Bibliothek

Notizen: The interaction potential energy surfaces for CN(X 2∑+, A 2∏)+He have been computed from ab initio MCSCF and MCSCF-CI wave functions using an extensive basis set. In the presence of the He atom the two degenerate components of the CN 2∏ state split into wave functions of A' and A‘ symmetry, and the symmetry of the 2∑+ state reduces to A'. The two adiabatic potentials for the A' states are transformed to a diabatic basis, which yields a fourth potential energy surface V1, describing the collision-induced electrostatic coupling between the two A' states. The degree of mixing of the two diabatic A' states has been determined by integration of the relevant nonadiabtic coupling matrix elements and, in a simpler method, from the coefficients of the MCSCF configurations. Both procedures yield virtually identical results. The nonadiabatic coupling matrix elements are strongly peaked near the CN bond distance at which the X 2∑+ and A 2∏ states cross in the isolated molecule. The diabatic coupling potential V1, however, is only weakly dependent on the CN bond distance, and decreases exponentially with the CN–He separation. Near the classical turning points for room temperature collisions the magnitude of V1 is approximately 50 cm−1. The V1 potential shows a bimodal character as a function of the collision angle θ. These results are discussed in connection with recent experiments of Dagdigian and co-workers.

Notizen: The present article describes fully quantum calculations of spin changing collisions of Ca(4s5p 1P)(arrow-right-and-left)Ca(4s5p 3P) in full collisions with all the noble gases (He, Ne, Ar, Kr, and Xe). The approach and scattering formalism follow our earlier article [J. Chem. Phys. 86, 4790 (1987)]. Flexible Morese-Spline–van der Waals functions are used to describe the relevant 1,3Σ and 1,3Π Ca*+M potential curves. The interpretation of the dependence of the cross section on initial polarization will be guided by diatomic spectroscopy and a consideration of the crossings between thse potential curves. The interpretation of the dependence of the cross section on initial polarization will be guided by diatomic spectroscopy and a consideration of the crossings between these potential curves. A new simple statistical model, based on the consideration of the reflection symmetry of the initially prepared state, will provide the point of departure for the prediction of the polarization dependence. The exact quantum cross sections agree well both with the predictions of the statistical model and with the recent experimental results from Leone's laboratory at JILA. In addition the calculated 1P→3P cross sections increase with decreasing collision energy, since the crucial 1Π→3Σ crossing point is reached by the attractive branch of the 1Π potential.

Notizen: A new method is presented for the exact quantum solution of certain two-state curve crossing problems, where electronic state ||1〉 is energetically open at one end of the range of integration, while state ||2〉, and, possibly, state ||1〉, is energetically open at the other end of the range of integration. The method involves the use of log-derivative propagators, but differs from the usual log-derivative integration scheme in that one must propagate through the range of integration not only the log-derivative matrix but also a transformation matrix which permits one to reconstruct the initial wave function after the integration is completed. The method is numerically stable and, in a "solution following'' approximation to the log-derivative propagators, converges as the fourth power of the step size. Application is made to several model problems. In one case the exact results are compared with the predictions of earlier semiclassical analyses [P. V. Coveney, M. S. Child, and A. Bárány, J. Phys. B 18, 457 (1985)]. The method is completely general, and can be applied to arbitrary potentials.

Notizen: Close-coupled scattering calculations have been carried out for rotationally inelastic collisions between HF molecules. Integral cross sections were determined for vibrationally elastic transitions j1 j2→j '1 j 2(v1v2), which refer to collisions HFa (v1, j1)+HFb (v2, j2)+ΔE→HFa (v1, j '1 )+HFb (v2, j 2), where ΔE is the energy gap. Total energies between 241.1 and 3900 cm−1 (0.03 and 0.48 eV) were considered. When v1=v2, the rotational exchange transitions j1 j2→j2 j1(v1v2) are energetically resonant (i.e., ΔE=0), and the corresponding cross sections increase as the collision energy decreases. Particularly large cross sections are obtained for the j j+1→j+1 j(vv) transitions, which are both resonant and coupled to first order by the dipole–dipole interaction. When v1≠v2, the j j+1→j+1 j(v1v2) transitions are no longer resonant, and the corresponding cross sections are greatly reduced at small to moderate collision energies. The dependence of the j1 j2→j '1 j 2(v1v2) cross sections upon the vibrational states of the molecules, the collision energy, and the interaction potential used is discussed.

