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 not 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. In this Article, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential, we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.

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 D3+ molecule unambiguously shows that it possesses an equilateral triangular structure. These results provide a major step forward in our understanding of the molecular structure from fundamental quantum principles.

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). It is revealed that GO can induce formation of self-structures of single-stranded poly(rA) including a duplex at pH 7. The phenomenon is analyzed by polymer melting measurements and observed by AFM. Details of the noncovalent interaction of poly(rA) with graphene are also investigated using molecular dynamics simulations. The adsorption of (rA)10 oligonucleotide on graphene is compared with the graphene adsorption of (rC)10. DFT calculations are used to determine equilibrium structures and the corresponding interaction energies of the adenine-GO complexes with different numbers of the oxygen-containing groups. The IR intensities and vibrational frequencies of free and adsorbed adenines on the GO surface are calculated. The obtained spectral transformations are caused by the interaction of adenine with GO.

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. As these Gaussian functions are eigenfunctions of the operator representing the square of the total angular momentum of the system, the problem separates and calculations of states corresponding to different values of the total rotational quantum number can be solved independently from each other. Due to thorough variational optimization of the Gaussian exponential parameters, the method allows us to generate very accurate wave functions. The optimization is aided by analytically calculated energy gradient determined with respect to the parameters. Three examples of calculations performed for diatomic and triatomic molecules are shown as an illustration of calculations that can be performed with this program. Finally, we discuss the limitations, applicability range, and bottlenecks of the program.

Non-adiabatic effects in the H3+ spectrum.

The effect of non-adiabatic coupling on the computed rovibrational energy levels amounts to about 2 cm-1 for H3+ 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. A new empirical method that uses the stockholder atoms-in-molecules approach to this effect is presented and applied to H3+. Furthermore, a highly accurate potential energy surface for the D3+ isotopologue, which includes relativistic and leading quantum electrodynamic terms, is constructed and used to analyse the observed rovibrational frequencies for this molecule. Accurate band origins are obtained that improve existing data. This article is part of a discussion meeting issue 'Advances in hydrogen molecular ions: H3+, H5+ and beyond'.

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. Using an enhanced and revised version of our previously developed QM/MM model, we perform simulations of HT through polyadenine, polycytosine, polyguanine, and polythymine stacks according to a multistep hopping mechanism. From these simulations, kinetic parameters for HT are obtained. The results indicate a particularly high efficiency of cytosine→cytosine hopping, which is about ten times higher than the G → G hopping. We also discuss possible improvement of cytosine HT by modifying the oxidoreductive properties of complementary guanine residues.

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. The states are visualized by density plots. The model is applied to a trapped HD molecule.

Eu@C72: 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. It is shown that the two non-IPR isomers with one pentagon-pentagon junction prevail at any relevant temperature and exhibit comparable populations. The IPR-satisfying structure is disfavored by both energy and entropy.

Lowest

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. The transition energies agree with the available experimental values within 0.2-0.3 cm^{-1}. Previously, such accuracy was achieved for three- and four-electron systems.

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 H2 molecule. It is also applied in calculations for LiH and H3+ molecular systems. The implementation completes our work on the leading relativistic correction for ECGs and paves the way for very accurate ECG calculations of ground and excited potential energy surfaces (PESs) of small molecules with two and more nuclei and two and more electrons, such as HeH-, H3+, HeH2+, and LiH2+. The PESs will be used to determine rovibrational spectra of the systems.

Isomeric Sc2O@C78 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 C2 losses or additions. However, the formation pathway has seldomly been defined at the atomic level due to the missing-link fullerenes. Herein, we present the isolation and crystallographic characterization of two isomeric clusterfullerenes Sc2O@C2v(3)-C78 and Sc2O@D3h(5)-C78, which are closely related via a single-step Stone-Wales (SW) transformation. More importantly, these novel Sc2O@C78 isomers represent the key links in a well-defined formation pathway for the majority of solvent-extractable clusterfullerenes Sc2O@C2n (n = 38-41), providing molecular structural evidence for the less confirmed fullerene formation mechanism. Furthermore, DFT calculations reveal a SWT with a notably low activation barrier for these Sc2O@C78 isomers, which may rationalize the established fullerene formation pathway. Additional characterizations demonstrate that these Sc2O@C78 isomers feature different energy bandgaps and electrochemical behaviors, indicating the impact of SW defects on the energetic and electrochemical characteristics of metallofullerenes.

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. There is also some shortening of the base-CNT distance by ca 0.13Ǻ. The visualization of the electrostatic potential distribution with the molecular graphics reveals that the positive potential due to the protonated bases extends to a cylindrical domain of the nanotube segment adjacent to the base binding site. Furthermore, subtraction of the electrostatic potential maps of the protonated bases from the maps of their complexes with CNTs reveals an area of negative potential on the CNT surface, which reflects the location of the adsorbed base. The positive charge transfer of ca 0.3 e from the protonated bases to the CNT strengthens the interaction in the CNT·Cyt·H+ and СNT·Ade·H+ complexes. The analysis of the frontier orbitals shows that the LUMOs of the complexes mainly reside on the CNT, while the HOMOs spread over both components of each complex. The observed effects may facilitate the design of nanomaterials involving nitrogen bases and CNTs.

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 17.4 kcal mol(-1) , respectively. Encapsulation equilibrium constants are computed by using partition functions based on the M06-2X/6-31G** and M06-2X/6-31++G** molecular data. Under high-temperature/high-pressure conditions, similar to that for the encapsulation of rare gases in fullerenes, the computed (H2 O)2 @C84 -to-H2 O@C84 ratio is close to 1:2.

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. The interaction energies corresponding to the graphene hybrids of the F1-F4 compounds for the two directions are found to be distinct, while tetracene (being a symmetrical molecule) shows a small difference between these binding energies. It is found that the back-side CH3 and CF3 groups have an important influence on the arrangements of F1 derivatives on graphene and on their binding energies. The contribution of the CF3 group to the total binding energy of the F3 molecule with graphene is the largest (3.4 kcal mol(-1) ) (the GZZ direction) while the CH3 group increases this energy of F2 only by 2.0 kcal mol(-1) (the GAC direction). It is shown that replacing the carbons with other atoms or adding a back-side group enables one to vary the polarizability of graphene.

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. Phys. 122, 024108 (2005)] suffered from a problem of energy discontinuities when the formal reference state was changing in the calculation of the potential energy curve (PEC). A simple remedy to the discontinuity problem is found and is presented in this work. It involves using natural complete active space self-consistent field active orbitals in the complete active space coupled-cluster calculations. The approach gives smooth PECs for different types of dissociation problems, as illustrated in the calculations of the dissociation of the single bond in the hydrogen fluorine molecule and of the symmetric double-bond dissociation in the water molecule.

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. The results allow to determine the ortho-para spin isomerization energies as a function of the vibrational quantum number.

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. The effectiveness of the new Gaussians in describing non-BO pure vibrational states is investigated by comparing them with r(m)-Gaussians containing preexponential multipliers in the form of non-negative powers of internuclear distances (the internuclear distance in the diatomic case). The testing is performed for a diatomic system with the nuclei interacting through a Morse potential. It shows that the new sin/cos-Gaussian basis set is capable of providing equally accurate results as obtained with the r(m)-Gaussians. However, especially for lower vibrational states, more sin/cos-Gaussians are needed to reach a similar accuracy level as obtained with the r(m)-Gaussians. Implementation of the sin/cos-Gaussians in non-BO calculations of diatomic and, in particular, of triatomic systems, which will follow, will provide further assessment of the efficiency of the new functions.

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.

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. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.