Alternant systems and their properties

Neutral, ionic, and complete alternant systems are studied using the alternancy symmetry adapted (ASA ) approach. This approach is based on an explicit construction of ASA operators that are up to the sign invariant with respect to the particle-hole symmetry transformation. These operators serve as building blocks of alternant systems, and they determine their characteristic properties. All Hamiltonians describing neutral alternant systems are explicitly constructed. Up to some minor restrictions, all Hamiltonians describing ionic and complete alternant systems are also explicitly constructed. Inversely, given a Hamiltonian ? in a second quantization notation, one can easily check whether or not this Hamiltonian describes a neutral (ionic, complete) alternant system. All linear properties characteristic to neutral (ionic, complete) alternant systems are obtained. In particular, all one- and two-particle properties are derived in an explicit form. The properties obtained substantially generalize “classical” properties of alternant systems such as, in the case of neutral alternant systems, uniform charge density distribution, vanishing bond orders between atomic sites of the same parity, and alternancy selection rules for the electric dipole transitions.     

Restricted open-shell Kohn–Sham theory: N unpaired electrons

We present an energy expression for restricted open-shell Kohn–Sham theory for N unpaired electrons. It is shown that it is possible to derive an explicit energy expression for all low-spin multiplets of systems that exhibit neither radial nor cylindrical symmetry. The approach was implemented in the CPMD code and tested for iron complexes.     

Microscopic Symmetry Imposed by Rotational Symmetry Boundary Conditions in Molecular Dynamics Simulation

A large number of viral capsids, as well as other macromolecular assemblies, have icosahedral structure or structures with other rotational symmetries. This symmetry can be exploited during molecular dynamics (MD) to model in effect the full viral capsid using only a subset of primary atoms plus copies of image atoms generated from rotational symmetry boundary conditions (RSBC). A pure rotational symmetry operation results in both primary and image atoms at short range, and within nonbonded interaction distance of each other, so that nonbonded interactions can not be specified by the minimum image convention and explicit treatment of image atoms is required. As such an unavoidable consequence of RSBC is that the enumeration of nonbonded interactions in regions surrounding certain rotational axes must include both a primary atom and its copied image atom, thereby imposing microscopic symmetry for some forces. We examined the possibility of artifacts arising from this imposed microscopic symmetry of RSBC using two simulation systems: a water shell and human rhinovirus 14 (HRV14) capsid with explicit water. The primary unit was a pentamer of the icosahedron, which has the advantage of direct comparison of icosahedrally equivalent spatial regions, for example regions near a 2-fold symmetry axis with imposed symmetry and a 2-fold axis without imposed symmetry. Analysis of structural and dynamic properties of water molecules and protein atoms found similar behavior near symmetry axes with imposed symmetry and where the minimum image convention fails compared with that in other regions in the simulation system, even though an excluded volume effect was detected for water molecules near the axes with imposed symmetry. These results validate the use of RSBC for icosahedral viral capsids or other rotationally symmetric systems.     

Atom-centered symmetry functions for constructing high-dimensional neural network potentials

Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calculations, and thus enable molecular dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the atomic positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as molecules, crystalline and amorphous solids, and liquids.     

补态关系和稀土离子光谱中的电子-空穴对称性

本文用电子-空穴共轭变换讨论补态关系,考察了存在于三价稀土离子光谱中的电子-空穴对称性。     

Practical modeling of molecular systems with symmetries

A new method for efficient modeling of macromolecular systems with symmetries is presented. The method is based on a hierarchical representation of the molecular system and a novel fast binary tree‐based neighbor list construction algorithm. The method supports all types of molecular symmetry, including crystallographic symmetry. Testing the proposed neighbor list construction algorithm on a number of different macromolecular systems containing up to about 200,000 of atoms shows that (1) the current binary tree‐based neighbor list construction algorithm scales linearly in the number of atoms for the central subunit, and sublinearly for its replicas, (2) the overall computational overhead of the method for a system with symmetry with respect to the same system without symmetry scales linearly with the cutoff value and does not exceed 50% for all but one tested macromolecules at the cutoff distance of 12 Å. (3) the method may help produce optimized molecular structures that are much closer to experimentally determined structures when compared with the optimization without symmetry, (4) the method can be applied to models of macromolecules with still unknown detailed structure. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Development of the cyclic cluster model formalism for Kohn-Sham auxiliary density functional theory methods

