Diabatic intermolecular potentials and bound states of open-shell atom–molecule dimers: Application to the F([sup 2]P)–H[sub 2] complex

Rotationally adiabatic pair interactions of para- and ortho-hydrogen with the halogen molecules F2, Cl2, and Br2

The present work is concerned with the weak interactions between hydrogen and halogen molecules, i.e., the interactions of pairs H2-X2 with X = F, Cl, Br, which are dominated by dispersion and quadrupole-quadrupole forces. The global minimum of the four-dimensional (4D) coupled cluster with singles and doubles and perturbative triples (CCSD(T)) pair potentials is always a T shaped structure where H2 acts as the hat of the T, with well depths (De) of 1.3, 2.4, and 3.1 kJ/mol for F2, Cl2, and Br2, respectively. MP2/AVQZ results, in reasonable agreement with CCSD(T) results extrapolated to the basis set limit, are used for detailed scans of the potentials. Due to the large difference in the rotational constants of the monomers, in the adiabatic approximation, one can solve the rotational Schrödinger equation for H2 in the potential of the X2 molecule. This yields effective two-dimensional rotationally adiabatic potential energy surfaces where pH2 and oH2 are point-like particles. These potentials for the H2-X2 complexes have global and local minima for effective linear and T-shaped complexes, respectively, which are separated by 0.4-1.0 kJ/mol, where oH2 binds stronger than pH2 to X2, due to higher alignment to minima structures of the 4D-pair potential. Further, we provide fits of an analytical function to the rotationally adiabatic potentials.

Ab Initio Treatment of the Chemical Reaction Precursor Complex Br(2P)−HCN. 1. Adiabatic and Diabatic Potential Surfaces

The three adiabatic potential surfaces of the Br(2P)-HCN complex that correlate to the 2P ground state of the Br atom were calculated ab initio. With the aid of a geometry-dependent diabatic mixing angle, also calculated ab initio, these adiabatic potential surfaces were transformed into a set of four diabatic potential surfaces required to define the full 3 x 3 matrix of diabatic potentials. Each of these diabatic potential surfaces was expanded in terms of the appropriate spherical harmonics in the atom-linear molecule Jacobi angle theta. The dependence of the expansion coefficients on the distance R between Br and the HCN center of mass and on the CH bond length was fit to an analytic form. For HCN in its equilibrium geometry, the global minimum with De = 800.4 cm(-1) and Re = 6.908a0 corresponds to a linear Br-NCH geometry, with an electronic ground state of Sigma symmetry. A local minimum with De = 415.1 cm-1, Re = 8.730a0, and a twofold degenerate Pi ground state is found for the linear Br-HCN geometry. The binding energy, De, depends strongly on the CH bond length for the Br-HCN complex and much less strongly for the Br-NCH complex, with a longer CH bond giving stronger binding for both complexes. Spin-orbit coupling was included and diabatic states were constructed that correlate to the ground 2P3/2 and excited 2P1/2 spin-orbit states of the Br atom. For the ground spin-orbit state with electronic angular momentum j = (3/2) the minimum in the potential for projection quantum number omega = +/-(3/2) coincides with the local minimum for linear Br-HCN of the spin-free case. The minimum in the potential for projection quantum number omega = +/-(1/2) occurs for linear Br-NCH but is considerably less deep than the global minimum of the spin-free case. According to the lowest spin-orbit coupling included adiabatic potential the two linear isomers, Br-NCH and Br-HCN, are about equally stable. In the subsequent paper, we use these potentials in calculations of the rovibronic states of the Br-HCN complex.

Ab initio treatment of the chemical reaction precursor complex Cl(2P)-HF. 1. Three-dimensional diabatic potential energy surfaces

