On Theoretical Study of a Molecular Dimer System

In this paper, the vibronic structure of a dimer system is studied both theoretically and numerically. To construct adiabatic potential surfaces and electronic and vibrational wave functions for a dimer system, the adiabatic approximation is applied to two identical molecules, each of which has two electronic states with one vibrational mode. In this scheme, the excitonic splitting results not only from the electronic coupling of two molecules, but also from the vibronic coupling in each molecule. By using the resulting wavefunctions and the corresponding energies, the absorption and fluorescence spectra are studied. The effect of temperature on these spectra is also studied.     

Theory of Vibrational Predissociation Spectroscopy

A theory of vibrational predissociation spectroscopy is developed based on the adiabatic approximation that separates the oscillations of the high frequency vibron and low frequency phonon. We find that some properties such as dissociation energy and the number of phonon modes have significant influence on the temperature dependent spectra. Thus a comparison between the present theory and experiment would be a useful approach in determining these properties.     

Semiclassical self-consistent field perturbation theory for the hydrogen atom in a magnetic field

A recently developed perturbation theory for solving self-consistent field equations is applied to the hydrogen atom in a strong magnetic field. This system has been extensively studied using other methods and is therefore a good test case for the new method. The perturbation theory yields summable large-order expansions. The accuracy of the self-consistent field approximation varies according to field strength and quantum state but is often higher than the accuracy from adiabatic approximations. A new derivation is presented for the asymptotic adiabatic approximation, the most useful of the adiabatic approaches. This derivation uses semiclassical perturbation theory without invoking an adiabatic hypothesis. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 183–192, 1998     

Potential‐Energy Surfaces,the Born–Oppenheimer Approximations,and the Franck–Condon Principle: Back to the Roots

The concept of a potential‐energy surface (PES) is central to our understanding of spectroscopy, photochemistry, and chemical kinetics. However, the terminology used in connection with the basic approximations is variously, and somewhat confusingly, represented with such phrases as “adiabatic”, “Born–Oppenheimer”, or “Born–Oppenheimer adiabatic” approximation. Concerning the closely relevant and important Franck–Condon principle (FCP), the IUPAC definition differentiates between a classical and quantum mechanical formulation. Consequently, in many publications we find terms such as “Franck–Condon (excited) state”, or a vertical transition to the “Franck–Condon point” with the “Franck–Condon geometry” that relaxes to the excited‐state equilibrium geometry. The Born–Oppenheimer approximation and the “classical” model of the Franck–Condon principle are typical examples of misused terms and lax interpretations of the original theories. In this essay, we revisit the original publications of pioneers of the PES concept and the FCP to help stimulate a lively discussion and clearer thinking around these important concepts.     

Nonadiabatic core polarization and penetration correction in alkali-like atoms: Model computations on excited states of helium

Correlation between the motion of a highly excited outer electron and that of the remaining ionic “core” of an atom is generally treated in an adiabatic approximation, in which it is assumed that the outer electron affects the core in the same way as a stationary point charge. An alternative approach to this correlation problem which avoids the adiabatic approximation is tested here on the 1s2p, 1s3d, and 1s4f states of helium. The results provide the first accurate test of the adiabatic approximation and of a simple correction for the nonzero velocity of the outer electron. The approach used here is based on neglect, in the “correlation” part of the wave function, of the possibility that the outer electron comes closer to the nucleus than any core electron (“penetration”). A correction for this neglect is derived and tested on a version of the adiabatic approximation that likewise neglects penetration.     

Adiabatic approximation of time-dependent density matrix functional response theory

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.     

What can we learn from the adiabatic connection formalism about local hybrid functionals?

