Configuration Interaction Potential Energy Surfaces Research Articles

Cold collisions of hot molecules.

In this Perspective, we review our recent work on rotationally inelastic collisions of highly vibrationally excited NO molecules prepared in single rotational and parity levels at v = 10 using stimulated emission pumping (SEP). This state preparation is employed in a recently developed crossed molecular beam apparatus where two nearly copropagating molecular beams achieve an intersection angle of 4° at the interaction region. This near-copropagating beam geometry of the molecular beams permits very wide tuning of the collision energy, from far above room temperature down to 2 K where we test the theoretical treatment of the attractive part of the potentials and the difference potential for the first time. We have obtained differential cross sections for state-to-state collisions of NO (v = 10) with Ar and Ne in both spin-orbit manifolds using velocity map imaging. Overall good agreement of the experimental results was seen with quantum mechanical close-coupling calculations done on both coupled-cluster and multi-reference configuration interaction potential energy surfaces. Probing cold collisions of NO carrying ∼2 eV of vibrational excitation allows us to test state-of-the-art theory in this extreme nonequilibrium regime.

Comparison of multireference configuration interaction potential energy surfaces for H + O2 → HO2: the effect of internal contraction

A comparison is presented of uncontracted multireference singles and doubles configuration interaction (MRCI) and internally contracted MRCI potential energy surfaces for the reaction \( {\mathrm H}\left( {^2 {\mathrm S}} \right) + {\mathrm O}_2 \left( {^3 \Sigma _{g}^ - } \right) \to {\mathrm H}{\mathrm O}_2 \left( {^2 {\mathrm A}^{\prime\prime}} \right) \). It is found that internal contraction leads to significant differences in the reaction kinetics relative to the uncontracted calculations.

Intramolecular energy transfer and predissociation in C-state HCN

Using our ab initio configuration interaction potential energy surface for the C state of HCN, we carried out classical trajectory calculations aimed at simulating the predissociation dynamics of various vibronic states of HCN and DCN. Our results provide an interpretation of the experimental photofragment excitation spectrum of this species. They also indicate that tunneling, which had been postulated as a rate-determining step in the predissociation, is not substantial. Intramolecular energy transfer seems to be the slow step. Finally, there is evidence that on a time scale up to one rotational period, the predissociation kinetics is quite mode specific.

A theoretical study of cyclohexadiene/hexatriene photochemical interconversion: multireference configuration interaction potential energy surfaces and transition probabilities for the radiationless decays

The overall energetics and the feature of reactive potential energy surfaces for the photochemical interconversion between cyclohexadiene (CHD) and all- cis-hexatriene (cZc-HT) have been investigated using the multireference configuration interaction (MRCI) calculations. The adiabatic and the diabatic potential energy surfaces of the ground and the excited states have been calculated along the Jacobi coordinates. The conical intersections among the states are estimated and the corresponding non-adiabatic transition probabilities are calculated using the semiclassical Zhu–Nakamura formula. The 1 1B–2 1A decay occurs by C 2-symmetry-breaking motion around the conical intersection. The non-adiabatic transition to 1 1A occurs by the motion toward the 5-membered ring.

Ab Initio calculations and vibrational energy level fits for the lower singlet potential-energy surfaces of C3

Ab initio multireference configuration interaction potential energy surfaces are computed for the eight lowest singlet surfaces of C(3). These reveal several important features, including several conical intersections in linear, nonlinear, and equilateral triangle geometries. These intersections are important because, particularly for the excited A (1)Pi(u) state, reasonable ab initio results could only be obtained by including nearby, near degenerate, (1)Sigma(u) (-) and (1)Delta(u) states that cross the A (1)Pi(u) state around 4500 cm(-1) above the equilibrium geometry, and a (1)Pi(g) state whose potential in turn crosses the other states about 2000 cm(-1) further up. These states are probably responsible for the complexity of the shorter wavelength UV absorption spectrum of C(3). The computed potential energy surface for the ground, X (1)Sigma(g) (+), state and for the lowest two excited singlet surfaces (which both correlate with the A (1)Pi(u) state in a collinear geometry) are fitted to analytic functional forms. Vibrational energy levels are calculated for both states, taking account of the Renner-Teller coupling in the excited A (1)Pi(u) state. The potential parameters for both states are then least-squares fitted to experimental data. The ground-state fit covers a range of approximately 8500 cm(-1) above the lowest level, and reproduces 100 observed vibrational levels with an average error of 2.8 cm(-1). The A (1)Pi(u) state surfaces cover a range of 3250 cm(-1) above the zero-point level, and reproduce the 44 observed levels in this range with an average error of 2.8 cm(-1).

