Paul J. Dagdigian

Clarification of the electronic asymmetry in Π‐state Λ doublets with some implications for molecular collisions

The asymmetry of the orbital part of the electronic wave functions and electronic charge distributions in 1Π, 2Π, and 3Π Λ doublets is carefully examined, to clear up considerable past confusion on this subject. The results are: (1) For 1Π and 3ΠΩ=1 states the electronic wave function in the e Λ‐doublet levels is symmetric with respect to reflection in the plane of rotation of the molecule and, in the f levels, antisymmetric. (2) For 2Π and 3Π0,2 states, in the Hund’s case (a) limit the electronic distributions in both Λ‐doublet levels are cylindrically symmetric. (3) As the case (b) limit is approached, the F1 e and F2 f wave functions of a 2Π state acquire an increasing degree of symmetric character with respect to reflection in the plane of rotation, while the F1 f and F2 e levels acquire antisymmetric character. In a 2Σ+–2Π radiative transition, the main branch P and R lines probe 2Π levels which are symmetric with respect to reflection in the plane of rotation while the main branch Q lines probe leve...

The inelastic scattering of 2Π [case (b)] molecules and an understanding of the differing Λ doublet propensities for molecules of π vs π3 orbital occupancy

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 re...

State‐to‐state collisional interelectronic and intraelectronic energy transfer involving CN A 2Π v=3 and X 2Σ+ v=7 rotational levels

Collisional transfer within the CN A 2Π v=3 vibrational manifold and to the X 2Σ+ v=7 manifold has been studied with initial and final rotational state resolution by an optical–optical double resonance technique. Despite the large energy gap between these two manifolds, the interelectronic cross sections are significant for only a relatively small range of ΔJ, and there is no observable propensity for energy resonant, large ΔJ transitions. The even–odd alternation vs N, observed previously in vA=7 collisions [N. Furio, A. Ali, and P. J. Dagdigian, J. Chem. Phys. 85, 3860 (1986)] and indicative of the near homonuclear form of the CN–Ar interaction potentials, is even more pronounced here for vA=3. The relative rate of intraelectronic and interelectronic energy transfer for the vA=3 N=6 F1f initial level was found to be comparable to that for the corresponding vA=7 level, despite the smaller Franck–Condon factor and larger energy gap to the neighboring vX=vA−4 manifold for the former.

State‐resolved study of collisional energy transfer between A 2Π v=7 and X 2Σ+ v=11 rotational levels of CN

Collisional transfer from the A 2Π state of CN has been studied with initial and final state resolution by an optical–optical double resonance technique. Specific rotational levels in the v=7 vibrational manifold of the A state of CN in a flow of several Torr of argon are prepared by pulsed laser excitation in the A–X (7,2) band. After a short time delay, a second laser probes the populations of quantum levels in this vibrational manifold and in the nearly isoenergetic v=11 manifold of the X 2Σ+ state by fluorescence excitation in the overlapped B–A (8,7) and B–X (8,11) bands. The interelectronic A→X transfer rate is found to be comparable to that for purely rotational collisional transitions within the A state for all incident levels studied, regardless of whether or not they possess significant X state character, because of isolated molecule non‐Born–Oppenheimer mixing. Reflecting the near homonuclear character of the CN–Ar interaction potentials, the final X state populations exhibited a significant ev...

Propensity rules in rotationally inelastic collisions of diatomic molecules in 3Σ electronic states

The formalism for the treatment of rotationally inelastic collisions of molecules in 3Σ electronic states is exposed, for the general case of intermediate coupling. The reduced matrix elements of the T operator are expressed in a Hund’s case (a) basis. Within the infinite‐order‐sudden (IOS) limit, the symmetry of the reduced T‐matrix elements and the large‐J limit of certain vector coupling coefficients can be used to derive several propensity rules bearing on changes in the Fi(i=1–3) label. In particular, for large J only the Fi conserving transitions will have large cross sections. From a physical viewpoint this propensity rule implies that the scattering, at least in the IOS limit at large J, is independent of Σ, the spin projection quantum number. The experimental study by Caughey and Crosley [J. Chem. Phys. 71, 736 (1979)] of rotational relaxation in the B 3Σu− state of S2 confirms our theoretical propensity rules, although the experimental rate constants for the F1 → F2, F3 transitions are considera...