Local hybrid functionals with position-dependent exact-exchange admixture are a promising new generation of exchange-correlation functionals for a large variety of applications. So far, the local mixing functions (LMFs) determining the position dependence have been largely constructed in an ad hoc manner, albeit based on physical reasoning. Here the basic formalism of the adiabatic connection is employed to investigate the formal basis of local hybrids and to construct a priori LMFs. Both a local spin density approximation to the LMF (AC-LSDA LMF) and generalized gradient approximation approximations (AC-PW91 LMF and AC-PBE LMF) turn out to provide inferior performance when used in local hybrids to compute atomization energies and reaction barriers compared to previous semiempirical LMFs. This is rationalized by limited flexibility of these first-principles LMFs and some basic limitations of the adiabatic connection formalism in this context. Graphical analyses and formal considerations provide nevertheless important new insight into the physical background of local hybrid functionals.     

Perspectives on double-excitations in TDDFT

The adiabatic approximation in time-dependent density functional theory (TDDFT) yields reliable excitation spectra with great efficiency in many cases, but fundamentally fails for states of double-excitation character. We discuss how double-excitations are at the root of some of the most challenging problems for TDDFT today. We then present new results for (i) the calculation of autoionizing resonances in the helium atom, (ii) understanding the nature of the double excitations appearing in the quadratic response function, and (iii) retrieving double-excitations through a real-time semiclassical approach to correlation in a model quantum dot.     

Vibrational bonding in collinear HIH,DID and HID models

Vibrationally bonded quantum states are found for collinear HIH, DID and HID models, which represent a new type of vibrationally adiabatic system. Quantum-mechanical calculations yield at least three bound states for an HIH model which has recently been predicted to have one bound state from classical-mechanical calculations. An adiabatic approximation for the motion along the reaction path is compared with results for the complete two-dimensional problem.     

Nonlinear quantum mechanical effects: real or artefact of inaccurate approximations?

We critically discuss the reliability of the discrete nonlinear Schrödinger equation (DNSE) approach in the case of a dissipative two-site system. By using the Wigner pseudo-probability formalism we show that the nonlinear effects predicted by this effective picture are generally incorrect except in the adiabatic limit with the two-site system much faster than its own thermal bath. This is the adiabatic condition opposite to that usually adopted to derive the DNSE and a simple explanation of this result is given by establishing a connection between the Hartree approximation and the DNSE. Theoretical arguments are provided to evaluate the error associated to the Hartree approximation, so as to assess under which physical circumstances this key approximation is reliable.     

An adiabatic capture theory and quasiclassical trajectory study of C + NO and O + CN on the 2A', 2A", and 4A" potential energy surfaces

The adiabatic capture centrifugal sudden approximation (ACCSA) has been applied to the C + NO and O + CN reactions, along with quasiclassical trajectory simulations. Existing global analytic fits to the potential energy surfaces of the CNO system in the (2)A', (2)A", and (4)A" electronic states have been used. Thermal rate constants for reaction in each of the electronic states have been calculated. In all cases a strong temperature dependence is evident in the calculated rate constants. The agreement between the calculated adiabatic capture and quasiclassical trajectory rate constants is excellent in some cases, but these rate constants differ considerably in other cases. This behavior is analyzed in terms of the anisotropy of the potential energy surfaces. On the basis of this analysis, we propose a new diagnostic for the reliability of ACCSA capture calculations.     

Assessment and formal properties of exchange-correlation functionals constructed from the adiabatic connection

We examine the development and investigate the performance of exchange-correlation functionals constructed from the adiabatic connection. Our method is based on a direct modeling of the adiabatic connection curve in the coupling-constant space and is very flexible in the models. Several different models are investigated in the construction of new families of exchange-correlation functionals. Also the performance of two of these models (MCY1 and MCY2) is investigated over a wider range of systems and properties, with comparison made to the performance of established functionals. Overall, the adiabatic functionals improve upon widely used hybrid and generalized gradient approximation functionals, particularly in correctly describing one-electron systems and reaction energy barriers.     

