Spectral difference Lanczos method for efficient time propagation in quantum control theory

Spectral difference methods represent the real-space Hamiltonian of a quantum system as a banded matrix which possesses the accuracy of the discrete variable representation (DVR) and the efficiency of finite differences. When applied to time-dependent quantum mechanics, spectral differences enhance the efficiency of propagation methods for evolving the Schrodinger equation. We develop a spectral difference Lanczos method which is computationally more economical than the sinc-DVR Lanczos method, the split-operator technique, and even the fast-Fourier-Transform Lanczos method. Application of fast propagation is made to quantum control theory where chirped laser pulses are designed to dissociate both diatomic and polyatomic molecules. The specificity of the chirped laser fields is also tested as a possible method for molecular identification and discrimination.     

Full S matrix calculation via a single real-symmetric Lanczos recursion: the Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H(2) reaction, revealing excellent performance characteristics.     

Quantum theory of chemical reactions in the presence of electromagnetic fields

We present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set representation of the total wave function in the space-fixed coordinate frame, the Fock-Delves hyperspherical coordinates, and the adiabatic partitioning of the total Hamiltonian of the reactive system. The adiabatic channel wave functions are expanded in basis sets of hyperangular functions corresponding to different reaction arrangements, and the interactions with external fields are included in each chemical arrangement separately. We apply the theory to examine the effects of electric fields on the chemical reactions of LiF molecules with H atoms and HF molecules with Li atoms at low temperatures and show that electric fields may enhance the probability of chemical reactions and modify reactive scattering resonances by coupling the rotational states of the reactants. Our preliminary results suggest that chemical reactions of polar molecules at temperatures below 1 K can be selectively manipulated with dc electric fields and microwave laser radiation.     

Quantum and classical dynamics of wave packets in an electromagnetic plane wave

Dynamics of a charged particle in a plane wave electromagnetic field is analyzed using the relativistic quantum and classical theory. Relativistic quantum dynamics is based on the Klein-Gordon equation. It is shown that the classical theory reproduces quantum results almost exactly.     

The symmetric groups and the Waller–Hartree spin-free method

The relations between the Waller–Hartree spin-free method and the symmetric group theory are given. It is shown that the Gallup method is a special case of ours with S = M. Furthermore, all the irreducible representation matrices and other matrices needed are written explicitly in terms of Sanibel coefficients which makes the method more useful. However, it was shown that the cases with S ≠ M for the spin-free pure spin states might be beyond the power of the symmetric group theory.     

Computing resonance energies, widths, and wave functions using a Lanczos method in real arithmetic

We introduce new ideas for calculating resonance energies and widths. It is shown that a non-Hermitian-Lanczos approach can be used to compute eigenvalues of H+W, where H is the Hamiltonian and W is a complex absorbing potential (CAP), without evaluating complex matrix-vector products. This is done by exploiting the link between a CAP-modified Hamiltonian matrix and a real but nonsymmetric matrix U suggested by Mandelshtam and Neumaier [J. Theor. Comput. Chem. 1, 1 (2002)] and using a coupled-two-term Lanczos procedure. We use approximate resonance eigenvectors obtained from the non-Hermitian-Lanczos algorithm and a very good CAP to obtain very accurate energies and widths without solving eigenvalue problems for many values of the CAP strength parameter and searching for cusps. The method is applied to the resonances of HCO. We compare properties of the method with those of established approaches.     

Quantum simulation of a hydrated noradrenaline analog with the torsional path integral method

An extended version of the torsional path integral Monte Carlo (TPIMC) method is presented and shown to be useful for studying the conformation of flexible molecules in solvated clusters. The new technique is applied to the hydrated clusters of the 2-amino-1-phenyl-ethanol (APE) molecule. APE + nH2O clusters with n = 0-4 are studied at 100 and 300 K using both classical and quantum simulations. Only at the lower temperature is the hydration number n found to impact the conformational distribution of the APE molecule. This is shown to be a result of the temperature-dependent balance between the internal energy and entropy contributions to the relative conformer free energies. Furthermore, at 100 K, large quantum effects are observed in the calculated conformer populations. A particularly large quantum shift of 30% of the total population is calculated for the APE + 2H2O cluster, which is explained in terms of the relative zero point energy of the lowest-energy hydrated structures for this cluster. Finally, qualitative agreement is found between the reported calculations and recent spectroscopy experiments on the hydrated clusters of APE, including an entropically driven preference for the formation of AG-type hydrated structures and the formation of a water "droplet" in the APE + 4H2O cluster.     

The conjugate gradient method applied to the direct second-order minimization of energy

The conjugate gradient method is proposed for minimizing the second-order Δε. Formulae for derivatives are expressed in a constructive way: they specify to which derivatives and with which weight each integral (belonging to a non-redundant list) contributes. The case of geminal functions is fully treated. A test calculation on the BeH molecule is shown.     