The three adiabatic potential surfaces of the Cl(2P)-HF complex that correlate with the 2P ground state of the Cl atom were calculated with the ab initio RCCSD(T) method (partially spin-restricted coupled cluster theory including single and double excitations and perturbative correction for the triples). With the aid of a geometry-dependent diabatic mixing angle, calculated by the complete active space self-consistent field (CASSCF) and multireference configuration-interaction (MRCI) methods, these adiabatic potential surfaces were converted to a set of four distinct diabatic potential surfaces required to define the full 3 x 3 matrix of diabatic potentials. Each of these diabatic potential surfaces was expanded in terms of the appropriate spherical harmonics in the angle theta between the HF bond axis r and the Cl-HF intermolecular axis R. The dependence of the expansion coefficients on the Cl-HF distance R and the HF bond length r(HF) was fit to an analytic form. The strongest binding occurs for the hydrogen-bonded linear Cl-HF geometry, with D(e) = 676.5 cm(-1) and R(e) = 6.217 a0 when r(HF) = r(e) = 1.7328 a0. This binding energy D(e) depends strongly on r(HF), with larger r(HF) causing stronger binding. An important contribution to the binding energy is provided by the interaction between the quadrupole moment of the Cl(2P) atom and the dipole of HF. In agreement with this electrostatic picture, the ground state of linear Cl-HF is a 2-fold degenerate electronic Pi state. For the linear Cl-FH geometry the states are in opposite order, i.e., the Sigma state is lower in energy than the Pi state. The following paper in this issue describes full three-dimensional computations of the bound states of the Cl-HF complex, based on the ab initio diabatic potentials of this paper.

Ab Initio Treatment of the Chemical Reaction Precursor Complex Br(2P)−HCN. 2. Bound-State Calculations and Infrared Spectra

Rovibronic energy levels and properties of the Br(2P)-HCN complex were obtained from three-dimensional calculations, with HCN kept linear and the CN bond frozen. All diabatic states that correlate to the 2P3/2 and 2P1/2 states of the Br atom were included and spin-orbit coupling was taken into account. The 3 x 3 matrix of diabatic potential surfaces was taken from the preceding paper (paper 1). In agreement with experiment, we found two linear isomers, Br-NCH and Br-HCN. The calculated binding energies are very similar: D0 = 352.4 cm(-1) and D0 = 349.1 cm(-1), respectively. We established, also in agreement with experiment, that the ground electronic state of Br-NCH has |Omega| = (1/2) and that Br-HCN has a ground state with |Omega| = (3/2), where the quantum number, Omega, is the projection of the total angular momentum, J, of the complex on the intermolecular axis R. This picture can be understood as being caused by the electrostatic interaction between the quadrupole of the Br(2P) atom and the dipole of HCN, combined with the very strong spin-orbit coupling in Br. We predicted the frequencies of the van der Waals modes of both isomers and found a direct Renner-Teller splitting of the bend mode in Br-HCN and a smaller, indirect, splitting in Br-NCH. The red shift of the CH stretch frequency in the complex, relative to free HCN, was calculated to be 1.98 cm(-1) for Br-NCH and 23.11 cm(-1) for Br-HCN, in good agreement with the values measured in helium nanodroplets. Finally, with the use of the same potential surfaces, we modeled the Cl(2P)-HCN complex and found that the experimentally observed linear Cl-NCH isomer is considerably more stable than the (not observed) Cl-HCN isomer. This was explained mainly as an effect of the substantially smaller spin-orbit coupling in Cl, relative to Br.

Electronic anisotropy between open shell atoms in first and second order perturbation theory

The interaction between two atoms in states with nonzero electronic orbital angular momenta is anisotropic and can be represented by a spherical tensor expansion. The authors derive expressions for the first order (electrostatic) and second order (dispersion and induction) anisotropic interaction coefficients in terms of the multipole moments and dynamic polarizabilities of the atoms and show that a complete description of the second order interaction requires odd rank or "out-of-phase" polarizabilities. The authors relate the tensorial expansion coefficients to the adiabatic Born-Oppenheimer potentials of the molecule and show that there are linear, and in some cases nonlinear, constraints on the van der Waals coefficients of these potentials.

Spin-orbit relaxation of Cl(P1∕22) and F(P1∕22) in a gas of H2

The authors present quantum scattering calculations of rate coefficients for the spin-orbit relaxation of F(2P1/2) atoms in a gas of H2 molecules and Cl(2P1/2) atoms in a gas of H2 and D2 molecules. Their calculation of the thermally averaged rate coefficient for the electronic relaxation of chlorine in H2 agrees very well with an experimental measurement at room temperature. It is found that the spin-orbit relaxation of chlorine atoms in collisions with hydrogen molecules in the rotationally excited state j=2 is dominated by the near-resonant electronic-to-rotational energy transfer accompanied by rotational excitation of the molecules. The rate of the spin-orbit relaxation in collisions with D2 molecules increases to a great extent with the rotational excitation of the molecules. They have found that the H2/D2 isotope effect in the relaxation of Cl(2P1/2) is very sensitive to temperature due to the significant role of molecular rotations in the nonadiabatic transitions. Their calculation yields a rate ratio of 10 for the electronic relaxation in H2 and D2 at room temperature, in qualitative agreement with the experimental measurement of the isotope ratio of about 5. The isotope effect becomes less significant at higher temperatures.

