The use of symmetry in direct Møller-Plesset second-order calculations

Summary An algorithm for utilising abelian point group symmetry in direct MP2 energy calculations is presented. This is based upon the direct MP2 method of Head-Gordon, Pople and Frisch. The method uses the petite atomic orbital integral list as in conventional transformations coupled with a symmetry adaption of the three quarter transformed integrals. Representative calculations for ethylene and benzene are presented which demonstrate the potential of the method.     

General method for symmetry orbitals and tensors in electronic structure calculations

The symmetry orbital tensor (SOT) method, which makes full use of symmetries in all point groups and can be applied to the self-consistent field (SCF) and post-SCF calculations, is introduced. The principal feature of this method is the definition of the symmetry orbitals (SOs). Any element in a molecular point group will transform one SO to another equivalent SO or simply to itself, and no mixture among SOs exists. Thus, although the SOs for non-Abelian point groups may adapt to reducible representations, their transformation properties are much simpler than in conventional treatments. This article also presents a general scheme to generate SOs for all point groups. The direct products of N SOs form an Nth-rank SOT group, and each matrix element between SOTs is the product of a physical factor and a geometric factor. Compared with the canonical molecular orbitals, the use of SOs can noticeably reduce the computation efforts by decreasing the number of integrals needed in the SCF calculations or the number of configurations needed in the configuration interaction (CI) calculations. The SOT-SCF and SOT-CI approaches are formulated and a preliminary SOT-SCF program is written. Pilot calculations demonstrate the value of the SOT approach, at least at the closed-shell Hartree–Fock level. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 305–321, 1999     

Mid-IR synchrotron radiation for molecular specific detection in microchip-based analysis systems

Microstructures constructed from SU-8 polymer and produced on CaF₂ base plates have been developed for microchip-based analysis systems used to perform FTIR spectroscopic detection using mid-IR synchrotron radiation. The high brilliance of the synchrotron source enables measurements at spot sizes at the diffraction limit of mid-IR radiation. This corresponds to a spatial resolution of a few micrometers (5–20 m). These small measurement spots are useful for lab-on-a-chip devices, since their sizes are comparable to those of the structures usually used in these devices. Two different types of microchips are introduced here. The first chip was designed for time-resolved FTIR investigations of chemical reactions in solution. The second chip was designed for chip-based electrophoresis with IR detection on-chip. The results obtained prove the operational functionality of these chips, and indicate the potential of these new devices for further applications in (bio)analytical chemistry.     

Symmetrizer: Algorithmic determination of point groups in nearly symmetric molecules

Symmetry is an extremely useful and powerful tool in computational chemistry, both for predicting the properties of molecules and for simplifying calculations. Although methods for determining the point groups of perfectly symmetric molecules are well‐known, finding the closest point group for a “nearly” symmetric molecule is far less studied, although it presents many useful applications. For this reason, we introduce Symmetrizer, an algorithm designed to determine a molecule's symmetry elements and closest matching point groups based on a user‐adjustable tolerance, and then to symmetrize that molecule to a given point group geometry. In contrast to conventional methods, Symmetrizer takes a bottom‐up approach to symmetry detection by locating all possible symmetry elements and uses this set to deduce the most probable point groups. We explain this approach in detail, and assess the flexibility, robustness, and efficiency of the algorithm with respect to various input parameters on several test molecules. We also demonstrate an application of Symmetrizer by interfacing it with the WebMO web‐based interface to computational chemistry packages as a showcase of its ease of integration. © 2012 Wiley Periodicals, Inc.     

Stochastic quantum molecular dynamics for finite and extended systems

We present a detailed account of the technical aspects of stochastic quantum molecular dynamics, an approach introduced recently by the authors [H. Appel, M. Di Ventra, Phys. Rev. B 80 (2009) 212303] to describe coupled electron-ion dynamics in open quantum systems. As example applications of the method we consider both finite systems with and without ionic motion, as well as describe its applicability to extended systems in the limit of classical ions. The latter formulation allows the study of important phenomena such as decoherence and energy relaxation in bulk systems and surfaces in the presence of time-dependent fields.     

Phase-fixed double-group 3-Γ symbols. II. General features of double groups and their 3-Γ symbols

Following a general exposition of the theory of 3- symbols [1], we now focus on the particular features encountered when dealing with double groups of (proper as well as improper) point groups.The paper starts with a brief outline of the definition of double groups adopted in the present work. After this, some properties of double group 3- symbols are discussed which are independent of the way the 3- symbols have been constructed. The main part of the paper then deals with the actual generation of 3- symbols for the non-commutative double groups.In the approach described, the 3- symbols become determined in part by adaption of the standard matrix irreps to subgroup hierarchies and then completely, phases included, by the specification of standard basis functions (or, equivalently, standard subduction coefficients).     

