum and two equivalent linear local minima. The bound rovibrational energy levels are obtained using the radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm. The observed band origin shift of the complex (0.0946 cm(-1)) is successfully reproduced by our calculation (0.1034 cm(-1)). The infrared spectra of the complex are also predicted. The fundamental band is in excellent agreement with the experiment. Most of the transitions corresponding to the observed hot band [M. J. Weida et al., J. Chem. Phys. 101, 8351 (1994)] are assigned reasonably.     

Ab initio potential energy and dipole moment surfaces of (H2O)2

A full-dimensional ab initio potential energy surface (PES) and dipole moment surface (DMS) are reported for the water dimer, (H2O)2. The CCSD(T)-PES is a very precise fit to 19,805 ab initio energies obtained with the coupled-cluster (CCSD(T)) method, using an aug-cc-pVTZ basis. The standard counterpoise correction was applied to approximately eliminate basis set superposition errors. The fit is based on an approach that incorporates the permutational symmetry of identical atoms [Huang, X.; Braams, B.; Bowman, J. M. J. Chem.Phys. 2005, 122, 044308]. The DMS is a fit to the dipole moment obtained with M?ller-Plesset (MP2) theory, using an aug-cc-pVTZ basis. The PES has an RMS fitting error of 31 cm(-1) for energies below 20,000 cm(-1), relative to the global minimum. This surface can describe various internal floppy motions, including various monomer inversions, and isomerization pathways. Ten characteristic stationary points have been located on the surface, four of which are transition structures and the rest are higher order saddle points. Their geometrical and vibrational properties are presented and compared with available previous theoretical work. The CCSD(T)-PES and MP2-DMS dissociate correctly (and symmetrically) to two H2O monomers, with D(e) = 1665.7 cm(-1) (19.93 kJ/mol). Accurate quantum calculations of the zero-point energy of the dimer (using diffusion Monte Carlo) and the monomers (using a vibrational configuration interaction approach) are reported, and these together with D(e) give a value of D0 of 1042 cm(-1) (12.44 kJ/mol). A best estimated value is 1130 cm(-1) (13.5 kJ/mol).     

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum

An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F(2) are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5 cm(-1) over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30 cm(-1) of the experimental value of 12 953+/-8 cm(-1). The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev. 41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.     

Potential energy surface and rovibrational calculations for the Mg+-H2 and Mg+-D2 complexes

A three-dimensional potential energy surface is developed to describe the structure and dynamical behavior of the Mg(+)-H(2) and Mg(+)-D(2) complexes. Ab initio points calculated using the RCCSD(T) method and aug-cc-pVQZ basis set (augmented by bond functions) are fitted using a reproducing kernel Hilbert space method [Ho and Rabitz, J. Chem. Phys. 104, 2584 (1996)] to generate an analytical representation of the potential energy surface. The calculations confirm that Mg(+)-H(2) and Mg(+)-D(2) essentially consist of a Mg(+) atomic cation attached, respectively, to a moderately perturbed H(2) or D(2) molecule in a T-shaped configuration with an intermolecular separation of 2.62 A? and a well depth of D(e) = 842 cm(-1). The barrier for internal rotation through the linear configuration is 689 cm(-1). Interaction with the Mg(+) ion is predicted to increase the H(2) molecule's bond-length by 0.008 A?. Variational rovibrational energy level calculations using the new potential energy surface predict a dissociation energy of 614 cm(-1) for Mg(+)-H(2) and 716 cm(-1) for Mg(+)-D(2). The H-H and D-D stretch band centers are predicted to occur at 4059.4 and 2929.2 cm(-1), respectively, overestimating measured values by 3.9 and 2.6 cm(-1). For Mg(+)-H(2) and Mg(+)-D(2), the experimental B and C rotational constants exceed the calculated values by ～1.3%, suggesting that the calculated potential energy surface slightly overestimates the intermolecular separation. An ab initio dipole moment function is used to simulate the infrared spectra of both complexes.     

