An efficient local coupled cluster method for accurate thermochemistry of large systems

An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described. All required two-electron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1-2 orders of magnitude, as compared to standard integral-direct methods. Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local second-order Mo?ller-Plesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented.     

Perturbative virtual SCF CI treatment for energy levels of coupled oscillator systems

A perturbative SCF CI treatment to obtain energy levels of coupled oscillator systems is proposed. The method uses the virtual SCF basis set, and the SCF equations are solved by means of a perturbative treatment that provides the diagonal matrix elements involved in the CI calculation. The off-diagonal matrix elements are calculated using a commutation relationship derived from exact quantum theorems. Numerical results for several systems are obtained and compared with those from others SCF, SCF CI , and variational treatments.     

Quantum solution of coupled harmonic oscillator systems beyond normal coordinates

Normal coordinates can be defined as orthogonal linear combinations of coordinates that remove the second order couplings in coupled harmonic oscillator systems. In this paper we go further and explore the possibility of using linear although non-orthogonal coordinate transformations to get the quantum solution of coupled systems. The idea is to use as non-orthogonal linear coordinates those which allow us to express the second-order Hamiltonian matrix in a block diagonal form. To illustrate the viability of this treatment, we first apply it to a system of two bilinearly coupled harmonic oscillators which admits analytical exact solutions. The method provides in this case, as an extra mathematical result, the analytical expressions for the eigenvalues of a certain type of symmetrical tridiagonal matrices. Second, we carry out a numerical application to the Barbanis coupled oscillators system, which contains a third order coupling term and cannot be solved in closed form. We demonstrate that the non-orthogonal coordinates used, named oblique coordinates, are much more efficient than normal coordinates to determine the energy levels and eigenfunctions of this system variationally.     

A new approach to the determination of good action-angle variables for coupled oscillator systems

A theory of action-angle variables for coupled oscillator systems is developed which involves solving the Schrödinger equation using a basis of WKB eigenfunctions, then using the logarithm of the resulting wavefunction to define the generator for the canonical transformation which determines the action-angle variables. This theory is based on the marriage between Miller's method for solving the Hamilton-Jacobi equation using the logarithm of the generating function, and the Ratner-Buch-Gerber method for solving the Schrödinger equation using WKB basis functions. A perturbation-theory analysis of this theory indicates that the semiclassical eigenvalues and canonical transformations obtained from it should become identical to their exact classical counterparts in the limit of large actions for each vibrational mode. Two methods for systematically improving the theory for the lower eigenstates are also proposed. Numerical applications of the theory are presented for two systems, the Morse oscillator and the Henon-Heiles two-mode hamiltonian. The resulting semiclassical eigenvalues are in excellent agreement with their exact quantum counterparts, with the magnitude of the error roughly independent of the energy of the eigenstate. Analogous good agreement is found in comparing the approximate and exact classical canonical transformations. In particular, for the Morse oscillator, good results are obtained for certain higher energy states where second-order classical perturbation theory makes serious errors. Other information examined includes surfaces of section for the Henon-Heiles system (comparing the analytical functions obtained from the present theory with results based on exact trajectory calculations) and vibrational distributions chosen to simulate trajectory calculations (using the present theory to determine bin boundaries for a histogram calculation). Again, the comparison in each case with accurate results is excellent, with maximum errors in action calculations of 0.02 h, and in angle calculations of 0.01 rad.     

Numerical solutions for a coupled non-linear oscillator

A second-order accurate numerical method has been proposed for the solution of a coupled non-linear oscillator featuring in chemical kinetics. Although implicit by construction, the method enables the solution of the model initial-value problem (IVP) to be computed explicitly. The second-order method is constructed by taking a linear combination of first-order methods. The stability analysis of the system suggests the existence of a Hopf bifurcation, which is confirmed by the numerical method. Both the critical point of the continuous system and the fixed point of the numerical method will be seen to have the same stability properties. The second-order method is more competitive in terms of numerical stability than some well-known standard methods (such as the Runge–Kutta methods of order two and four).     

An efficient method for large scale configuration interaction calculations

An efficient method of handling large scale configuration interaction calculations is developed and applied to the H₂O molecule as a test case. The method, which is based upon matrix partitioning, is shown to be capable of calculating the ¹B₁ spectrum of H₂O to an accuracy level of 0.1 eV for each state with very moderate computational effort.     