Energetics and spin‐ and Λ‐doublet selectivity in the infrared multiphoton dissociation HN3(X̃ 1A’)→N2(X 1Σ+g)+NH(X 3Σ−,a 1Δ): Theory

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 ...

Quantum interpretation of fully state-selected rotationally inelastic collision experiments

We develop an expression for the cross section corresponding to fully oriented rotationally inelastic atom–diatomic molecule collisions in the general case where both the initial and final axes of quantization are arbitrarily oriented with respect to the initial relative velocity vector. The cross section appears as an inner product of a tensor cross section and various rotation matrix elements. Considerable simplification occurs if one averages over the final orientation of the rotational angular momentum. The thermal averaging appropriate to a beam–gas configuration can be reduced to a one‐dimensional integration. A detailed discussion is devoted to the potential use of laser induced fluorescence detection to determine experimentally the orientation dependence of rotationally inelastic collisions.

Collision‐induced transitions between molecular hyperfine levels: Quantum formalism, propensity rules, and experimental study of CaBr(X 2Σ+)+Ar

The general quantum treatment of collisions of a 2Σ+ molecule with hyperfine structure is presented. The recoupling technique introduced by Corey and McCourt into the field of molecular collisions [J. Phys. Chem. 87, 2723 (1983)] allows us to represent hyperfine‐state‐resolved tensor opacities, and hence cross sections, in terms of the corresponding nuclear‐ and also electron‐spin‐free quantities. The formalism also predicts (independent of the dynamical limit) that the largest F→F′ cross sections will be those for which ΔF=ΔJ, a rule well known for radiative transitions. Hyperfine‐state‐resolved scattering involving collisions of CaBr(X 2Σ+) with Ar is also studied here experimentally by electric quadrupole state selection and cw dye laser fluorescence detection. The relative final F′ distributions were determined for the N=3,e→N=5,e and N=2,e→N=1,e collisional transitions. These results clearly exhibit the ΔF=ΔJ propensity rule. Moreover, the F′ distributions were predicted with nearly quantitative accu...

Determination of the absolute chemiluminescence cross section and photon yield for the Ca(4s4p 3P) + N2O reaction

Abstract A novel method for determining absolute chemiluminescence cross sections without knowledge of the absolute detection sensitivity is described for reactions involving electronically excited reactants. A study of the Ca(4s4p 3 P) + N 2 O reaction under single-collision conditions is presented, and photon yield of 10 ± 3% is determined with the help of a measured beam attenuation cross section.

Nitramine propellant ignition and combustion research

Abstract The efficient and successful design of new generations of highly energetic propellants based on evolving nitramine chemistry will require a thorough knowledge of the chemical and physical parameters controlling their ignition and combustion. The necessary level of insight can be attained and successfully embodied in the predictive computer models necessary for effective propellant design, development and testing activities if a coordinated, hierarchical program of theoretical modeling and confirming and supporting experiments is designed and properly executed. This paper reviews the current state of our understanding of the chemistry and physics of nitramine propellant ignition and combustion, and develops and motivates the basic research program necessary to put advanced nitramine propellant development on a firm and effective scientific basis. Confronting and solving problems involving complex physicochemical phenomena which intertwine complex heat, mass and radiative transfer processes with chemical kinetics is a challenge which physical and engineering scientists are becoming much more adept at meeting. Modern theoretical and experimental tools are now available which allow the design and utilization of much more comprehensive analytical models as well as their concomitant supporting and confirming experimental measurements. Significant recent progress on these types of complex problems in the fields of atmospheric chemistry, hydrocarbon combustion chemistry, chemical laser development and advanced materials processing lead us to believe that similar, focused efforts on advanced nitramine propellant development will be both timely and fruitful.