A new ab initio interaction energy surface and high-resolution spectra of the H2-CO van der Waals complex

A new four-dimensional intermolecular potential-energy surface for the H(2)-CO complex is presented. The ab initio points have been computed on a five-dimensional grid including the dependence on the H-H separation (the C-O separation was fixed). The surface has then been obtained by averaging over the intramolecular vibration of H(2). The coupled-cluster supermolecular method with single, double, and noniterative triple excitations has been used to calculate the interaction energy. The correlation part of the interaction energy has been obtained from extrapolations based on calculations in a series of basis sets. An analytical fit of the ab initio potential-energy surface has the global minimum of -93.049 cm(-1) at the intermolecular separation of 7.92 bohr for the linear geometry with the C atom pointing toward the H(2) molecule. For the other linear geometry, with the O atom pointing toward H(2), the local minimum of -72.741 cm(-1) has been found for the intermolecular separation of 7.17 bohr. The potential has been used to calculate the rovibrational energy levels of the para-H(2)-CO complex. The results agree very well with those observed by McKellar [A. R. W. McKellar J. Chem. Phys. 108, 1811 (1998)]: the discrepancies are smaller than 0.1 cm(-1). The calculated dissociation energy is equal to 19.527 cm(-1) and significantly smaller than the value of 22 cm(-1) estimated from the experiment. Predictions of rovibrational energy levels for ortho-H(2)-CO have also been done and can serve as a guidance to assign recorded experimental spectra. The interaction second virial coefficient has been calculated and compared with the experimental data.     

Theoretical spectroscopy of the N2HAr+ complex

The six-dimensional potential energy surface of the electronic ground state of N2HAr+ is determined by ab initio computations at the CCSD(T) level of theory. The potential energy surface is used to derive a set of spectroscopic data for N2HAr+ and N2DAr+ using second order perturbation theory. Full six-dimensional (6-D) rotation-vibration computations are also carried out using an analytical representation of the surface for J=0 and 1, in order to deduce the rovibrational spectra of N2HAr+ and its deuterated isotopomer. Our variationally determined anharmonic wavenumbers differ by less than 15 cm(-1) from the most accurate experimental values. Strong anharmonic resonances are found between the rovibrational levels of both cations even at low energies.     

Communication: rigorous calculation of dissociation energies (D0) of the water trimer, (H2O)3 and (D2O)3

Using a recent, full-dimensional, ab initio potential energy surface [Y. Wang, X. Huang, B. C. Shepler, B. J. Braams, and J. M. Bowman, J. Chem. Phys. 134, 094509 (2011)] together with rigorous diffusion Monte Carlo calculations of the zero-point energy of the water trimer, we report dissociation energies, D(0), to form one monomer plus the water dimer and three monomers. The calculations make use of essentially exact zero-point energies for the water trimer, dimer, and monomer, and benchmark values of the electronic dissociation energies, D(e), of the water trimer [J. A. Anderson, K. Crager, L. Fedoroff, and G. S. Tschumper, J. Chem. Phys. 121, 11023 (2004)]. The D(0) results are 3855 and 2726 cm(-1) for the 3H(2)O and H(2)O + (H(2)O)(2) dissociation channels, respectively, and 4206 and 2947 cm(-1) for 3D(2)O and D(2)O + (D(2)O)(2) dissociation channels, respectively. The results have estimated uncertainties of 20 and 30 cm(-1) for the monomer plus dimer and three monomer of dissociation channels, respectively.     

MRDCI study of the low-lying electronic states of PbSi

Electronic states of the PbSi molecule up to 4 eV have been studied by carrying out ab initio based MRDCI calculations which include relativistic effective core potentials (RECPs) of both the atoms. The use of semicore RECPs of Pb produces better dissociation limits than the full-core one. However, the (3)P(0)-(3)P(1) splitting due to Pb is underestimated by about 4000 cm(-1). At least 25 bound electronic states of the Λ-S symmetry are predicted for PbSi. The computed zero-field-splitting in the ground state is about 544 cm(-1). A strong spin-orbit mixing changes the nature of the potential energy curves of many Ω states. The overall splitting among the spin components of A(3)Π is computed to be 4067 cm(-1). However, the largest spin-orbit splitting is reported for the (3)Δ state. A number of spin-allowed and spin-forbidden transitions are predicted. The partial radiative lifetime for the A(3)Π-X(3)Σ(-) transition is of the order of milliseconds. The computed bond energy in the ground state is 1.68 eV, considering the spin-orbit coupling. The vertical ionization energy for the ionization to the X(4)Σ(-) ground state of PbSi(+) is about 6.93 eV computed at the same level of calculations.     

