Nonadiabatic Perturbation Theory Research Articles

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory.

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.

Precision tests of nonadiabatic perturbation theory with measurements on the DT molecule

This paper presents new measurements and calculations on the rovibrational transitions of DT, an istopolog of the hydrogen molecule composed of deuterium and tritium. The authors show an improved accuracy with respect to previous results and a good agreement between experiment and theory.

Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory

We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation, obtained within nonadiabatic perturbation theory, including the mixed nonadiabatic-relativistic effects. Quantum electrodynamic corrections in the leading $\alpha^5\,m$ and the next-to-leading $\alpha^6\,m$ orders, as well as finite nuclear size effect, are also taken into account but within the Born-Oppenheimer approximation only. Final results for the transition wavelength between rovibrational levels achieve accuracy of the order of $10^{-3}$--$10^{-7}$ cm$^{-1}$, and are provided by simple to use computer code.

Nonadiabatic relativistic correction in H2 , D2 , and HD

We calculate the nonadiabatic relativistic correction to rovibrational energy levels of H$_2$, D$_2$, and HD molecules using the nonadiabatic perturbation theory. This approach allows one to obtain nonadiabatic corrections to all the molecular levels with the help of a single effective potential. The obtained results are in very good agreement with the previous direct calculation of nonadiabatic relativistic effects for dissociation energies and resolve the reported discrepancies of theoretical predictions with recent experimental results.

Pair Potential with Submillikelvin Uncertainties and Nonadiabatic Treatment of the Halo State of the Helium Dimer.

The pair potential for helium is computed with accuracy improved by an order of magnitude relative to the best previous determination. For the well region, its uncertainties are now below 1millikelvin. The main improvement is due to the use of explicitly correlated wave functions at the nonrelativistic Born-Oppenheimer (BO) level of theory. The diagonal BO and the relativistic corrections are obtained from large full configuration interaction calculations. Nonadiabatic perturbation theory is used to predict the properties of the halo state of the helium dimer. Its binding energy and the average value of the interatomic distance are found to be 138.9(5)neV and 47.13(8)Å. The binding energy agrees with its first experimental determination of 151.9(13.3)neV [Zeller etal., Proc. Natl. Acad. Sci. U.S.A. 113, 14651 (2016)PNASA60027-842410.1073/pnas.1610688113].

Lepton-number violating effects in neutrino oscillations

We develop a non-adiabatic perturbation theory for oscillations involving an arbitrary number of neutrino and antineutrino species, including the possibility of lepton number violation which we treat as a small effect. We interpret the physics of such an approach for the one generation case by introducing the notion of adiabaticity for neutrino and antineutrino oscillations in analogy to flavor oscillations. We find that in a CP-odd matter environment a small lepton number violation in vacuo can be enhanced. Eventually, we apply the perturbation theory to the two generation case and work out an example for manifestations of lepton number violation, which can be solved both perturbatively as well as analytically thereby further clarifying the nature of the perturbation expansion.

Kinetics of Catalytic OH Dissociation on Metal Surfaces

A tunnel mechanism of OH dissociation reaction on metal surfaces is suggested and analyzed. Expressions for the rate constant and the activation energy are obtained by calculating the transition probability on semiempirical potential energy surfaces in the framework of the nonadiabatic perturbation theory. The analysis of the transition probability leads to a linear Brønsted–Evans–Polanyi (BEP) relationship between the activation energies and the surface reaction energies (ΔI), correlated by Ea = 0.73ΔI + 18 (kcal/mol). This relationship is compared with published literature data. The effect of the electron coupling on the pre-exponential factor is discussed, and the kinetic isotope effect of hydrogen for the reaction is predicted.

Adiabatic and nonadiabatic perturbation theory for coherence vector description of neutrino oscillations

The standard wave function approach for the treatment of neutrino oscillations fails in situations where quantum ensembles at a finite temperature with or without an interacting background plasma are encountered. As a first step to treat such phenomena in a novel way, we propose a unified approach to both adiabatic and non-adiabatic two-flavor oscillations in neutrino ensembles with finite temperature and generic (e.g. matter) potentials. Neglecting effects of ensemble decoherence for now we study the evolution of a neutrino ensemble governed by the associated Quantum Kinetic Equations, which apply to systems with finite temperature. The Quantum Kinetic Equations are solved formally using the Magnus expansion and it is shown that a convenient choice of the quantum mechanical picture (e.g. the interaction picture) reveals suitable parameters to characterize the physics of the underlying system (e.g. an effective oscillation length). It is understood that this method also provides a promising starting point for the treatment of the more general case in which decoherence is taken into account.