Potential energy curves for the interaction of a low-energy positron with matter: The case He+e+

In this introductory exploration of the title theme, we treat a positron as a light nucleus and work within the quasi-molecule approximation to obtain, for the first time, adiabatic potential energy curves for its scattering by the He atom. We then show that different elastic and inelastic processes that contribute to the total scattering cross section can be rationalized in molecular terms as dissociation and non-adiabatic couplings. Particularly, some new insights on positronium yielding are presented.     

Generator coordinate method in time-dependent density-functional theory: memory made simple

The generator coordinate (GC) method is a variational approach to the quantum many-body problem in which interacting many-body wave functions are constructed as superpositions of (generally nonorthogonal) eigenstates of auxiliary Hamiltonians containing a deformation parameter. This paper presents a time-dependent extension of the GC method as a new approach to improve existing approximations of the exchange-correlation (XC) potential in time-dependent density-functional theory (TDDFT). The time-dependent GC method is shown to be a conceptually and computationally simple tool to build memory effects into any existing adiabatic XC potential. As an illustration, the method is applied to driven parametric oscillations of two interacting electrons in a harmonic potential (Hooke's atom). It is demonstrated that a proper choice of time-dependent generator coordinates in conjunction with the adiabatic local-density approximation reproduces the exact linear and nonlinear two-electron dynamics quite accurately, including features associated with double excitations that cannot be captured by TDDFT in the adiabatic approximation.     

An adiabatic linearized path integral approach for quantum time correlation functions: electronic transport in metal-molten salt solutions

We generalize the linearized path integral approach to evaluate quantum time correlation functions for systems best described by a set of nuclear and electronic degrees of freedom, restricting ourselves to the adiabatic approximation. If the operators in the correlation function are nondiagonal in the electronic states, then this adiabatic linearized path integral approximation for the thermal averaged quantum dynamics presents interesting and distinctive features, which we derive and explore in this paper. The capability of these approximations to accurately reproduce the behavior of physical systems is demonstrated by calculating the diffusion constant for an excess electron in a metal-molten salt solution.     

Neglect of four- and approximation of one-, two-, and three-center two-electron integrals in a symmetrically orthogonalized basis

A new integral approximation for use in molecular electronic structure calculations is proposed as an alternative to the traditional neglect of diatomic differential overlap models. The similarity between the symmetrically orthogonalized and the original basis functions (assumed orthonormal within each atomic set but nonorthogonal between different centers) is used to construct a robust approximation for the two-electron integrals, with the error being quadratic in the deviation between the products of the functions. Invariance properties of this procedure are rigorously proved. Numerical studies on a representative set of molecules at valence-only minimal basis Hartree-Fock level show that the approximation introduces relatively small errors, encouraging its future application in the semiempirical field.     

Path-integral simulations beyond the adiabatic approximation

Within the adiabatic approximation, it is trivial to generalize existing imaginary time path-integral techniques to the case of multiple electronic surfaces. However, there are many times where nonadiabatic effects can play an important role. To this end, we reformulate the well-known path-integral expressions to incorporate multiple potential surfaces, without necessitating the adiabatic approximation. We show that the resulting expression, like its adiabatic counterpart, can be interpreted in terms of a simple classical isomorphic system and thus is amenable to simulation through Monte Carlo techniques. We derive simple expressions to compute expectation values of a general operator in both the nuclear coordinate and electronic state, and demonstrate the existence of a simple internal diagnostic that can be used to evaluate the magnitude of equilibrium nonadiabatic effects.     

The quasiparticle concept in vibrational–electronic problems in molecules. I. Partitioning of the vibrational–electronic Hamiltonian

The partitioning of the vibrational–electronic Hamiltonian is presented. This partitioning is based on a new quasiparticle transformation that is constructed in such a way that the adiabatic approximation is included into the unperturbed Hamiltonian; nonadiabacity, anharmonicity, and electron correlation are treated as perturbations. We also present the second quantization treatment for bosons. The many body perturbation theory expansion for the vibrational–electronic Hamiltonian is suggested. A comparison of this approach is made with gradient techniques.