Improved results for the excited states of nitric oxide, including the B/C avoided crossing

The potential energy surfaces of ten electronic states of nitric oxide (NO) have been reexamined computationally, with state energies calculated using ab initio multireference methods. Our wave function expansions of 10x10(6) configurations improve upon the results of de Vivie and Peyerimhoff [J. Chem. Phys. 89, 3028 (1988)], who obtained excellent results from expansions of 16 000 configurations in 1988. We present results for the adiabatic properties r(e), B(e), T(e), and omega(e), demonstrating standard errors of 0.012 A, 0.026 cm(-1), 620 cm(-1), and 41 cm(-1), respectively. Vertical excitation energies and oscillator strengths are also presented, as are potential energy surface curves, with special attention to the B/C avoided crossing. The technical issue of state-averaging effects is also discussed.     

Microwave spectrum of the HD2O+ ion: inversion-rotation transitions and inversion splitting

Inversion-rotation spectral lines of the dideuterated hydronium ion, HD2O+, have been observed by a source-modulation millimeter- to submillimeter-wave spectrometer. The ion was generated by a hollow-cathode discharge in a gas mixture of D2O and H2O in a free-space cell. Ten inversion-rotation lines were measured precisely for the lowest pair of inversion doublets in the frequency region from 380 to 730 GHz. The observed lines include the most astronomically important transitions, 0(00) (-)-1(10)+ for the para species at 380 538.031(32) MHz and 1(01) (-)-1(11)+ for the ortho species at 728 420.189(34) MHz, which could be used as a radio astronomical probe investigating interstellar chemistry of deuterium fractionation. An analysis of the measured lines has yielded the rotational constants in the ground doublet states and the inversion splitting. The inversion splitting in the ground state was determined to be 808 866(34) MHz, that is, 26.980 87(113) cm(-1), where the numbers in parentheses give uncertainties estimated from the Jacobian matrix of the assumed centrifugal distortion constants. The determined inversion splitting is off by -0.51 cm(-1) from the predicted value of 27.49 cm(-1) by Rajamaki et al. using high-order coupled cluster ab initio calculation [J. Chem. Phys. 118, 10929 (2003)], and by -0.0510 cm(-1) from the observed value of 27.0318(72) cm(-1) by Dong et al. using high-resolution jet-cooled infrared spectroscopy [J. Chem. Phys. 122, 224301 (2005)] beyond the quoted uncertainty.     

Accurate ab initio determination of the adiabatic potential energy function and the Born-Oppenheimer breakdown corrections for the electronic ground state of LiH isotopologues

High level ab initio potential energy functions have been constructed for LiH in order to predict vibrational levels up to dissociation. After careful tests of the parameters of the calculation, the final adiabatic potential energy function has been composed from: (a) an ab initio nonrelativistic potential obtained at the multireference configuration interaction with singles and doubles level including a size-extensivity correction and quintuple-sextuple ζ extrapolations of the basis, (b) a mass-velocity-Darwin relativistic correction, and (c) a diagonal Born-Oppenheimer (BO) correction. Finally, nonadiabatic effects have also been considered by including a nonadiabatic correction to the kinetic energy operator of the nuclei. This correction is calculated from nonadiabatic matrix elements between the ground and excited electronic states. The calculated vibrational levels have been compared with those obtained from the experimental data [J. A. Coxon and C. S. Dickinson, J. Chem. Phys. 134, 9378 (2004)]. It was found that the calculated BO potential results in vibrational levels which have root mean square (rms) deviations of about 6-7 cm(-1) for LiH and ～3 cm(-1) for LiD. With all the above mentioned corrections accounted for, the rms deviation falls down to ～1 cm(-1). These results represent a drastic improvement over previous theoretical predictions of vibrational levels for all isotopologues of LiH.     