The development of the cyclic cluster model (CCM) formalism for Kohn-Sham auxiliary density functional theory (KS-ADFT) methods is presented. The CCM is a direct space approach for the calculation of perfect and defective systems under periodic boundary conditions. Translational symmetry is introduced in the CCM by integral weighting. A consistent weighting scheme for all two-center and three-center interactions appearing in the KS-ADFT method is presented. For the first time, an approach for the numerical integration of the exchange-correlation potential within the cyclic cluster formalism is derived. The presented KS-ADFT CCM implementation was applied to covalent periodic systems. The results of cyclic and molecular cluster model (MCM) calculations for trans-polyacetylene, graphene, and diamond are discussed as examples for systems periodic in one, two, and three dimensions, respectively. All structures were optimized. It is shown that the CCM results represent the results of MCM calculations in the limit of infinite molecular clusters. By analyzing the electronic structure, we demonstrate that the symmetry of the corresponding periodic systems is retained in CCM calculations. The obtained geometric and electronic structures are compared with available data from the literature.     

Potential magnetic properties of nanotubes (n, 0) with Klein and Fujita edges

Analytical solutions for localized states of zigzag-type nanotube (NT) fragments with various combinations of Klein and Fujita borders are considered using the Hückel approach. It is shown that the equations for determining molecular orbitals (MOs) in systems with two Klein edges are similar to equations for systems with two Fujita edges. An analytical formula for the energies of all ?? MOs is obtained for systems that have a Klein edge on one side and a Fujita edge on the other. It is established that these systems have n orbitals with energy ?? that are localized on the Fujita and Klein edges in dependence on the MO symmetry. The degeneracy of edge orbitals indicates that there is a tendency toward single occupancy of them and to the appearance of spin (magnetic) properties. In addition, the energies of the states of different multiplicity for NT fragments (8, 0) are calculated using the CASSCF approach. It is shown that the ground state has a multiplicity of 9, as was also indicated by estimates obtained using the density functional method (B3LYP). It is concluded that zigzag-type NTs with asymmetric edges have a tendency to exhibit spin properties. It is noted that the construction of nanoscale magnetic materials based on them is very promising.     

On use of the Amber potential with the Langevin dipole method

Inclusion of solvent effects in biomolecular simulations is most ideally done using explicit methods, as they are able to capture the heterogeneous environment typical of biomolecules and systems involving them (e.g., proteins at solid interfaces). Common explicit methods based on molecular solvent models (e.g., TIP and SPC models) and molecular dynamic or Monte Carlo simulation are computationally expensive and are, therefore, not well-suited to situations where many simulations are required (e.g., in the ab initio structure prediction or design contexts). In such cases, more coarse-grained explicit approaches such as the Langevin dipole (LD) method of Warshel and co-workers are more appropriate. The recent incarnations of the LD method appear to produce good solvation free energy estimates. These incarnations use charges and solute structures obtained from high-level quantum mechanics simulations. As such an approach is clearly not possible for larger solutes or when many structures are to be considered, an alternative must be sought. One possibility is to use structures and charges derived from an existing analytical potential model-we report on such a coupling here with the Amber potential model. The accuracy and computational performance of this hybrid approach, which we term LD-Amber to distinguish it from previous incarnations of the LD method, was assessed by comparing results obtained from the approach with those from experiment and other theoretical methods for the solvation of 18 amino acid analogues and the alanine dipeptide. This comparison shows that the LD-Amber approach can yield results in line with experiment both qualitatively and quantitatively and is as accurate as other explicit methods while being computationally much cheaper.     

Continuous symmetry numbers and entropy

Traditionally, entropy changes are corrected for rotational permutability only if the molecule is perfectly rotationally symmetric. By this approach, only a small fraction of all known molecules must be evaluated in terms of symmetry numbers, while all other molecules are totally exempt of these considerations. A general approach which encompasses all molecules, symmetric or not, is proposed here. It is based on introducing the notion of continuity to symmetry numbers and on allowing noninteger values. In the first part of the account, we provide arguments as to why continuity is needed and what difficulties one may encounter by adopting the "black-or-white" approach to symmetry. In the second part, we provide a working methodology of how to evaluate the symmetry number content of any molecule, symmetric or not. Finally, in the third part, we demonstrate the implications of this approach on entropy issues involving melting points, Jahn-Teller distortions (of fullerene) upon ionization, molecular distortion due to overcrowdedness, permutability of isotopes, and the structure of proton sponges. It is shown that continuous symmetry numbers provide entropy values, which better agree with experimental observations, and that they are capable of identifying correlations between symmetry and physical/chemical measurables.     

