Highly accurate HF dimer ab initio potential energy surface.

A highly accurate, (HF)2 potential energy surface (PES) is constructed based on ab initio calculations performed at the coupled-cluster single double triple level of theory with an aug-cc-pVQZ-F12 basis set at about 152 000 points. A higher correlation correction is computed at coupled-cluster single double triple quadruple level for 2000 points and is considered alongside other more minor corrections due to relativity, core-valence correlation, and Born-Oppenheimer failure. The analytical surface constructed uses 500 constants to reproduce the ab initio points with a standard deviation of 0.3 cm-1. Vibration-rotation-inversion energy levels of the HF dimer are computed for this PES by variational solution of the nuclear-motion Schrödinger equation using the program WAVR4. Calculations over an extended range of rotationally excited states show very good agreement with the experimental data. In particular, the known empirical rotational constants B for the ground vibrational states are predicted to better than about 2 MHz. B constants for excited vibrational states are reproduced several times more accurately than by previous calculations. This level of accuracy is shown to extend to higher excited inter-molecular vibrational states v and higher excited rotational quantum numbers (J, Ka).

Symmetry-Adapted Ro-vibrational Basis Functions for Variational Nuclear Motion Calculations: TROVE Approach.

We present a general, numerically motivated approach to the construction of symmetry-adapted basis functions for solving ro-vibrational Schrödinger equations. The approach is based on the property of the Hamiltonian operator to commute with the complete set of symmetry operators and, hence, to reflect the symmetry of the system. The symmetry-adapted ro-vibrational basis set is constructed numerically by solving a set of reduced vibrational eigenvalue problems. In order to assign the irreducible representations associated with these eigenfunctions, their symmetry properties are probed on a grid of molecular geometries with the corresponding symmetry operations. The transformation matrices are reconstructed by solving overdetermined systems of linear equations related to the transformation properties of the corresponding wave functions on the grid. Our method is implemented in the variational approach TROVE and has been successfully applied to many problems covering the most important molecular symmetry groups. Several examples are used to illustrate the procedure, which can be easily applied to different types of coordinates, basis sets, and molecular systems.

The Renner effect in the X 2A" and à 2A' electronic states of HSO/HOS.

We report a theoretical investigation of the X (2)A" and à (2)A' electronic states of HSO/HOS. Three-dimensional potential energy surfaces for the X (2)A" and à (2)A' electronic states of HSO/HOS have been calculated ab initio by the core-valence MR-SDCI+Q/[aug-cc-pCVQZ(S,O),aug-cc-pVQZ(H)] method, and near-global potential energy surfaces have been constructed. These surfaces have been used, in conjunction with our computer program DR, for calculating HSO/HOS rovibronic energies in the electronic states X (2)A" and à (2)A'. Both electronic states have nonlinear equilibrium geometries and they correlate with (2)Π states at the H-S-O and H-O-S linear configurations so that they exhibit the double Renner effect. The present DR calculation of the rovibronic energies for the X (2)A" and à (2)A' electronic states of HSO/HOS is complicated by the Renner-interaction breakdown of the Born-Oppenheimer approximation and by HSO/HOS isomerization. Calculated energies are reported together with analyses of the rovibronic wave functions for selected states. These analyses explore the interplay between the effects of, on one hand, Renner interaction and, on the other hand, isomerization tunneling in the rovibronic dynamics of HSO/HOS.

Variational calculation of highly excited rovibrational energy levels of H2O2.

Results are presented for highly accurate ab initio variational calculation of the rotation-vibration energy levels of H2O2 in its electronic ground state. These results use a recently computed potential energy surface and the variational nuclear-motion programs WARV4, which uses an exact kinetic energy operator, and TROVE, which uses a numerical expansion for the kinetic energy. The TROVE calculations are performed for levels with high values of rotational excitation, J up to 35. The purely ab initio calculations of the rovibrational energy levels reproduce the observed levels with a standard deviation of about 1 cm(-1), similar to that of the J = 0 calculation, because the discrepancy between theory and experiment for rotational energies within a given vibrational state is substantially determined by the error in the vibrational band origin. Minor adjustments are made to the ab initio equilibrium geometry and to the height of the torsional barrier. Using these and correcting the band origins using the error in J = 0 states lowers the standard deviation of the observed-calculated energies to only 0.002 cm(-1) for levels up to J = 10 and 0.02 cm(-1) for all experimentally known energy levels, which extend up to J = 35.

Calculation of rotation-vibration energy levels of the water molecule with near-experimental accuracy based on an ab initio potential energy surface.

