Molecular Structure Theory without the Born-Oppenheimer Approximation: Rotationless Vibrational States of LiH.

Low-lying rotationless states of the lithium hydride molecule are studied in the framework of the variational method without assuming the Born-Oppenheimer (BO) approximation. Highly accurate solutions to the six-particle (two nuclei and four electrons) Schrödinger equation are obtained by means of expanding the wave functions of the considered states in terms of many thousands of all-particle explicitly correlated Gausssians. The basis functions are optimized independently for each state using the analytic energy gradient with respect to the nonlinear parameters.

Gaussians for Electronic and Rovibrational Quantum Dynamics.

The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wave packets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy.

Quantum Definition of Molecular Structure.

Molecular structure, a key concept of chemistry, has remained elusive from the perspective of all-particle quantum mechanics, despite many efforts. Viewing molecular structure as a manifestation of strong statistical correlation between nuclear positions, we propose a practical method based on Markov chain Monte Carlo sampling and unsupervised machine learning. Application to the D molecule unambiguously shows that it possesses an equilateral triangular structure.

Adsorption of Polyadenylic acid on graphene oxide: experiments and computer modeling.

In this work, we study the adsorption of poly(rA) on graphene oxide (GO) using AFM and UV absorption spectroscopies. A transformation of the homopolynucleotide structure on the GO surface is observed. It is found that an energetically favorable conformation of poly(rA) on GO is achieved after a considerable amount of time (days).

Computer program ATOM-MOL-nonBO for performing calculations of ground and excited states of atoms and molecules without assuming the Born-Oppenheimer approximation using all-particle complex explicitly correlated Gaussian functions.

In this work, we describe a computer program called ATOM-MOL-nonBO for performing bound state calculations of small atoms and molecules without assuming the Born-Oppenheimer approximation. All particles forming the systems, electrons and nuclei, are treated on equal footing. The wave functions of the bound states are expanded in terms of all-particle one-center complex explicitly correlated Gaussian functions multiplied by Cartesian angular factors.

Non-adiabatic effects in the H spectrum.

The effect of non-adiabatic coupling on the computed rovibrational energy levels amounts to about 2 cm for H and must be included in high-accuracy calculations. Different strategies to obtain the corresponding energy shifts are reviewed in the article. A promising way is to introduce effective vibrational reduced masses that depend on the nuclear configuration.

Theoretical modeling of DNA electron hole transport through polypyrimidine sequences: a QM/MM study.

The phenomenon of DNA hole transport (HT) has attracted of scientists for several decades, mainly due to its potential application in molecular electronics. As electron holes mostly localize on purine bases in DNA, the majority of scientific effort has been invested into chemically modifying the structures of adenine and guanine in order to increase their HT-mediating properties. In this work we examine an alternative, never yet explored, way of affecting the HT efficiency by forcing electron holes to localize on pyrimidine bases and move between them.

A computational quantum-mechanical model of a molecular magnetic trap.

A model for describing the states of a molecular system trapped in a cavity created by a fast-rotating strong magnetic field is proposed and implemented. All-particle explicitly correlated Gaussian functions with shifted centers are employed in the model to expand the wave functions of the system. Both "internal" states associated with the system's rovibrational and electronic motions and the "external" states associated with translational motion of the center of mass of the system in the cavity are calculated.

Eu@C: Computed Comparable Populations of Two Non-IPR Isomers.

Relative concentrations of six isomeric Eu@C 72 -one based on the IPR C 72 cage (i.e., obeying the isolated-pentagon rule, IPR), two cages with a pentagon-pentagon junction (symmetries C 2 and C 2 v ), a cage with one heptagon, a cage with two heptagons, and a cage with two pentagon-pentagon fusions-are DFT computed using the Gibbs energy in a broad temperature interval.

Lowest ^{2}S Electronic Excitations of the Boron Atom.

A theoretical ab initio approach for calculating bound states of small atoms is developed and implemented. The approach is based on finite-nuclear-mass [non-Born-Oppenheimer (non-BO)] nonrelativistic variational calculations performed with all-particle explicitly correlated Gaussian functions and includes the leading relativistic and quantum electrodynamics energy corrections determined using the non-BO wave functions. The approach is applied to determine the total and transition energies for the lowest four ^{2}S electronic excitations of the boron atom.

Orbit-orbit relativistic correction calculated with all-electron molecular explicitly correlated Gaussians.

An algorithm for calculating the first-order electronic orbit-orbit magnetic interaction correction for an electronic wave function expanded in terms of all-electron explicitly correlated molecular Gaussian (ECG) functions with shifted centers is derived and implemented. The algorithm is tested in calculations concerning the H molecule. It is also applied in calculations for LiH and H molecular systems.

Isomeric ScO@C Related by a Single-Step Stone-Wales Transformation: Key Links in an Unprecedented Fullerene Formation Pathway.

It has been proposed that the fullerene formation mechanism involves either a top-down or bottom-up pathway. Despite different starting points, both mechanisms approve that particular fullerenes or metallofullerenes are formed through a consecutive stepwise process involving Stone-Wales transformations (SWTs) and C losses or additions. However, the formation pathway has seldomly been defined at the atomic level due to the missing-link fullerenes.