Ab Initio Construction of Quasiadiabatic Potential-Energy Surfaces for Cycloaddition Reactions of Ethene and Substituted Allylic Cations

The nature of some well known 2π + 2π cycloaddition reactions was studied by explicit construction of the quasiadiabatic potential-energy surfaces for the cycloaddition of ethene and various monosubstituted allylic cations. Such surfaces determined by ab initio MO computations are particularly suitable for analysis of symmetry selection rules. By examining the characteristics of such surfaces, we have studied the substituent effect and the role played by the positive charge in such systems. Qualitative discussion based on simplified MO, involving fewer electrons, is also given.     

Graphical techniques in the configuration interaction approach based on pure slater determinants

A graphical approach to the configuration interaction in the basis of pure Slater determinants is presented. The formulation based on the spin-separated two-slope graph (SSTSG ), enabling the selection of determinants with the fixed M_s value, has a direct relation to the well-known concept of the group-function product. The commonly used excitation criterion and the spatial (Abelian) symmetry properties are analyzed in terms of the graph's internal structure. The Slater formulae for the Hamiltonian matrix elements between determinants, in the particle-hole formalism and in the spin-separated form, are related to different classes of loops within graphs. Some aspects of implementation within both the matrix-element-driven (ME ) and integral driven (ID , direct) CI algorithms are discussed. The presented formulation, of a general complete active space (CAS ) CI type, is a basis of the Graphical Determinantal Configuration Interaction (GDCI ) computer program.     

Direct MRCI method for the calculation of relativistic many-electron wavefunctions. I. General formalism

The formalism of a quasi- or full-relativistic multireference CI method has been developed and implemented. The scheme is appropriate for the calculation of molecular systems in which the relativistic effects are of the same order of magnitude as the correlation contributions. In this contribution some important symmetry aspects of a relativistic many-electron wave function are discussed and the consequences for the CI matrix structure are shown. An efficient CI strategy in the form of a direct CI is presented, which avoids the construction of the whole CI matrix. Based on a determinantal expansion of molecular spinor products, the individual one- and two-electron molecular integrals are processed, and the molecular symmetry is easily accounted for by a proper linear combination of Slater determinants in the CI starting vector. For an efficient CI organization some powerful techniques of the graphical unitary group approach have been transferred to the relativistic case.     

The structure of intermediate ribbon phases in surfactant systems

Intermediate phases consisting of elongated rods with a non-circular cross section (i.e. ribbons) that pack on a deformed hexagonal lattice are often formed in surfactant systems. The crystallographic lattice of such a ribbon phase can be either of oblique (or two dimensional monoclinic), primitive rectangular, centred rectangular or hexagonal symmetry, all of which are observed according to the literature. We have studied a ribbon phase that is formed in the dodecyl-1,3-propylene-bisamine/HCl/water system, by means of SAXS experiments, and a centred rectangular structure is obtained. In addition, we have reviewed, and partially reinterpreted, previously published results on the structure of different ribbon phases. 21 scattering data sets for ribbon phases of lower than hexagonal symmetry have been analysed. Both the centred rectangular (cmm) and the primitive rectangular (pmm) symmetry fit 10 of the data sets, whereas only a centred rectangular lattice can be fitted to the other 11 data sets. There is no experimental indication that supports the existence of an oblique ribbon (p2) phase. The underlying physical reasons for the observation that the centred rectangular structure is favoured are discussed in terms of a cell model approach. The energetically most favoured cell model has a centred rectangular symmetry (cmm), in accord with the experimental data, and is termed the hexagon-rod model. This model can be used to evaluate the dimensions of the deformed rods of the centred rectangular ribbon phase from scattering data and NMR data separately. One major advantage of the hexagon-rod model is that the smallest dimension of the aggregate is not required as an input parameter in the calculations. Axial ratios between 1·2:1:1-2:1 for the aggregates are obtained when this model is applied to SAXS, SANS and NMR data for the centred rectangular ribbon phase for none different systems.     

The structure of intermediate ribbon phases in surfactant systems

Abstract

Intermediate phases consisting of elongated rods with a non-circular cross section (i.e. ribbons) that pack on a deformed hexagonal lattice are often formed in surfactant systems. The crystallographic lattice of such a ribbon phase can be either of oblique (or two dimensional monoclinic), primitive rectangular, centred rectangular or hexagonal symmetry, all of which are observed according to the literature. We have studied a ribbon phase that is formed in the dodecyl-1,3-propylene-bisamine/HCl/water system, by means of SAXS experiments, and a centred rectangular structure is obtained. In addition, we have reviewed, and partially reinterpreted, previously published results on the structure of different ribbon phases. 21 scattering data sets for ribbon phases of lower than hexagonal symmetry have been analysed. Both the centred rectangular (cmm) and the primitive rectangular (pmm) symmetry fit 10 of the data sets, whereas only a centred rectangular lattice can be fitted to the other 11 data sets. There is no experimental indication that supports the existence of an oblique ribbon (p2) phase. The underlying physical reasons for the observation that the centred rectangular structure is favoured are discussed in terms of a cell model approach. The energetically most favoured cell model has a centred rectangular symmetry (cmm), in accord with the experimental data, and is termed the hexagon-rod model. This model can be used to evaluate the dimensions of the deformed rods of the centred rectangular ribbon phase from scattering data and NMR data separately. One major advantage of the hexagon-rod model is that the smallest dimension of the aggregate is not required as an input parameter in the calculations. Axial ratios between 1·2:1:1-2:1 for the aggregates are obtained when this model is applied to SAXS, SANS and NMR data for the centred rectangular ribbon phase for none different systems.     