Mg2H2: new insight on the Mg-Mg bonding and spectroscopic study

The six dimensional potential energy surface of the electronic ground state X?(1)Σ(g)(+) of Mg(2)H(2) has been generated by the coupled-cluster approach with single, double and perturbative triple excitations [CCSD(T)] combined with the aug-cc-pCVTZ basis set for Mg atoms and the aug-cc-pVTZ basis set for the H atoms. The analytical representation of this surface was used in variational calculations of the rovibrational energies of Mg(2)H(2), Mg(2)D(2), and HMg(2)D for J = 0 and 1. For Mg(2)H(2), the rotational constant B(0) is computed to be 0.1438 cm(-1), and the fundamental anharmonic wavenumbers are calculated to be ν(1) = 1527.3 cm(-1) (Σ(g)(+)), ν(2) = 275.3 cm(-1) (Σ(g)(+)), ν(3) = 1503.6 cm(-1) (Σ(u)(+)), ν(4) = 312.9 cm(-1) (Π(g)), and ν(5) = 256.5 cm(-1) (Π(u)). In addition, the electronic ground states of Mg(2)H, MgH(2), Mg(2), and MgH have been investigated in order to compute the bonding energies of Mg(2)H(2) and to explain the strength of the Mg-Mg bond in this tetra-atomic molecule. The nature of the low-lying excited states of Mg(2)H(2) is also studied.     

Theoretical study of the mechanism and rate constant of the B + CO2 reaction

The different stationary points on the potential energy surface relative to the title reaction have been reinvestigated at the B3LYP/aug-cc-pVDZ level with relative energies computed at the CCSD(T)/aug-cc-pVTZ level with B3LYP/aug-cc-pVDZ optimized geometries and by using the G3B3 composite method. Two entrance channels have been identified. The first one corresponds to boron addition at one of the oxygen atoms of the CO 2 molecule leading to trans-BOCO, which is found to be about 27 kcal/mol exothermic with a potential energy barrier of 16.4 kcal/mol (G3B3). The second channel, which has not been identified in previous theoretical works, corresponds to a direct insertion of the boron atom into a CO bond and leads to OBCO. The B + CO 2 --> OBCO step is found to be about 84 kcal/mol exothermic and needs to overcome a potential energy barrier of only 3.6 kcal/mol (G3B3). The rate constant at 300 K of the insertion step, calculated by using TST theory with G3B3 calculated activation energy value, is 5.4 10 (-14) cm (3) molecule (-1) s (-1), in very good agreement with the experimental data ((7.0 +/- 2.8) 10 (-14) cm (3) molecule (-1) s (-1), DiGiuseppe, T. G.; Davidovits, P. J. Chem. Phys. 1981, 74, 3287). The one corresponding to the addition process is found to be several orders of magnitude smaller because of a much higher potential energy barrier. The addition channel would not contribute to the title reaction even at high temperature. A modified Arrhenius equation has been fitted in the 300-1000 K temperature range, which might be useful for chemical models.     

Ab initio vibrational state calculations with a quartic force field: applications to H2CO, C2H4, CH3OH, CH3CCH, and C6H6

For polyatomic molecules, n-mode coupling representations of the quartic force field (nMR-QFF) are presented, which include terms up to n normal coordinate couplings in a fourth-order polynomial potential energy function. The computational scheme to evaluate third-and fourth-order derivatives by finite differentiations of the energy is fully described. The code to generate the nMR-QFF has been implemented into GAMESS program package and interfaced with the vibrational self-consistent field (VSCF) and correlation corrected VSCF (cc-VSCF) methods. As a demonstration, fundamental frequencies have been calculated by the cc-VSCF method based on 2MR-QFF for formaldehyde, ethylene, methanol, propyne, and benzene. The applications show that 2MR-QFF is a highly accurate potential energy function, with errors of 1.0-1.9% relative to the experimental value in fundamental frequencies. This approach will help quantitative evaluations of vibrational energies of a general molecule with a reasonable computational cost.