Frontiers in Quantum Methods and Applications in Chemistry and Physics

It has long been known that there are multiple solutions to the self-consistent Hartree-Fock equations. This can be problematic if careful attention is not given to the orbital occupation and electronic state in the converged wave function. The issues with convergence have been demonstrated through the calculation of potential energy curves for O₂, F₂, Cl₂, Br₂, LiF, NaCl, CaO, MgO, ScO, FeO, TiO, YO, and ZrO. Hartree-Fock (HF) calculations were used to compute the points on the potential energy surface, with dynamic electron correlation included through the use of the completely renormalized coupled cluster, including singles, doubles, and perturbative triples [CR-CC(2,3)]. Even in regions with little to no multireference character, as determined by the T₁/D₁ diagnostics, HF does not always converge to the ground electronic state. As HF provides the reference wave function for CR-CC(2,3), and other post-Hartree-Fock ab initio methods, treatment of electron correlation does not necessarily result in a smooth potential energy curve, especially if HF is unable to produce a smooth curve. Even the convergence rate of multireference methods can be affected as the initial orbitals that form the basis for multireference calculations are frequently obtained from HF calculations.

A general geometric representation of sphere-sphere interactions is derived using the bispherical coordinate system. It presents a dimensionless, scaled surface-to-surface separation parameter \( s^{*}\), which is valid for all possible combinations of sphere size and separation distance. The proposed geometric description is not limited to sphere-sphere interactions, but also describes interactions that involve a point particle or a plane. The surface-to-surface separation parameter approaches the limit of \( s^{*} = 1 \) if the radii of both spheres are much smaller than the actual surface-to-surface separation distance s, i.e. in the limit of two point particles. On the other hand, the geometric limit of \( s^{*} = 0\) corresponds to two planes, namely when the radii of both spheres are much larger than s.

We present a detailed study of the optical properties of tetrahedral silver clusters ranging from Ag₁₀ to Ag₂₂₀ using frequency domain (FD) and real-time (RT) time-dependent density functional theory. We compare the electronic structure and optical properties of the clusters calculated with different exchange-correlation functionals, different basis sets, and different DFT software packages. We also present an analysis of the orbital contributions to the density of states, which for the larger clusters can be decomposed into surface and bulk contributions. We find that the description of optical properties is nearly insensitive to the choice of exchange-correleation functional and results are consistent for FD and RT implementations. Optical properties are sensitive to basis set selection however, and it is critical that the basis set correctly describes d-orbitals. We show that FD-TDDFT provides insights into the collective excitation nature of a plasmonic nanoparticle allowing us to investigate the hot electron distribution produced immediately after plasmonic excitation. This analysis shows that the electron distribution is largely a flat function of electron energy in the range between zero and the photon energy for a plasmonic transition whereas it is strongly peaked close to zero for an interband transition.

A consistent relativistic approach, based on the atomic gauge-invariant relativistic perturbation theory and the exchange perturbation theory, is presented and applied to calculating the interatomic potentials, van der Waals constants, hyperfine structure line collision shift and broadening for heavy atoms in an atmosphere of the buffer inert gas. The corresponding data on the collision hyperfine line shift and broadening for the thallium, alkali (Rb, Cs) and lanthanide (ytterbium) atoms in an atmosphere of the inert gas (He, Kr, Xe) are listed and compared with available alternative theoretical and experimental results.

Behavior of shared proton in symmetric dimers of ammonia and lower amine homologs were studied by several theoretical methods. Corresponding optimized structures by density functional theory show an intuitive hypsochromic shift as the degree of methylation is enhanced. Inclusion of nuclear quantum effect, however, changes the whole picture. It was found out that the fundamental vibrational transition corresponding to the shared proton’s stretching motion, ν_sp is counter intuitive. Based from these calculations, there is a bathochromic shift from ammonia to trimethylamine. These ramifications do clearly indicate that proton is a quantum object. Furthermore, spectroscopic features for the stretching modes of the shared proton and H-bond donor-acceptor atoms were proposed.

Fatty Acid Amide Hydrolase (FAAH) is a very interesting serine hydrolase that promotes the hydrolysis of both amides and esters, such as the endogenous cannabinoid anandamide or N-arachidonoyl ethanolamine (AEA), and the sleep-inducing lipid oleamide. The therapeutic potential from the pharmacological modulation of this enzyme is vast, including relevant neurological and inflammatory disorders. Different computational approaches have fallen upon the characterization of the oleamide-FAAH monomer complex. With this study, we propose a description of both the dimeric and monomeric FAAH complexes with the substrate anandamide, in order to look for relevant interactions in the active-site and differences in the monomer and dimer incorporation approaches. The study involves a comparative analysis of several important molecular aspects for which are vital not only motion but also the conformational sampling of both enzyme and substrate as well as their interaction, with the inclusion of solvent. This work comprises a flexibility analysis of FAAH through Root Mean Square Fluctuation (RMSF), Solvent Accessible Surface Accessible Area (SASA) measurements on the substrate and enzyme, Radial Distribution Functions (RDFs) of the water molecules hydrating anandamide, as well as a study on significant hydrogen bonds between the active-site residues and the substrate. The results highlight meaningful interacting residues of the FAAH active-site with the AEA substrate, and the importance of considering the dimeric complex when flexibility effects are relevant.