Notizen: We present a detailed study of the mechanism of spin–changing transitions between 1P and 3P electronic states corresponding to the nsn'p Rydberg state of an alkaline earth atom in collision with a structureless, spherical partner. This type of process takes place on four potential curves and involves collisional coupling between the electronic angular momentum L of the electronically excited atom, the spin S of the atom in the final 3P state, and the orbital angular momentum l associated with the relative motion of the collision partners. We review the use of Hund's case coupling schemes in describing the collision and present a careful analysis of the initial state preparation under conditions of laser excitation in a crossed beam experiment. This underlies the development of a new statistical model for the dependence of the spin–changing cross section on the alignment of the pump laser. Finally, we describe a new technique to follow the redistribution of flux onto locally adiabatic states as the initially excited atom is approached by the closed-shell partner. This is used to show that dynamical corrections to our simple statistical model are small.

Notizen: We present the general quantum theory of collisions of a symmetric top molecule with an uncorrugated surface. The similarities between the description of collisions of a molecule with a structureless atom and a flat surface allow us to exploit earlier gas-phase results. We then derive several collisional propensity rules: (1) In experiments in which both inversion states in the initial J,K doublets of para-NH3 are equally populated, both inversion states of all collisionally excited levels must also be equally populated. If, however, the initial inversion level can be state selected, then unequal populations will be observed in collisionally excited inversion doublets. (2) For transitions from the J=0 level of ortho-NH3 into rotational levels of the K=3 stack, a strong propensity will exist toward conservation of the inversion symmetry for transitions into levels with J' odd, but toward a change in the inversion symmetry for transitions into levels with J' even. (3) If the odd terms in the angular expansion of the potential dominate, then for transitions out of rotational levels with J〉0 in the K=0 stack of ortho-NH3 into rotational levels of the K=3 stack, a strong propensity will exist toward population of the upper level of the inversion doublet if the initial state has even J, and toward population of the lower level if the initial state has odd J. Using the similarities between the wave functions of a symmetric top and those of a linear polyatomic molecule with degenerate bending modes, we derived several propensity rules for the specific case of collisions of CO2 (0000) with an uncorrugated surface. In collisions which excite the low-lying (0110) bending vibration, if the initial rotational quantum number is small, then we predict that the probability of transition into a final state with J' odd will be much larger than for transition into a final state with J' even.

Notizen: Using recent ab initio interaction potential energy surfaces for the CN (X 2Σ+, A 2Π)+He system [H.-J. Werner, B. Follmeg, and M. H. Alexander, J. Chem. Phys. 89, 3139 (1988)], we have calculated fully quantum cross sections for inelastic transitions between individual rovibrational levels of the A 2Π and the X 2Σ+ states of CN. We have concentrated on the transitions studied experimentally by Dagdigian and co-workers for CN+Ar, namely transitions between the rotational levels of the A, v=8 and X, v'=12, the A, v=7 and X, v'=11, and the A, v=3 and X, v'=7 vibrational manifolds. In the case of the 8→12 and 7→11 transitions the cross sections are large (0.1–1 A(ring)2), and the dependence on initial Λ doublet level and on final rotational quantum number displays the same subtle alternations as seen experimentally. In the case of the 3→7 transitions, for which the vibrational levels are energetically much more separated, the calculated cross sections for CN+He are extremely small (10−5 A(ring)2), far smaller than observed experimentally for CN+Ar. In order to resolve this discrepancy, we have carried out some additional ab initio calculations for the CN+Ar system, but the change in the interelectronic coupling potential appears not to be large enough to explain the magnitude of the experimental cross sections.

Notizen: The quantum formalism for the scattering of a diatomic molecule in a 2Π electronic state which is well described by Hund's case (b) limit is investigated here. For a particular JFi→J'F'1 transition, quantum interference effects will lead to preferential population of one of the final state Λ doublet levels. The nonstatistical population of final state Λ doublet levels arises from an interference between terms in the expansion of the two electrostatic potential energy surfaces, of A' and A‘ reflection symmetry, which describe the interaction between a molecule in a Π electronic state and a closed-shell partner. The particular Λ doublet level preferred is opposite for molecules of π1 vs π3 electron occupancy. The physical origin of this reversal in the Λ doublet propensity is a direct reflection of the fact that for the former the A' potential surface is more repulsive since the sole π electron lies in the triatomic plane in this case, whereas for molecules of π3 electron occupancy the A' surface is less repulsive than the A‘ surface since for the A' surface only one of the three π electrons lies in the triatomic plane. The magnitude of these Λ doublet propensities is illustrated by calculated cross sections for the CH(X 2Π)–He system using the ab initio potential energy surfaces calculated by the Argonne theoretical group, and these cross sections are compared to those of the crossed molecular study of Liu and Macdonald [J. Chem. Phys. 91, xxxx (1989)]. A similar analysis is carried out for collisions of a molecule of π3 electron occupancy and is illustrated by inelastic collisions of OH(X2Π).