Finite nuclear mass corrections to electric and magnetic interactions in diatomic molecules

In order to interpret precise measurements of molecular properties, finite nuclear mass corrections to the Born-Oppenheimer approximation have to be accounted for. It is demonstrated that they can be obtained systematically using nonadiabatic perturbation theory. The formulas for the leading corrections to the relativistic contribution to energy, the transition electric dipole moment, the electric polarizability, and the magnetic shielding constant are derived. They can be conveniently calculated for a fixed position of nuclei, as in the Born-Oppenheimer approximation, and then averaged over the rovibrational function.

High order nonadiabatic perturbation theory on different adiabatic bases

A new partitioning of the nonadiabatic terms of a Hamiltonian consisting of a “slow” and a “fast” subsystem is introduced for high order numerical calculations of perturbation series. The Hamiltonian H(ν,λ) depends on two parameters, λ and ν. While the momentum dependent part of the perturbation is taken to be a linear function of the perturbation parameter λ, the other nonadiabatic terms are either assumed to be independent of λ, or depend quadratically on it. Especially the diagonal correction is partitioned into a constant and a quadratic function of λ. This partitioning will be controlled by the parameter ν. In zeroth order, the Hamiltonian will therefore be either the Born–Oppenheimer Hamiltonian, when ν=1, or the Born–Huang Hamiltonian, when ν=0. For other values of ν, more general adiabatic bases result. The new partitioning, in combination with the Hutson and Howard approach, forms a new method for the calculation of nonadiabatic perturbation series which is tested on a set of four model Hamiltonians. These have been studied already by Špirko et al. in a similar context. It is shown that the new method, as compared to traditional approaches, strongly enhances the rate of convergence and the accuracy of summability of the perturbation series, especially in the case of nearly avoided intersections or of near degeneracies.

Raman dispersion spectroscopy on the highly saddled nickel(II)-octaethyltetraphenylporphyrin reveals the symmetry of nonplanar distortions and the vibronic coupling strength of normal modes

We have measured the polarized Raman cross sections and depolarization ratios of 16 fundamental modes of nickel octaethyltetraphenylporphyrin in a CS2 solution for 16 fundamental modes, i.e., the A1g-type vibrations ν1, ν2, ν3, ν4, ν5, and φ8, the B1g vibrations ν11 and ν14, the B2g vibrations ν28, ν29, and ν30 and the antisymmetric A2g modes ν19, ν20, ν22, and ν23 as function of the excitation wavelength. The data cover the entire resonant regions of the Q- and B-bands. They were analyzed by use of a theory which describes intra- and intermolecular coupling in terms of a time-independent nonadiabatic perturbation theory [E. Unger, U. Bobinger, W. Dreybrodt, and R. Schweitzer-Stenner, J. Phys. Chem. 97, 9956 (1993)]. This approach explicitly accounts in a self-consistent way for multimode mixing with all Raman modes investigated. The vibronic coupling parameters obtained from this procedure were then used to successfully fit the vibronic side bands of the absorption spectrum and to calculate the resonance excitation profiles in absolute units. Our results show that the porphyrin macrocycle is subject to B2u-(saddling) and B1u-(ruffling) distortions which lower its symmetry to S4. Thus, evidence is provided that the porphyrin molecule maintains the nonplanar structure of its crystal phase in an organic solvent. The vibronic coupling parameters indicate a breakdown of the four-orbital model. This notion is corroborated by (ZINDO/S) calculations which reveal that significant configurational interaction occurs between the electronic transitions into |Q〉- and |1B〉-states and various porphyrin→porphyrin, metal→porphyrin, and porphyrin→metal transitions. The intrastate coupling parameters are used to estimate the excited electronic states’ displacements along the normal coordinates with respect to the ground state and their contributions to the reorganization energy. It turns out that the |B〉-state is predominantly affected by symmetric A1g-displacements, whereas the |Q〉-state is subject to A2g, B1g, and B2g displacements of its equilibrium configuration. While the former is induced by the combined effect of ruffling and saddling, the latter arises from Jahn–Teller coupling within the degenerate states.