The adiabatic theory requires the time scale of the changes in the Hamiltonian to be larger than the time scale of the changes in the system. The solution of the wave equation is expressed in terms of the instantaneous solutions. A formalism known as the adiabatic Floquet theory is being currently applied to describe photodissociation of molecules at high intensity in the optical range, where these conditions are not fufilled. We show how to justify this approach, and we use the direct solution of the time-dependent Schrodinger equation to confirm its validity.

We examine theoretically photoionization processes of molecules component of explosives having at least one explosophore group NO₂. We review previous results obtained for the nitramide, N,N-dimethylnitramine and 1,1-diamino-2,2-dinitroethylene (FOX-7 or DADNE) molecules and present new results for the two conformers of nitromethane. A systematization of the results is given. The calculations employed the Symmetry-Adapted-Cluster Configuration Interaction (SAC-CI) ab initio wave function and the monopole approximation to compute photoionization cross sections. Assignments of the ionization bands are provided. The overall agreement between computed spectra, ionization potentials and experiment is very good. We show that the SAC-CI ionization potentials are far superior when compared with Koopmans theorem values and much closer to experimental values.

We present the results of a theoretical study of π-electron dynamics in a nonplanar chiral aromatic molecule (P)-2,2′-biphenol. Coherent ring currents, which are one of the main observables of coherent π-electron dynamics, are generated by applying the linearly polarized UV pulse laser, where a pair of coherent quasi-degenerated excited states is created. In this paper we review the formulations of the time-dependent coherent ring currents and angular momentum which were obtained using the density matrix theory based on the LCAO MO approximation. The results of the numerical simulation of coherent π-electron ring currents and angular momentum in (P)-2,2′-biphenol are shown. We also propose an ultrafast quantum switching method of π-electron rotations and perform the sequential switching among four rotational patterns which are performed by the overlapped pump-dump laser pulses with properly selected laser polarizations, time delay and relative phases. Finally we refer to an outline for the extension of our method to N aromatic rings chain (N ≥ 3).

The dynamical structure factor S(q, E) related to the scattering of particles on mobile adsorbates is evaluated quantum mechanically from the formula proposed by van Hove (Phys. Rev. 95: 249–262, 1954) using eigenfunctions and eigenvalues obtained with the Multiconfiguration Time Dependent Hartree method. Three different one dimensional models for the CO/Cu(100) system and a three dimensional model for H/Pd(111) are investigated. Results are discussed in connection with recent ³He spin echo experiments reported in the literature.

We present an advanced approach to construction of the electron Green’s function of the Dirac equation with a non-singular central nuclear potential and complex energy. The Fermi-model and relativistic mean-field (RMF) nuclear potentials are used. The radial Green’s function is represented as a combination of two fundamental solutions of the Dirac equation. The approach proposed includes a procedure of generating the relativistic electron functions with performance of the gauge invariance principle. In order to reach the gauge invariance principle performance we use earlier developed QED perturbation theory approach. In the fourth order of the QED perturbation theory (PT) there are diagrams, whose contribution into imaginary part of radiation width Im δE for the multi-electron system accounts for multi-body correlation effects. A minimization of the functional Im δE leads to integral-differential Dirac-Kohn-Sham-like density functional equations. Further check for the gauge principle performance is realized by means of the Ward identities. In the numerical procedure we use the effective Ivanova-Ivanov’s algorithm, within which a determination of the Dirac equation fundamental solutions is reduced to solving the single system of the differential equations. This system includes the differential equations for the nuclear potential and equations for calculating the integrals of \( {\iint {dr_{1} dr_{2} } } \) type in the Mohr’s formula for definition of the self-energy shift to atomic levels energies. Such a approach allows to compensate a main source of the errors, connected with numerical integration \( \int {d\xi } \) and summation on χ in the Mohr’s expressions during calculating the self-energy radiative correction to the atomic levels energies. As illustration, data on the nuclear finite size effect and self-energy Lamb shift contributions to the energy of 2s-2p_1/2 transition for the Li-like ions of argon, iron, krypton and uranium are presented and compared with available theoretical and experimental results.

This work makes the case that everything in the universe (all particles, fields and forces) is derived from the single building block of 4 dimensional spacetime. The tremendously large impedance of spacetime (c³/G) permits small amplitude waves in spacetime to be the universal building block. The spacetime wave-based fermion model is shown to plausibly possess the correct spin, energy and the ability to appear to be point particles in experiments. This model also generates the weak gravity curvature of spacetime and the gravitational force between particles. The electrostatic force between fundamental particles is also derived and shown to be related to the gravitational force through a simple difference in exponents. A new constant of nature is proposed which converts electrical charge into a strain of space. The distortion of spacetime produced by photons is also analyzed.

A Zero-Energy Universe Scenario (ZEUS) is portrayed and its implications are examined and clarified. The formulation is based on the algebra of observables, e.g. the momentum-energy and their canonical conjugate partner space-time. Operators represent them in quantum theory and classical canonical variables in nonquantum applications. Conjugate operator/variable arrays impart a united edifice for a zero-energy universe scenario, which corresponds to using a non-positive definite metric for the manifestation of unstable states as recently employed in the field of chemical physics. Analogous formulations within a general complex symmetric setting provide a compelling analogy between Einstein’s theory of general gravity and Gödel’s first incompleteness theorem. This scenario brings together up-to-date theories in chemical physics with modern research in biology, physics, and astronomy. This unification establishes an edifice for the various arrows of time as well as authenticates Darwin’s Paradigm of Evolution from the microscopic realm to the cosmological domain.