Triplet Excitons in Small Helium Clusters.

An electron traveling through liquid helium with sufficient kinetic energy can create a low-lying triplet exciton via inelastic scattering. Accompanying repulsion between the exciton and nearby atoms results in bubble formation. That is not all, however. Repulsion compresses an "incipient He2* exciton", pushing it into a region where an He2* moiety commences evolution toward its potential energy minimum. The above picture follows from ab initio calculations of the two lowest adiabatic potential energy surfaces for collinear three-atom systems and dynamics studies launched on the lowest adiabat that calculate said surface on the fly. The timescale for launching trajectories toward the He2* moiety is significantly shorter than the timescale for pushing helium away from the exciton in large systems, making results with three atoms relevant to liquid helium. This explains how He2* might be created in the aftermath of electron-impact excitation of He*. Interplay between the lowest adiabats is discussed, underscoring the importance of nonadiabatic processes in such systems. Results with eight-atom systems further illustrate the critical role of nonadiabatic transitions.

Formation of He4+ via electron impact of helium droplets.

Electron impact ionization of superfluid helium droplets containing several thousand atoms produces a broad distribution of Hen+ ions that peaks at n = 2 and decreases monotonically toward larger n. In larger droplets (say 105 or more atoms), however, the He4+ signal intensity is anomalously large. We have studied the mechanism for the formation of He4+ ions in large helium droplets by varying the duration of the electron impact excitation pulse. Droplets of different average sizes were generated using the expansion of helium at 20 bars and 9-20 K through a pulsed valve nozzle. The resulting ions were analyzed by time-of-flight mass spectroscopy (TOFMS) and quadrupole mass spectroscopy (QMS). The intensity distributions obtained with the TOFMS technique initially showed much smaller He4+ signals than those obtained using QMS. However, we discovered that the intensity anomaly is associated with the duration of the electron bombardment pulse in the TOFMS instrument. Measurements with different electron bombardment pulse durations enabled us to discern a characteristic time of ∼10 µs for enhanced He4+ production in large droplets under our experimental conditions. A qualitative model is presented in which metastables interact on droplet surfaces, yielding two He2+ cores that share a Rydberg electron while minimizing repulsion between the cores. This is the He4+(4A2) state suggested by Knowles and Murrell.

Photoinitiated Dynamics in Amorphous Solid Water via Nanoimprint Lithography.

Laser pulses that act on fragile samples often alter them irreversibly, motivating single-pulse data collection. Amorphous solid water (ASW) is a good example. In addition, neither well-defined paths for molecules to travel through ASW nor sufficiently small samples to enable molecular dynamics modeling have been achieved. Combining nanoimprint lithography and photoinitiation overcomes these obstacles. An array of gold nanoparticles absorbs pulsed (10 ns) 532 nm radiation and converts it to heat, and doped ASW films grown at about 100 K are ejected from atop the irradiated nanoparticles into vacuum. The nanoparticles are spaced from one another by sufficient distance that each acts independently. Thus, a temporal profile of ejected material is the sum of about 106 "nanoexperiments," yielding high single-pulse signal-to-noise ratios. The size of a single nanoparticle and its immediate surroundings is sufficiently small to enable modeling and simulation at the atomistic (molecular) level, which has not been feasible previously. An application to a chemical system is presented in which H/D scrambling is used to infer the presence of protons in films composed of D2O and H2O (each containing a small amount of HDO contaminant) upon which a small amount of NO2 has been deposited. The pulsed laser heating of the nanoparticles promotes NO2/N2O4 hydrolysis to nitric acid, whose protons enhance H/D scrambling dramatically.

Geometric phase and gauge connection in polyatomic molecules.

Geometric phase is an interesting topic that is germane to numerous and varied research areas: molecules, optics, quantum computing, quantum Hall effect, graphene, and so on. It exists only when the system of interest interacts with something it perceives as exterior. An isolated system cannot display geometric phase. This article addresses geometric phase in polyatomic molecules from a gauge field theory perspective. Gauge field theory was introduced in electrodynamics by Fock and examined assiduously by Weyl. It yields the gauge field A(µ), particle-field couplings, and the Aharonov-Bohm phase, while Yang-Mills theory, the cornerstone of the standard model of physics, is a template for non-Abelian gauge symmetries. Electronic structure theory, including nonadiabaticity, is a non-Abelian gauge field theory with matrix-valued covariant derivative. Because the wave function of an isolated molecule must be single-valued, its global U(1) symmetry cannot be gauged, i.e., products of nuclear and electron functions such as χ(n)ψ(n) are forbidden from undergoing local phase transformation on R, where R denotes nuclear degrees of freedom. On the other hand, the synchronous transformations (first noted by Mead and Truhlar): ψ(n)→ψ(n)e(iζ) and simultaneously χ(n)→χ(n)e(-iζ), preserve single-valuedness and enable wave functions in each subspace to undergo phase transformation on R. Thus, each subspace is compatible with a U(1) gauge field theory. The central mathematical object is Berry's adiabatic connection i, which serves as a communication link between the two subsystems. It is shown that additions to the connection according to the gauge principle are, in fact, manifestations of the synchronous (e(iζ)/e(-iζ)) nature of the ψ(n) and χ(n) phase transformations. Two important U(1) connections are reviewed: qA(µ) from electrodynamics and Berry's connection. The gauging of SU(2) and SU(3) is reviewed and then used with molecules. The largest gauge group applicable in the immediate vicinity of a two-state intersection is U(2), which factors to U(1) × SU(2). Gauging SU(2) yields three fields, whereas U(1) is not gauged, as the result cannot be brought into registry with electronic structure theory, and there are other problems as well. A parallel with spontaneous symmetry breaking in electroweak theory is noted. Loss of SU(2) symmetry as the energy gap between adiabats increases yields the inter-related U(1) symmetries of the upper and lower adiabats, with spinor character imprinted in the vicinity of the degeneracy.