Analysis of pseudo jahn–teller distortion based on natural bond orbital theory: Case study for silicene

Ground state (GS) instability of nondegenerate molecules in high symmetric structures is understood through Pseudo Jahn–Teller mixing of the electronic states through the vibronic coupling. The general approach involves setting up of a Pseudo Jahn–Teller (PJT) problem wherein one or more symmetry allowed excited states couple to the GS to create vibrational instability along a normal mode. This faces two major complications namely (1) estimating the adiabatic potential energy surfaces for the excited states which are often difficult to describe in case the excited states have charge-transfer or multi-excitonic (ME) character and (2) finding out how many such excited states (all satisfying the symmetry requirements for vibronic coupling) of increasing energies need to be coupled with the GS for a particular PJT problem. An analogous alternative approach presented here for the well-known case of symmetry breaking of planar (D_6h) hexasilabenzene (Si₆H₆) to the buckled (D_3d) structure involves identifying the second-order donor–acceptor, hyperconjugative interactions (E²_{i → j}) that stabilize the distorted structure. Following the recent work of Nori-Shargh and Weinhold, one observes that the orbitals involved in the vibronic coupling between the S₀/S_n states and those for the donor (filled)–acceptor (empty) interactions are identical. In fact, deletion of any particular pair of E²_{i → j} interaction creates vibrational instability in the buckled structure and as a corollary, deleting it for the planar structure removes its instability. The one-to-one correlation between the natural bond orbital theory and PJT theory assists in an intuitive identification of the relevant (few) excited states from a manifold of computed ones that cause symmetry breaking by vibronic coupling. © 2019 Wiley Periodicals, Inc.     

Atom distributions in binary atom clusters: a perturbational approach and its validation in a case study

An approach to describe heteroatomic clusters A(n)B(N-n) as perturbed homoatomic ones is presented. By first treating the homoatomic systems A(N) or/and B(N) and subsequent application of first-order perturbation theory it is possible to estimate relative stabilities of the 2(N) possible distributions of the atom types A and B at the N atomic sites in a very efficient manner. The approach was tested considering Ir(n)Pt(13-n) as an example (treated with density functional methods). One observes good correlation between relative stabilities estimated from the homoatomic cases and those obtained from explicit treatments of the binary systems. Moreover we rationalize the observed correlation of atom type and atom position in Ir(n)Pt(13-n).     

Quasispin symmetry for the derivation of coupled cluster equations for the Hubbard model of benzene

The concept of quasispin is applied to a special case of the Pariser–Parr–Pople (PPP ) model of the benzene molecule, namely, the Hubbard Hamiltonian. Added to the spin, space, and alternancy symmetries already taken into account in the PPP Hamiltonian, this new symmetry, called quasispin symmetry, has the effect of reducing the size of the CI matrix. Coupled cluster (CC ) equations are then obtained after applying the CC approach with doubles as well as its extension that accounts for triexcited clusters (CCSDT -1). The derivation of these equations following the use of quasispin to the Hubbard model of benzene constitutes the most simple nontrivial example of CC results. In addition, the CC equations can be written in explicit algebraic form using the symbolic computation language MAPLE.     

Calculation of correlation energy by many-body diagrammatic perturbation theory

The many-body diagrammatic perturbation theory is used for calculation of the correlation energy of closed-shell molecular systems. We apply Brueckner's concept of the two-particle renormalized interaction defined by a non-linear diagrammatic expression containing all possible (diagonal and/or non-diagonal) particle-particle, hole-hole and particle-hole intermediate elementary processes. Then, a “second-order” simple diagrammatic expression for the correlation energy can be formed, where the correlation energy is approximated by all the diagrams with biexcited intermediate states. An illustrative numerical application for the LiH molecule is presented. This article is dedicated to the memory of our friends and colleagues Dr. Jarka Surá and Dr. Marta Černayová, who tragically died in July 1976.