Interactions of 2P Atoms with Closed-Shell Diatomic Molecules: Alternative Diabatic Representations for the Electronic Anisotropy

The matrices of electrostatic and spin-orbit Hamiltonians for the system of a 2P atom interacting with a closed shell diatomic molecule in uncoupled, coupled, and complex-valued representations for electronic diabatic basis functions are rederived, and the unitary transformations connecting them are given explicitly. The links to previous derivations are established and existing inconsistencies are identified and eliminated. It is proven that the block-diagonalization of a 6 x 6 matrix of the electronic Hamiltonian is a result of using the basis functions with well-defined properties with respect to time reversal. Consideration of time-reversal symmetry also enforces phase consistency relevant for applications to multisurface reactive scattering and photodetachment spectroscopy calculations, as well as for perspective studies of inelastic effects in cold and ultracold environments. These and further developments are briefly sketched.

Ab Initio Treatment of the Chemical Reaction Precursor Complex Cl(2P)−HF. 2. Bound States and Infrared Spectrum

Bound energy levels and properties of the Cl(2P)-HF complex were obtained from full three-dimensional (3D) calculations, with the use of the ab initio computed diabatic potential surfaces from the preceding paper and the inclusion of spin-orbit coupling. For a better understanding of the dynamics of this complex we also computed a 2D model in which the HF bond length r was frozen at the vibrationally averaged values r0 and r1 and a 2 + 1D model in which the 3D potentials were averaged over the v(HF) = 0 and v(HF) = 1 vibrational wave functions of free HF. Also 1D calculations were made in which both r and the Cl-HF distance R were frozen. The complex is found to have the linear hydrogen bonded Cl-HF structure, with ground-state quantum numbers J = 3/2 for the overall angular momentum and /omega/ = 3/2 for its projection on the intermolecular axis R. The binding energy is D0 = 432.25 cm(-1) for v(HF) = 0 and D0 = 497.21 cm(-1) for v(HF) = 1. Bending modes with /omega/ = 1/2 and /omega/ = 5/2 are split by the Renner-Teller effect, since the electronic ground state is a degenerate 2pi state. A series of intermolecular (R) stretch modes was identified. Rotational constants and e-f parity splittings were extracted from the levels computed for J = 1/2 to 7/2. The computed red shift of the HF stretch frequency of 64.96 cm(-1) and the 35Cl-37Cl isotope shift of 0.033 cm(-1) are in good agreement with the values of 68.77 and 0.035 cm(-1) obtained from the recent experiment of Merritt et al. (Phys. Chem. Chem. Phys. 2005, 7, 67), after correction for the effect of the He nanodroplet matrix in which they were measured.

Interactions in open-shell clusters: ab initio study of pre-reactive complex O(3P) + HCl

Van der Waals interactions between the ground-state triplet O(3P) atom and the closed-shell HCl molecule are investigated in the pre-reactive region. Three adiabatic (two of A'' symmetry and one of A' symmetry) and four non-relativistic diabatic potential energy surfaces are obtained by combining a restricted open-shell coupled cluster approach with the multireference configuration interaction method. The lower A'' adiabatic potential surface has a single minimum (D(e) = 589 cm(-1)) for a linear O...HCl configuration. The upper A'' potential has a weak (D(e) = 65 cm(-1)) minimum for a linear HCl...O configuration. The A' adiabatic potential has a weak (124 cm(-1)) T-shaped minimum. Adiabatic potentials intersect once in the O...HCl linear configuration and twice in the linear HCl...O geometry. The role of electrostatic interactions in shaping these potentials is discussed. The effects of spin-orbit coupling on this interaction are also investigated assuming a constant value of the SO parameter.