Notizen: The direct rotationally electronically inelastic scattering of NO from a rigid, uncorrugated Ag(111) surface is studied using the semiclassical self-consistent eikonal method (SCEM). Final rotational state distributions, summed over spin–orbit and Λ-doublet levels, are in good agreement with the exact quantum calculations of Smedley, Corey, and Alexander [J. Chem. Phys. 87, 3218 (1987)]. In addition to reproducing the rotational rainbows at low and high values of the final rotational quantum number J', the SCEM calculation reproduces fine structure dependence of the final rotational distributions which is sensitive to quantum interference effects. Besides providing a quantitative alternative to fully quantum close coupling, the semiclassical method gives new insight into the dynamics of the collision process. For a translational energy of 6700 cm−1, population of states higher than J'=42.5 is dynamically limited, even though final rotational states up to J'=61.5 are energetically accessible. Similar dynamical constraints are observed for translational energies from 3200 to 10 700 cm−1. The dynamical constraints do not exist at Etot =2500 cm−1, resulting in an overestimation of the rotational excitation by the SCEM calculation. Translational-to-rotational energy transfer has a nonlinear dependence on initial translational energy over an energy range of 2500–10 700 cm−1. Additionally, the location of the high J' rotational rainbow has a weak dependence on initial translational energy within this energy range. With increasing translational energy, the rotational distribution shifts to higher J' while the high J' rotational rainbow shifts to slightly lower J'. Also, the highest rotational state with significant population is only weakly dependent on the initial translational energy. By contrast, at a translational energy of 6700 cm−1, translational-to-rotational energy transfer is strongly dependent on initial rotational energy.

Notizen: An investigation of the energetics and mechanism of the dissociation of ground state HN3(X˜ 1A') into ground state N2(X 1∑+g)+NH(X 3∑−) products is presented. This process, which can be induced by multiphoton infrared pumping, occurs through a crossing between the lowest-energy singlet potential energy, which correlates asymptotically with electronically excited NH products (a 1Δ), and the lowest triplet surface. By means of ab initio CASSCF and MCSCF-CI calculations we have determined that the geometry at the minimum singlet–triplet crossing corresponds to an approximately linear N3 backbone with a perpendicular NH bond. The interior N–N distance is ∼3.6 bohr. This transition state lies ∼12 500 cm−1 above the energy of X˜ 1A' state of HN3 at the experimental equilibrium geometry. Since the N–N and N–H bonds are perpendicular at this transition state, there will be no torques tending to twist the system out of a planar geometry. The crucial singlet–triplet coupling occurs because the HN3 wave function in the region of this transition state can be considered an equal admixture of N2(X)⋅NH(a 1Δ) andN2(X)⋅NH(b 1∑+). Since the ground state HN3 wave function as well as the relevant spin–orbit Hamiltonian are symmetric with respect to reflection of the spatial and spin components of all the electrons in the plane of the molecule, and since the NH fragment must rotate in the plane of the initital HN3 molecule if the dissociation is planar, NH products can be formed only in states in which the wave function (electronic+rotational) is also symmetric with respect to this operation. For a molecule in a 3∑− electronic state the wave functions in only the F1 and F3 multiplets will be symmetric so that one would expect population in only the F1 and F3 levels. A similar symmetry argument implies that the NH products formed in the lowest spin-allowed channel [N2(X 1∑+g)+NH(a 1Δ)] will be found predominantly in the Δ(A') Λ-doublet state, which is symmetric with respect to reflection of the spatial coordinates of the electrons in the plane of rotation. This spin- and Λ-doublet selectivity has been found experimentally by Stephenson, Casassa, and King (accompanying article). The implications of similar spin selectivity in other photodissociation processes leading to molecules in 3∑− states, e.g., SO(X 3∑−) and O2(X 3∑−g), are also considered.