Theoretical study of the interaction of AlH(X 1Σ+,A 1Π) with Ar: Potential energy surfaces and bend–stretch levels of the ArAlH(X,A) van der Waals complex

Multireference, configuration interaction potential energy surfaces (PES’s) are reported for the interaction of Ar with the AlH radical in its ground (X 1Σ+) and first singlet excited (A 1Π) electronic states. To assist in the assignment of the van der Waals bend–stretch vibrational quantum numbers in the accompanying experimental spectroscopic study of the ArAlH complex [E. Hwang and P. J. Dagdigian, J. Chem. Phys. 102, 2426 (1995)], slightly modified versions of these PES’s have been employed to calculate the vibrational energy levels of the ArAlH(X,A) van der Waals complex, both within the adiabatic bender model and in full variational calculations. Additionally, the band strengths for electronic transitions out of the ground and first vibrationally excited level of ArAlH(X) have been calculated for comparison with the relative band intensities measured by Hwang and Dagdigian.

Potential energy surfaces for the interaction of CH(X 2Π,B 2Σ−) with Ar and an assignment of the stretch-bend levels of the ArCH(B) van der Waals molecule

New multireference, configuration-interaction potential energy surfaces are reported for the interaction of Ar with the CH radical in its ground (X 2Π) and second excited (B 2Σ−) electronic states. These potential energy surfaces are then used in an adiabatic analysis of the rovibronic levels of the ArCH(X) and ArCH(B) van der Waals complexes. A qualitative discussion of the expected features in the B̃←X̃ electronic spectrum of ArCH is presented, and these are compared with the experimental spectrum reported earlier by Lemire et al. [J. Chem. Phys. 99, 91 (1993)].

Variational calculations of rovibrational states of Li 2K +

The low-lying rovibrational states for the ground electronic state of Li 2K + were calculated using an ab initio variational solution of the nuclear Schrödinger equation. A discrete configuration interaction potential energy surface was generated and an analytical representation was obtained using a power series expansion. This force filed was embedded in the Eckart-Watson Hamiltonian from which rovibrational wavefunctions and eigenenergies were variationally calculated. An SCF dipole moment surface was generated and used to calculate absolute line intensities and square dipole moment matrix elements for some of the most intense transitions within the P, Q and R branches, between the vibrational ground state and the low-lying rovibrational states.

Semiclassical calculation of the vibrational structure of the B̃ 1B u Rydberg state of t r a n s-di-imide from a b i n i t i o configuration interaction potential energy surfaces

The applicability of the SDCI and CEPA methods to the excited state of the title molecule is investigated. Two basis sets are used, one of triple zeta quality extended with diffuse functions and another which also contained polarization functions. For the subsequent CI calculations closed shell as well as open shell, molecular orbitals are used. We investigate the Pople correction as a way to obtain size consistent results from the SDCI calculation. For each method, a two-dimensional potential energy surface of the 1(4ag,5bu) Rydberg state of trans-di-imide (HNNH) is calculated. The vibrational fine structure in the corresponding B̃←X̃ UV absorption spectrum is derived from these surfaces and the result is compared to the spectrum measured by Neudorfl et al. [P. S. Neudorfl, R. A. Back, and A. E. Douglas, Can. J. Chem. 59, 506 (1981)]. A semiclassical method [K. S. Sorbie, Mol. Phys. 32, 1577 (1976)] is used to obtain the vibrational frequencies. A slightly modified version of the Heller frozen Gaussian approximation [E. J. Heller, J. Chem. Phys. 75, 2923 (1981)] is proposed and used to obtain the intensities of the vibrational bands. We conclude that it is important to use the open shell molecular orbital basis and the SDCI plus Pople correction, or even better, the CEPA. Both methods give good results for the vertical transition energy and excited state geometry. The error in the vibrational frequencies is in the order of 10%, but the NN-stretch mode is best described by the CEPA method.