An elongation method for large systems toward bio-systems

The elongation method, proposed in the early 1990s, originally for theoretical synthesis of aperiodic polymers, has been reviewed. The details of derivation of the localization scheme adopted by the elongation method are described along with the elongation processes. The reliability and efficiency of the elongation method have been proven by applying it to various models of bio-systems, such as gramicidin A, collagen, DNA, etc. By means of orbital shift, the elongation method has been successfully applied to delocalized π-conjugated systems. The so-called orbital shift works in such a way that during the elongation process, some strongly delocalized frozen orbitals are assigned as active orbitals and joined with the interaction of the attacking monomer. By this treatment, it has been demonstrated that the total energies and non-linear optical properties determined by the elongation method are more accurate even for bio-systems and delocalized systems like fused porphyrin wires. The elongation method has been further developed for treating any three-dimensional (3D) systems and its applicability is confirmed by applying it to entangled insulin models whose terminal is capped by both neutral and zwitterionic sequences.     

Application of the effective harmonic oscillator method to computing the thermal averages for a system of coupled anharmonic oscillators

By treating the Hamiltonian for coupled oscillators with polynomial anharmonicity by the Gibbs-Bogoliubov inequality, the effective harmonic oscillator (EHO) method is developed and applied to computing the thermal averages for polyatomic molecules. Practical utility is demonstrated with calculations of electron diffraction quantities, namely the distance r_a and amplitude l, and of the vibrational partition functions for CO₂, CS₂, SO₂ and H₂O from spectroscopic data on the force fields. The results are compared with those in the literature obtained by more accurate techniques. A comparison of r_a and l was also made with the results of electron diffraction measurements.     

LBGK method coupled to time splitting technique for solving reaction-diffusion processes in complex systems

A new approach to numerically solve a reaction-diffusion system is given, specifically developed for complex systems including many reacting/diffusing species with broad ranges of rate constants and diffusion coefficients, as well as complicated geometry of reacting interfaces. The approach combines a Lattice Boltzmann (LB) method with a splitting time technique. In the present work, the proposed approach is tested by focusing on the typical reaction process between a metal ion M and a ligand L, to form a complex ML with M being consumed at an electrode. The aim of the paper is to systematically study the convergence conditions of the associated numerical scheme. We find that the combination of LB with the time splitting method allows us to solve the problem for any value of association and dissociation rate constant of the reaction process. Also, the method can be extended to a mixture of ligands. We stress two main points: (1) the LB approach is particularly convenient for the flux computation of M and (2) the splitting time procedure is very well suited for reaction processes involving association-dissociation rate constants varying on many orders of magnitude.     

iVI: An iterative vector interaction method for large eigenvalue problems

Based on the generic “static‐dynamic‐static” framework for strongly coupled basis vectors (Liu and Hoffman, Theor. Chem. Acc. 2014, 133, 1481), an iterative Vector Interaction (iVI) method is proposed for computing multiple exterior or interior eigenpairs of large symmetric/Hermitian matrices. Although it works with a fixed‐dimensional search subspace, iVI can converge quickly and monotonically from above to the exact exterior/interior roots. The efficacy of iVI is demonstrated by taking both mathematical and physical matrices as examples. © 2017 Wiley Periodicals, Inc.     

An accurate method for intermolecular interaction measurement at low microwave frequencies

An accurate microwave method for very sensitive measurements of intermolecular interactions of non-polar gases is described. It is based on the precise determination of the O factor of a resonant cavity using an indirect method and computer analysis of the experimental points. This method has been successfully applied for the measurement of the collision induced absorption of CO₂ at the low-frequency spectral wing.     

An organic-based pH oscillator

In a recent paper, we suggested that the acid- or base-catalyzed dehydration of a hydrated carbonyl compound provides a suitable foundation for an organic-based pH oscillator. Here we present the first experimental example of such an oscillator in a flow reactor, utilizing the base-catalyzed dehydration of methylene glycol as a source of positive feedback (OH- autocatalysis) coupled with the base-catalyzed hydrolysis of gluconolactone for negative feedback (H+ production). The large amplitude oscillations (between pH 7 and 10) are reproduced in a kinetic model of the reaction. Such experiments present new possibilities in the design of pH oscillators.     

On-line solvent evaporator for coupled LC systems

The mobile phase of a fraction eluted from a first LC column is removed by an on-line evaporator in order to reconcentrate the solute material or to exchange the eluent before performing a subsequent LC separation. Evaporation essentially occurs by concurrent evaporation, i.e. the solvent evaporates at a rate equal to the flow rate of the incoming eluent, and is driven by the overflow principle, i.e. vapors leave the tube as a result of the expansion resulting from evaporation. The liquid is introduced into a small tube (e.g., 4 cm × 1.3 mm i.d.) which is packed, e.g., with a coarse silica gel. The outlet of the evaporator is connected to vacuum in order to enable evaporation at reduced temperature and to increase retention of the volatile components. With normal phase eluents, evaporation rates may approach 1 ml/min; n-dodecane was the most volatile n-alkane fully retained by the evaporator.     