Vibrational circular dichroism and electric-field shielding tensors: A new physical interpretation based on nonlocal susceptibility densities

Motion of nuclei within a molecule induces a magnetic moment me in the electronic charge distribution, giving a nonzero electronic contribution to the magnetic transition dipole that produces vibrational circular dichroism. In this paper, we develop a new susceptibility density theory for the induced magnetic moment. The theory is based on the response of the electrons to changes in the nuclear Coulomb field, due to shifts in nuclear positions. The electronic response to these changes depends on the same susceptibility densities that determine response to external fields. Our analysis suggests a new physical picture of vibrational circular dichroism. It yields an equation for the density of the induced electronic magnetic moment within a molecule; it also yields a new relation connecting the electric-field shielding at nucleus I of a molecule in an applied magnetic field of frequency ω to the derivative of me with respect to the velocity of nucleus I, regarded as a parameter in the electronic wave function. Within our theory, the derivative of me with respect to nuclear velocity separates into quantum-mechanical and classical components in close analogy with the Hellmann–Feynman theorem for forces on nuclei. In matrix-element form, results from our theory are identical to those obtained with nonadiabatic perturbation theory, to leading order. In general, the leading nonadiabatic corrections to electronic properties are determined directly by the electrons’ response to the changes in the nuclear Coulomb field, when the nuclei move.

Rate theories and puzzles of hemeprotein kinetics.

The binding of dioxygen and carbon monoxide to heme proteins such as myoglobin and hemoglobin has been studied with flash photolysis. At temperatures below 200 K, binding occurs from within the heme pocket and, contrary to expectation, with nearly equal rates for both ligands. This observation has led to a reexamination of the theory of the association reaction taking into account friction, protein structure, and the nature of electronic transitions. The rate coefficients for the limiting cases of large and small friction are found with simple arguments that use characteristic lengths and times. The arguments indicate how transition state theory as well as calculations based on nonadiabatic perturbation theory, which is called the Golden Rule, may fail. For ligand-binding reactions the data suggest the existence of intermediate states not directly observed so far. The general considerations may also apply to other biomolecular processes such as electron transport.

Novel theory of the HD dipole moment. I. Theory.

A novel theory of the electric dipole moments of homopolar but isotopically asymmetric molecules (such as HD, HT, or DT) is formulated, such that electrical asymmetry and the resulting dipole moment arise as purely electronic properties within a suitable Born-Oppenheimer approximation, and nonadiabatic (rovibronic) perturbations play no part in the theory. It is shown thereby that a much simpler and more direct explanation for these dipole moments can be given than that invoking non- adiabatic perturbations: The dipole moment arises from isotopic variation of the local effective electronic reduced mass and its effects on binding energies and sizes of orbitals. It is an odd function of the isotopic splitting parameter ${\ensuremath{\alpha}}_{0}$=(1/2)\ensuremath{\lambda}m/\ensuremath{\mu}, where \ensuremath{\lambda}=(${M}_{A}$-${M}_{B}$)/(${M}_{A}$+${M}_{B}$) is the nuclear mass asymmetry for nuclei A,B and (m/\ensuremath{\mu}) is the electron-nuclear mass ratio (for HD, this parameter is 1.36\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$). A canonical transformation exhibiting these effects (in the form of an asymmetric effective potential) is the basis for the new formulation. Since ${\ensuremath{\alpha}}_{0}$ is small the resulting dipole moment function is essentially linear in ${\ensuremath{\alpha}}_{0}$, and hence the dipole moment functions for HT and DT may be computed by rescaling the results for HD. Since the problem is purely electronic in the new formulation, variational and convergence studies are easy to carry out. In this and the following paper we formulate the new theory in detail and carry out variation-perturbation calculations of the HD dipole moment. The results are in good agreement with theoretical results obtained by nonadiabatic perturbation theory and demonstrate that this approach to isotopically induced dipole moments is valid.