COMPLX: a computer algorithm for the detection of protein-ligand and other macromolecular complexes in mass spectra

A new algorithm has been designed and tested to identify protein, or any other macromolecular, complexes that have been widely reported in mass spectral data. The program takes advantage of the appearance of multiply charged ions that are common to both electrospray ionization and, to a lesser extent, matrix-assisted laser desorption/ionization (MALDI) mass spectra. The algorithm, known as COMPLX for the COMposition of Protein-Ligand compleXes, is capable of identifying complexes for any protein or macromolecule with a binding partner of molecular mass up to 100 000 Da. It does so by identifying ion pairs present in a mass spectrum that, when they share a common charge, have an m/z value difference that is an integer fraction of a ligand or binding partner molecular mass. Several additional criteria must be met in order for the result to be ranked in the output file including that all m/z values for ions of the protein or complex have progressively lower values as their assigned charge increases, the difference between the m/z values for adjacent charge states (z, z + 1) decrease as the assigned charge state increases, and the ratio of any two m/z values assigned to a protein or complex is equal to the inverse ratio of their charge. The entries that satisfy these criteria are then ranked according to the appearance of ions in the mass spectrum associated with the binding partner, the length of a continuous series of charges across any set of ions for a protein and complex and the lowest error recorded for the molecular mass of the ligand or binding partner. A diverse range of hypothetical and experimental mass spectral data were used to implement and test the program, including those recorded for antibody-peptide, protein-peptide and protein-heme complexes. Spectra of increasing complexity, in terms of the number of ions input, were also successfully analysed in which the number of input m/z values far exceeds the few associated with a macromolecular complex. Thus the program will be of value in a future goal of proteomics, where mass spectrometry already plays a central role, for the direct analysis of protein and other associations within biological extracts.     

Enhanced sampling method in molecular simulations using genetic algorithm for biomolecular systems

We propose a molecular simulation method using genetic algorithm (GA) for biomolecular systems to obtain ensemble averages efficiently. In this method, we incorporate the genetic crossover, which is one of the operations of GA, to any simulation method such as conventional molecular dynamics (MD), Monte Carlo, and other simulation methods. The genetic crossover proposes candidate conformations by exchanging parts of conformations of a target molecule between a pair of conformations during the simulation. If the candidate conformations are accepted, the simulation resumes from the accepted ones. While conventional simulations are based on local update of conformations, the genetic crossover introduces global update of conformations. As an example of the present approach, we incorporated genetic crossover to MD simulations. We tested the validity of the method by calculating ensemble averages and the sampling efficiency by using two kinds of peptides, ALA3 and (AAQAA)₃. The results show that for ALA3 system, the distribution probabilities of backbone dihedral angles are in good agreement with those of the conventional MD and replica-exchange MD simulations. In the case of (AAQAA)₃ system, our method showed lower structural correlation of α-helix structures than the other two methods and more flexibility in the backbone ψ angles than the conventional MD simulation. These results suggest that our method gives more efficient conformational sampling than conventional simulation methods based on local update of conformations. © 2018 Wiley Periodicals, Inc.     

Hindered internal rotation in molecular systems: quantum statistics of equilibrium and rate constants in the Wigner function formalism

Summary The quantum statistics of a symmetric hindered internal rotator in a molecule or molecular complex is developed within the Wigner function formalism. Different shapes of the rotational barrier are considered. The partition function and the thermodynamic functions are given as Wigner-Kirkwood series expansions in terms of powers of Planck's constant squared. One gets simple closed expressions containing the modified Bessel functionsJ ₀ andJ ₁ of the argumentiV ₀/2kT whereV ₀ is the barrier height. Some problems concerning the evaluation of equilibrium and rate constants of chemical reactions are discussed.Supported by the Alexander von Humboldt-Stiftung     

Performance of the computer algorithm COMPLX for the detection of protein complexes in the mass spectra of simulated biological mixtures

The performance of the algorithm COMPLX for detecting protein-ligand or other macromolecular complexes has been tested for highly complex data sets. These data contain m/z values for ions of proteins of the SWISS-PROT database within simulated biological mixtures where each component shares a similar molecular weight and/or isoelectric point (pI). As many as 1600 ion signals were entered to challenge the algorithm to identify ion signals associated with a single protein complex that has been ionised and detected within a mass spectrometer. Despite the complexity of such data sets, the algorithm is shown to be able to identify the presence of individual bimolecular complexes. The output data can be re-evaluated by the user as necessary in light of any additional information that is known concerning the nature of predicted associations, as well as the quality of the data-set in terms of errors in m/z values as a direct consequence of the mass calibration or resolution achieved. The data presented illustrates that the best results are obtained when output results are ranked according to the largest continuous series of ion pairs detected for a protein or macromolecule and its complex for which the ligand mass is assigned the lowest mass error.     