Dissociation of vibronic states of C–1A′ DCN: Quantum treatment

The rates of dissociation of several vibrational states of nπ* excited (C–1A′) DCN have been determined via quantum dynamical means in which only the CD stretching and DCN bending motions are treated. The ab initio configuration interaction potential energy surface used in our earlier classical trajectory study of these same dissociation rates was employed in the present study. The results of this quantal study tend to support our earlier prediction that v2→v1 (bending-to-stretching) energy transfer plays an important role in determining the dissociation rates of these vibronic states. Surprisingly, the absolute rates obtained via the quantum method are in quite close agreement with a certain component of the classically determined rates.

Importance of correlation energy in collision dynamics: Quasiclassical trajectory study of collinear He+H 2+(υ′)→HeH + + H using HF and CI potential-energy surfaces

We have investigated the need to include correlation energy in potential-energy surface calculations by studying the collinear He + H 2 +(υ′) → HeH +(υ) + H reaction dynamics as a test case. We have utilised the Hartree-Fock (HF) and configuration interaction (CI) potential-energy surfaces for this system recently published by McLaughlin and Thompson. The quasiclassical trajectory method has been used to follow the molecular dynamics. There are quantitative and even some qualitative differences in the reaction probability results on the two surfaces. The state (υ′)-selected reaction probability ( P υ′ R) is generally larger on the CI than on the HF surface. Increase in υ′ from 0 to 1 results in a marginal increase in P υ′ R on the former and a substantial increase on the latter; further increase in υ′ results in a dramatic decrease in P υ′ R on the CI and not on the HF surface. The average product vibrational energy ( V) and enhancment of V with increase in reagent vibrational energy ( V′) are also sensitive to the inclusion of correlation energy for low υ′. Quasiclassical trajectory results for the reverse (exothermic) reaction show much larger V′ on the HF than on the CI surface in agreement with the larger vibrational enhancement for the endothermic reaction noticed on the former than on the latter. Interestingly, experimental results on the effect of reagent vibration on the reaction cross section for the endothermic reaction are in accord, qualitatively, with the results on the HF surface and not on the more accurate CI surface demonstrating the inadequacy of the collinear model for this endothermic reaction. The state-selected and overall rate constants on the two surfaces are in good agreement with each other, when accounted for the difference in the barrier height for the endothermic reaction on the two surfaces, except for υ′= 0. We have also examined the effect of changing the reagent mass combination on the importance of correlation energy on collision dynamics. For the H + LH and L + HH ( H = 80 amu, L = 1 amu) mass combinations we find the reaction probabilities to be too small (for V′ corresponding to υ′= 0 and 3 for H 2 +) to be distinguished for the two surfaces. For the H + HL mass combination, the results are qualitatively the same as for the He + H 2 + mass combination. In the case of nonreactive collisions, the energy dependence of the probability ( P O→1) for υ′ = 0 → 1 transition is distinctly different on the two surfaces. However, the rate constants ( k 0→1) and P 0→-2 and P 0→3 are relatively insensitive to the inclusion of correlation energy.

Rotational excitation of CO by He impact

To study rotational excitations of CO by He impact, configuration-interaction potential energy surfaces have been computed with two different basis sets. The surfaces are compared to one another, to an electron-gas surface, and to an experimentally determined surface. In addition, converged close-coupling calculations of the collision cross sections have been done on these surfaces for energies up to 100 cm−1 and compared. On the most accurate CI surface, cross sections have been computed using the infinite-order sudden (IOS) and quasi-classical methods as well.

Coupled-channel study of rotational excitation of a rigid asymmetric top by atom impact: (H2CO,He) at interstellar temperatures

A quantum mechanical scattering study is carried out to test a collisional pumping model for cooling the 6 and 2 cm doublets of interstellar formaldehyde. The Arthurs and Dalgarno formalism is extended to the collision of an s-state atom with a rigid asymmetric top molecule and applied to rotational excitation of ortho formaldehyde by helium impact. Using a previously determined configuration interaction potential energy surface, the coupled-channel (CC) equations are integrated at 12 scattering energies between 20 and 95°K. Up to 16 ortho formaldehyde states, yielding a maximum of 62 CC equations, are retained to test convergence of computed cross sections. Resonance structure is obtained at ∼20.2, 32.7, and 47.7°K. The computed inelastic cross sections are averaged over a Maxwell–Boltzmann distribution and the resultant rates used to solve the equations of statistical equilibrium for the relative populations. The 6 and 2 cm doublets are found to be cooled only upon inclusion of the j=3 doublet.