Photon and electron spins.

It is easy to draw an intuitive parallel between the classical free electromagnetic field and its corresponding quantum, the photon-a spin-1 object. The situation with a massive particle such as an electron is less clear, as a real-world analog of the classical field whose quantum is the massive particle is not available. It is concluded that the fermion particle perspective provides the best avenue for an intuitive grasp of the spin of an elementary fermion.

Statistics of indistinguishable particles.

The wave function of a system containing identical particles takes into account the relationship between a particle's intrinsic spin and its statistical property. Specifically, the exchange of two identical particles having odd-half-integer spin results in the wave function changing sign, whereas the exchange of two identical particles having integer spin is accompanied by no such sign change. This is embodied in a term (-1)(2s), which has the value +1 for integer s (bosons), and -1 for odd-half-integer s (fermions), where s is the particle spin. All of this is well-known. In the nonrelativistic limit, a detailed consideration of the exchange of two identical particles shows that exchange is accompanied by a 2pi reorientation that yields the (-1)(2s) term. The same bookkeeping is applicable to the relativistic case described by the proper orthochronous Lorentz group, because any proper orthochronous Lorentz transformation can be expressed as the product of spatial rotations and a boost along the direction of motion.

Effective Hamiltonian models and unimolecular decomposition.

Partitioning Hilbert space into two subspaces by using orthogonal projection operators yields compact forms for effective Hamiltonians for each of the subspaces. When one (the Q space) contains molecular bound states and the other (the P space) contains dissociative continua, a simple form for the non-Hermitian Q-space effective Hamiltonian, H(eff), can be obtained, subject to reasonable approximations. Namely, H(eff) = H0 - ivariant Planck's/2pi Gamma/2, where H0 is Hermitian, and the width operator variant Planck's/2pi Gamma accounts for couplings of the Q-space levels to the P-space continua. The P/Q partitioning procedure has been applied in many areas of atomic, molecular, and nuclear physics with widespread success. Inputting into this formalism ideas from random matrix theory in order to model independent open channels yields the random matrix H(eff) model. Despite numerous efforts, this model has failed to model satisfactorily the statistical transition-state theory of unimolecular decomposition (hereafter referred to as TST) in the regime of overlapping resonances, where nearly all such reactions occur. All statistical models of unimolecular decomposition are premised on rapid intramolecular vibrational redistribution (IVR) for a given set of good quantum numbers. The phase space thus accessed results in a threshold reaction rate of 1/h rho, and for K independent open channels, the rate is K/h rho. This reaction rate corresponds to a resonance width of K/2pi rho, and when K increases, the resonances (which are rho(-1) apart) overlap. In this regime, the random matrix H(eff) model fails because it does not introduce independent open channels. To illustrate the source of the problem, an analysis is carried out of a simple model that is obviously and manifestly inconsistent with TST. This model is solved exactly, and it is then put in the form of the random matrix H(eff) model, illustrating the one-to-one correspondence. This reveals the deficiencies of the latter. In manipulating this model into the form H0 - ivariant Planck's/2pi Gamma/2, it becomes clear that the independent open channels in the random matrix H(eff) model are inconsistent with TST. Rather, this model is one of gateway states (i.e., bound states that are coupled to their respective continua as well as to a manifold of zero-order bound states, none of which are coupled directly to the continua). Despite the fact that the effective Hamiltonian method is, by itself, beyond reproach, the random matrix H(eff) model is flawed as a model of unimolecular decomposition in several respects, most notably, bifurcations of the distributions of resonance widths in the regime of overlapping resonances.

The Landau-Zener formula.

The Landau-Zener formula for the probability that a nonadiabatic transition has taken place is derived without solving directly the usual second-order differential equation. This is achieved in just a few steps by using contour integration.

On the ultraviolet photodissociation of H(2)Te.

The photodissociation of H(2)Te through excitation in the first absorption band is investigated by means of multireference spin-orbit configuration interaction (CI) calculations. Bending potentials for low-lying electronic states of H(2)Te are obtained in C(2v) symmetry for Te-H distances fixed at the ground state equilibrium value of 3.14a(0), as well as for the minimum energy path constrained to R(1)=R(2). Asymmetric cuts of potential energy surfaces for excited states (at R(1)=3.14a(0) and theta;=90.3 degrees ) are obtained for the first time. It is shown that vibrational structure in the 380-400 nm region of the long wavelength absorption tail is due to transitions to 3A('), which has a shallow minimum at large HTe-H separations. Transitions to this state are polarized in the molecular plane, and this state converges to the excited TeH((2)Pi(1/2))+H((2)S) limit. These theoretical data are in accord with the selectivity toward TeH((2)Pi(1/2)) relative to TeH((2)Pi(3/2)) that has been found experimentally for 355 nm H(2)Te photodissociation. The calculated 3A(')<--XA(') transition dipole moment increases rapidly with HTe-H distance; this explains the observation of 3A(') vibrational structure for low vibrational levels, despite unfavorable Franck-Condon factors. According to the calculated vertical energies and transition moment data, the maximum in the first absorption band at approximately 245 nm is caused by excitation to 4A("), which has predominantly 2(1)A(") ((1)B(1) in C(2v) symmetry) character.