The Heitler-London interaction energy using the oscillator model

The oscillator model is used to compute the Heitler-London energy and the exchange potential for two interacting hydrogen atoms. With a single oscillator frequency it is not possible to obtain satisfactory results. Allowing the oscillator frequency to vary with internuclear separation enables reasonable values to be obtained.     

Analytic gradient for the multireference Brillouin-Wigner coupled cluster method and for the state-universal multireference coupled cluster method

We present the analytic gradient theory and its pilot implementation for the multireference Brillouin-Wigner coupled cluster (BWCC) method and for the state-universal multireference coupled cluster method. The analytic gradient has been derived for three cases: (i) BWCC method without a size-extensivity correction, (ii) BWCC method with the iterative size-extensivity correction, and (iii) for the rigorously size-extensive state-universal method. The pilot implementation is based on full-configuration interaction expansions and is presently limited to single and double excitation levels; however, the resulting equations are general. For BWCC methods, they also do not contain terms explicitly mixing amplitudes of different reference configurations and can thus be implemented in an efficient way. The analytic gradients have been verified with respect to numerically computed ones on the example of CH2 molecule, and geometry optimizations of CH2 and SiH2 have been carried out.     

A convenient method for the measurements of transverse relaxation rates in homonuclear scalar coupled spin systems

A new solution-state NMR method is proposed to determine apparent transverse NMR relaxation rates in both weakly and strongly scalar coupled two-spin systems.     

An efficient self-optimized sampling method for rare events in nonequilibrium systems

Rare events such as nucleation processes are of ubiquitous importance in real systems.The most popular method for nonequilibrium systems,forward flux sampling(FFS),samples rare events by using interfaces to partition the whole transition process into sequence of steps along an order parameter connecting the initial and final states.FFS usually suffers from two main difficulties:low computational efficiency due to bad interface locations and even being not applicable when trapping into unknown intermediate metastable states.In the present work,we propose an approach to overcome these difficulties,by self-adaptively locating the interfaces on the fly in an optimized manner.Contrary to the conventional FFS which set the interfaces with equal distance of the order parameter,our approach determines the interfaces with equal transition probability which is shown to satisfy the optimization condition.This is done by firstly running long local trajectories starting from the current interface i to get the conditional probability distribution Pc(>i|i),and then determining i+1by equaling Pc(i+1|i)to a give value p0.With these optimized interfaces,FFS can be run in a much more efficient way.In addition,our approach can conveniently find the intermediate metastable states by monitoring some special long trajectories that neither end at the initial state nor reach the next interface,the number of which will increase sharply from zero if such metastable states are encountered.We apply our approach to a two-state model system and a two-dimensional lattice gas Ising model.Our approach is shown to be much more efficient than the conventional FFS method without losing accuracy,and it can also well reproduce the two-step nucleation scenario of the Ising model with easy identification of the intermediate metastable state.     

An algorithm for self-consistent field MO LCAO computations on conjugated systems with allowance for configuration interaction

The Pariser-Parr-Pople method is described briefly. An algorithm is presented for quantum-mechanical computation of molecular structures. A program for the BESM-2M computer is presented.     

An improved fluorometric coupled enzymatic method for the determination of pyrophosphate in plasma and platelets

A fluorometric coupled enzymatic method for the determination of pyrophosphate is described. The kinetic method can determine pyrophosphate in amounts as low as 0.5 pmol. Intra- and interassay CV's were both less than 1% and recoveries were found to be quantitative. No significant interference was observed from EDTA, heparin, magnesium, or calcium. Correlation with an established method was significant (r = 0.87).Clinical studies of the applicability of the procedure were demonstrated by the measurement of pyrophosphate in plasma and platelets. Mean pyrophosphate levels in plasma and platelets of “normal” subjects were found to be 3.27 ± 0.2 μM and 2.40 ± 0.10 nmol/10⁸ platelets or 17.59 ± 1.44 nmol/mg platelet protein, respectively.Pyrophosphate levels in plasma and platelets of patients on hemodialysis were determined and found to be significantly lower than the “normal” population. This finding may in part explain the occurrence of metastatic calcification seen in this patient population.