A recently computed, high-accuracy ab initio Born-Oppenheimer (BO) potential energy surface (PES) for the water molecule is combined with relativistic, adiabatic, quantum electrodynamics, and, crucially, nonadiabatic corrections. Calculations of ro-vibrational levels are presented for several water isotopologues and shown to have unprecedented accuracy. A purely ab initio calculation reproduces some 200 known band origins associated with seven isotopologues of water with a standard deviation (σ) of about 0.35 cm(-1). Introducing three semiempirical scaling parameters, two affecting the BO PES and one controlling nonadiabatic effects, reduces σ below 0.1 cm(-1). Introducing one further rotational nonadiabatic parameter gives σ better than 0.1 cm(-1) for all observed ro-vibrational energy levels up to J = 25. We conjecture that the energy levels of closed-shell molecules with roughly the same number of electrons as water, such as NH3, CH4, and H3O(+), could be calculated to this accuracy using an analogous procedure. This means that near-ab initio calculations are capable of predicting transition frequencies with an accuracy only about a factor of 5 worse than high resolution experiments.

Spectroscopy of H3+ based on a new high-accuracy global potential energy surface.

The molecular ion H(3)(+) is the simplest polyatomic and poly-electronic molecular system, and its spectrum constitutes an important benchmark for which precise answers can be obtained ab initio from the equations of quantum mechanics. Significant progress in the computation of the ro-vibrational spectrum of H(3)(+) is discussed. A new, global potential energy surface (PES) based on ab initio points computed with an average accuracy of 0.01 cm(-1) relative to the non-relativistic limit has recently been constructed. An analytical representation of these points is provided, exhibiting a standard deviation of 0.097 cm(-1). Problems with earlier fits are discussed. The new PES is used for the computation of transition frequencies. Recently measured lines at visible wavelengths combined with previously determined infrared ro-vibrational data show that an accuracy of the order of 0.1 cm(-1) is achieved by these computations. In order to achieve this degree of accuracy, relativistic, adiabatic and non-adiabatic effects must be properly accounted for. The accuracy of these calculations facilitates the reassignment of some measured lines, further reducing the standard deviation between experiment and theory.

Theoretical rotation-torsion energies of HSOH.

The rotation-torsion energies in the electronic ground state of HSOH are obtained in variational calculations based on a newly computed ab initio CCSD(T)/aug-cc-pV(Q+d)Z potential energy surface. Using the concept of the reaction path Hamiltonian, as implemented in the program TROVE (theoretical rovibrational energies), the rotation-vibration Hamiltonian is expanded around geometries on the torsional minimum energy path of HSOH. The calculated values of the torsional splittings are in excellent agreement with experiment; the root-mean-square (rms) deviation is 0.0002 cm(-1) for all experimentally derived splittings (with J < or = 40 and K(a) < or = 4). The model provides reliable predictions for splittings not yet observed. The available experimentally derived torsion-rotation term values (with J < or = 40 and K(a) < or = 4) are reproduced ab initio with an rms deviation of 1.2 cm(-1) (0.7 cm(-1) for J < or = 20), which is improved to 1.0 cm(-1) (0.07 cm(-1) for J < or = 20) in an empirical adjustment of the bond lengths at the planar trans configuration. The theoretical torsional splittings of HSOH are analyzed in terms of an existing semiempirical model for the rotation-torsion motion. The analysis explains the irregular variation of the torsional splittings with K(a) that has been observed experimentally.

Vibrational energies of PH3 calculated variationally at the complete basis set limit.

The potential energy surface for the electronic ground state of PH(3) was calculated at the CCSD(T) level using aug-cc-pV(Q+d)Z and aug-cc-pVQZ basis sets for P and H, respectively, with scalar relativistic corrections included. A parametrized function was fitted through these ab initio points, and one parameter of this function was empirically adjusted. This analytical PES was employed in variational calculations of vibrational energies with the newly developed program TROVE. The convergence of the calculated vibrational energies with increasing vibrational basis set size was improved by means of an extrapolation scheme analogous to the complete basis set limit schemes used in ab initio electronic structure calculations. The resulting theoretical energy values are in excellent agreement with the available experimentally derived values.

Water line lists close to experimental accuracy using a spectroscopically determined potential energy surface for H2(16)O, H2(17)O, and H2(18)O.

Line lists of vibration-rotation transitions for the H(2) (16)O, H(2) (17)O, and H(2) (18)O isotopologues of the water molecule are calculated, which cover the frequency region of 0-20 000 cm(-1) and with rotational states up to J=20 (J=30 for H(2) (16)O). These variational calculations are based on a new semitheoretical potential energy surface obtained by morphing a high accuracy ab initio potential using experimental energy levels. This potential reproduces the energy levels with J=0, 2, and 5 used in the fit with a standard deviation of 0.025 cm(-1). Linestrengths are obtained using an ab initio dipole moment surface. That these line lists make an excellent starting point for spectroscopic modeling and analysis of rotation-vibration spectra is demonstrated by comparison with recent measurements of Lisak and Hodges [J. Mol. Spectrosc. (unpublished)]: assignments are given for the seven unassigned transitions and the intensity of the strong lines are reproduced to with 3%. It is suggested that the present procedure may be a better route to reliable line intensities than laboratory measurements.