New implementation of molecular double point‐group symmetry in four‐component relativistic Gaussian‐type spinors

A new, practical implementation of double‐group symmetry to relativistic Gaussian spinors is presented for four‐component relativistic molecular calculations. We show that the systematic adaptability to irreducible representations under arbitrary point‐group symmetry, as well as Kramers (time‐reversal) symmetry, is inherent in the present basis spinors, which possess the analytic structure of Dirac atomic spinors. The implementation of double‐group symmetry entails significant computational efficiencies in the relativistic second‐order Møller–Plesset perturbation calculation on Au₂ and the density functional theory (DFT) calculation with the B3LYP functional on octahedral UF₆, in which the highest symmetries used are, respectively, C and D. The four‐component B3LYP equilibrium geometry of UF₆ is reported. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Fast construction of assembly trees for molecular graphs

A number of modeling and simulation algorithms using internal coordinates rely on hierarchical representations of molecular systems. Given the potentially complex topologies of molecular systems, though, automatically generating such hierarchical decompositions may be difficult. In this article, we present a fast general algorithm for the complete construction of a hierarchical representation of a molecular system. This two-step algorithm treats the input molecular system as a graph in which vertices represent atoms or pseudo-atoms, and edges represent covalent bonds. The first step contracts all cycles in the input graph. The second step builds an assembly tree from the reduced graph. We analyze the complexity of this algorithm and show that the first step is linear in the number of edges in the input graph, whereas the second one is linear in the number of edges in the graph without cycles, but dependent on the branching factor of the molecular graph. We demonstrate the performance of our algorithm on a set of specifically tailored difficult cases as well as on a large subset of molecular graphs extracted from the protein data bank. In particular, we experimentally show that both steps behave linearly in the number of edges in the input graph (the branching factor is fixed for the second step). Finally, we demonstrate an application of our hierarchy construction algorithm to adaptive torsion-angle molecular mechanics.     

Finite group theory for large systems. 3. Symmetry-generation of reduced matrix elements for icosahedral C(20) and C(60) molecules

This paper uses symmetry-generation to simplify the determination of Hamiltonian reduced matrix elements. It is part of a series on using computers to apply finite group theory to quantum mechanical calculations on large systems. Symmetry-generation is an expression of the whole molecule as a sum of symmetry transformations on a smaller reference structure. Then on a suitably-conditioned symmetry-adapted basis, the reduced matrix elements of the Hamiltonian are averages of certain elements of the simpler reference structure matrix. The smaller the reference structure, the greater is the computational savings. Single atom reference structures are used here for the Hückel treatment of icosahedral C(20) and C(60) fullerenes. The analytical power of this approach is illustrated by determining the two bond lengths of C(60) from spectral data.     

Efficient treatment of out-of-plane bend and improper torsion interactions in MM2, MM3, and MM4 molecular mechanics calculations

Simple and very efficient formulas are presented for four-body out-of-plane bend (used in MM2 and MM3 force fields) and improper torsion (used in the MM4 force field) internal coordinates and their first and second derivatives. The use of a small set of bend and stretch intermediates allows for order of magnitude decreases in calculation time for potential energies and their first and second derivatives, which are required in molecular mechanics calculations. The formulas are eminently suitable for use in molecular simulations of systems with complicated bond networks. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1804–1811, 1997     

Local physical quantities for spin based on the relativistic quantum field theory in molecular systems

Local physical quantities for spin are investigated on the basis of the four‐ and two‐component relativistic quantum theory. In the quantum field theory, local physical quantities for spin such as the spin angular momentum density, spin torque density, zeta force density, and zeta potential play important roles in spin dynamics. We discuss how to calculate these local physical quantities based on the two‐component relativistic quantum theory. Some different types of relativistic numerical calculations of local physical quantities in Li atom and C₆H₆ are demonstrated and compared. Local physical quantities for each orbital are also discussed, and it is seen that a total local zeta potential is given as a result of some cancellation of large contributions from each orbital. © 2016 Wiley Periodicals, Inc.     

Algorithms for the assessment of peak purity in liquid chromatography with photodiode-array detection. Part II

Two modifications of the algorithm based on the Gram-Schmidt orthogonalization technique for the assessment of peak purity are presented. The performance of this approah is investigated for liquid chromatography with photodiode-array detection (LC-DAD) data, although its applicability is not restricted to this experimental model. This method is applied to simulated and experimental data where two compounds are eluting, but can be applied when more compounds are eluting. The results are compared with the ones obtained previously with the first version of this algorithm.     

Peak parking method for measurement of molecular diffusivity in liquid phase systems

The combination of series of measurements of band broadening made with the peak parking (PP) method, using successively an open capillary tube and a HPLC column, gives a convenient procedure for the measurement of the molecular diffusivity (D_m) of compounds in solutions, of their axial dispersion coefficient (D_ax,m) in chromatographic columns, and of the tortuosity or obstructive factor of the column bed. The molecular diffusivity measured for benzene in methanol was in excellent agreement with literature data. The ratio of the axial dispersion coefficient to this diffusivity gives the obstructive factor (γ_m) of the packed bed, which was 0.74 for the column used. The values of D_m in other solutions were obtained from the D_ax,m values measured by the PP method, by correcting the D_ax,m values with the γ_m value. The D_m values determined by this method were in good agreement with those previously reported or estimated using literature correlations. These results showed that the PP method is effective for the experimental measurement of D_m.