The effect of protonation of cytosine and adenine on their interactions with carbon nanotubes.

Placing electrical charges on nanomaterials is a means to extend their functional capabilities in nanoelectronics and sensoring applications. This paper explores the effect of charging nitrogen bases cytosine (Cyt) and adenine (Ade) via protonation on their noncovalent interaction with carbon nanotubes (CNT) using quantum chemical calculations performed at the M05-2X/6-31++G** level of theory alongside with a molecular graphics method. It is shown that the protonation of the bases causes threefold increase of the interaction energy in the CNT·Cyt·H and СNT·Ade·H complexes as compared to the CNT complexes formed with neutral bases.

Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers.

Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H2 and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.

Computed Relative Populations of D2 (22)-C84 Endohedrals with Encapsulated Monomeric and Dimeric Water.

Water monomer and dimer encapsulations into D2 (22)-C84 fullerene are evaluated. The encapsulation energy is computed at the M06-2X/6-31++G** level, and it is found that the monomer and dimer storage in C84 yields an energy gain of 10.7 and 17.

Noncovalent Interaction of Graphene with Heterocyclic Compounds: Benzene, Imidazole, Tetracene, and Imidazophenazines.

Noncovalent functionalization of graphene with organic molecules offers a direct route to multifunctional modification of this nanomaterial, leading to its various possible practical applications. In this work, the structures of hybrids formed by linear heterocyclic compounds such as imidazophenazine (F1) and its derivatives (F2-F4) with graphene and the corresponding interaction energies are studied by using the DFT method. Special attention is paid to the hybrids where the attached molecule is located along the graphene zigzag (GZZ ) and armchair (GAC ) directions.

Discontinuities-free complete-active-space state-specific multi-reference coupled cluster theory for describing bond stretching and dissociation.

The earlier proposed multi-reference state-specific coupled-cluster theory with the complete active space reference [CASCC; Lyakh et al., J. Chem.

Direct non-Born-Oppenheimer variational calculations of all bound vibrational states corresponding to the first rotational excitation of D2 performed with explicitly correlated all-particle Gaussian functions.

Direct variational calculations where the Born-Oppenheimer approximation is not assumed are done for all rovibrational states of the D2 molecule corresponding to first excited rotational level (the N = 1 states). All-particle explicitly correlated Gaussian basis functions are used in the calculations. The exponential parameters of the Gaussians are optimized with the aid of analytically calculated energy gradient determined with respect to these parameters.

Communication: Visible line intensities of the triatomic hydrogen ion from experiment and theory.

The visible spectrum of H3(+) is studied using high-sensitivity action spectroscopy in a cryogenic radiofrequency multipole trap. Advances are made to measure the weak ro-vibrational transitions from the lowest rotational states of H3(+) up to high excitation energies providing visible line intensities and, after normalisation to an infrared calibration line, the corresponding Einstein B coefficients. Ab initio predictions for the Einstein B coefficients are obtained from a highly precise dipole moment surface of H3(+) and found to be in excellent agreement, even in the region where states have been classified as chaotic.

Non-Born-Oppenheimer calculations of the pure vibrational spectrum of T₂ including relativistic corrections.

We report very accurate calculations of the complete pure vibrational spectrum of the T2 molecule with an approach where the Born-Oppenheimer (BO) approximation is not assumed. As the considered states correspond to the zero total angular momentum, their non-BO wave functions are spherically symmetric and are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even nonnegative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α(2) (where α is the fine structure constant) calculated as expectation values of the operators representing these effects.

A comparison of two types of explicitly correlated Gaussian functions for non-Born-Oppenheimer molecular calculations using a model potential.

A new functional form of the explicitly correlated Gaussian-type functions (later called Gaussians or ECGs) for performing non-Born-Oppenheimer (BO) calculations of molecular systems with an arbitrary number of nuclei is presented. In these functions, the exponential part explicitly depends on all interparticle distances and the preexponential part depends only on the distances between the nuclei. The new Gaussians are called sin/cos-Gaussians and their preexponential part is a product of sin and/or cos factors.

An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom in L = 0, M = 0 states using all-electrons explicitly correlated Gaussian basis functions.

An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground (4)S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 and M = 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters.

Accurate potential energy curve of the LiH+ molecule calculated with explicitly correlated Gaussian functions.

Very accurate calculations of the ground-state potential energy curve (PEC) of the LiH(+) ion performed with all-electron explicitly correlated Gaussian functions with shifted centers are presented. The variational method is employed. The calculations involve optimization of nonlinear exponential parameters of the Gaussians performed with the aid of the analytical first derivatives of the energy determined with respect to the parameters.

Charge asymmetry in the rovibrationally excited HD molecule.

The recently developed method for performing all-particle non-Born-Oppenheimer variational calculations on diatomic molecular systems excited to the first excited rotational state and simultaneously vibrationally excited is employed to study the charge asymmetry and the level lifetimes of the HD molecule. The method uses all-particle explicitly correlated Gaussian functions. The nonlinear parameters of the Gaussians are optimized with the aid of the analytical energy gradient determined with respect to these parameters.

Prediction of (1)P Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians.

Benchmark variational calculations are performed for the seven lowest 1s(2)2s np ((1)P), n = 2...