Multidimensional quantum trajectories: applications of the derivative propagation method

In a previous publication [J. Chem. Phys. 118, 9911 (2003)], the derivative propagation method (DPM) was introduced as a novel numerical scheme for solving the quantum hydrodynamic equations of motion (QHEM) and computing the time evolution of quantum mechanical wave packets. These equations are a set of coupled, nonlinear partial differential equations governing the time evolution of the real-valued functions C and S in the complex action, S=C(r,t) + iS(r,t)/Planck's over 2pi, where Psi(r,t)=exp(S). Past numerical solutions to the QHEM were obtained via ensemble trajectory propagation, where the required first- and second-order spatial derivatives were evaluated using fitting techniques such as moving least squares. In the DPM, however, equations of motion are developed for the derivatives themselves, and a truncated set of these are integrated along quantum trajectories concurrently with the original QHEM equations for C and S. Using the DPM quantum effects can be included at various orders of approximation; no spatial fitting is involved; there is no basis set expansion; and single, uncoupled quantum trajectories can be propagated (in parallel) rather than in correlated ensembles. In this study, the DPM is extended from previous one-dimensional (1D) results to calculate transmission probabilities for 2D and 3D wave packet evolution on coupled Eckart barrier/harmonic oscillator surfaces. In the 2D problem, the DPM results are compared to standard numerical integration of the time-dependent Schrodinger equation. Also in this study, the practicality of implementing the DPM for systems with many more degrees of freedom is discussed.     

Comparative study on interaction of bovine serum albumin with dissymmetric and symmetric gemini surfactant by spectral method

The interaction between bovine serum albumin (BSA) with N, N′-bis(dimethylalkyl) ethylammonium dibromide (C₁₂C₂C_m, m = 8, 12) was investigated by spectral methods. It can be seen that C₁₂C₂C₈ and C₁₂C₂C₁₂ mainly interact with tryptophan residues of BSA from synchronous fluorescence spectra. Fluorescence, far-UV, and near-UV circular dichrosim spectra of BSA are changed by addition of dissymmetric and symmetric gemini surfactant. For surfactant solution, the polarity of the microenvironment surrounding pyrene is lower while the fluorescence lifetime of it is longer and the microviscosity is higher in the presence of BSA than those in the absence of BSA. But compared with C₁₂C₂C₁₂, C₁₂C₂C₈ has lower binding ability with BSA due to the shorter hydrophobic tail and lower symmetry.     

New four-stages symmetric six-step method with improved phase properties for second order problems with periodical and/or oscillating solutions

In this paper, we build, for the first time in the literature, a new four-stages symmetric six-step finite difference pair with optimized properties. The method:

1. 1.
   is a symmetric non-linear six-step method,
    
2. 2.
   is of four stages
    
3. 3.
   is of fourteenth algebraic order,
    
4. 4.
   has eliminated the phase-lag,
    
5. 5.
   has eliminated the first and second derivatives of the phase-lag.
    

An analysis of the new proposed method is given in details in this paper. More specifically, we present:

1. 1.
   the building of the new four-stages symmetric six-step method,
    
2. 2.
   the computation of the local truncation error of the new proposed method,
    
3. 3.
   the comparative local truncation error analysis of the new proposed method with other finite difference pairs of the same family.
    
4. 4.
   the stability and the interval of periodicity analysis and
    
5. 5.
   finally, the investigation and evaluation of the computational efficiency of the new proposed scheme for the approximate solution of the Schrödinger equation.
    

The theoretical, computational and numerical results for the new proposed method show its effectiveness compared with other known or recently obtained finite difference pairs in the literature.

     

Control of glued structures by the electromagnetic acoustic variant of the impedance method

The functionality of the electromagnetic acoustic variant of the impedance method of controlling multilayer glued structures with metallic casings is studied. It is shown that the main advantage of this variant is the possibility of carrying out control without any direct contact of the working part of the converter with the surface of the examined article.     

Single and double Suzuki-Miyaura couplings with symmetric dihalobenzenes

[reaction: see text] m- or p-Diiodobenzene undergoes selective double coupling reactions with arylboronic acids and esters. Selectivity for double coupling over single coupling is remarkably strong: even with a diiodobenzene:monoboronic acid ratio of 10:1, the products of double coupling are formed in good yields. Steric hindrance and electronic influences of the boronic acid or ester, and reaction conditions do not appear to impact significantly upon the outcome of the reaction. In contrast, m- and p-dibromobenzenes undergo single couplings with aryl boronic acids with high selectivity.     

Quantum chemical study of the substituent effect on pKa of molecules with conjugated bonds using the PPP method

It is shown that the change of pK_a of unsubstituted heterocyclic compounds on substitution is proportional to the difference of the residual -electron charges at the position where the functional group is introduced in the unsubstituted heterobase and its conjugated acid.Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 24, No. 1, pp. 13–20, January–February, 1988.The author expresses his gratitude to M. M. Mestechkin and N. G. Korzhenevskaya for the discussion.     

Line-intersection method for determining the configurational parameters of cross propagation in copolymerization

For the evaluation of the configurational parameters in cross propagation, Σ_s and Σ_p for binary vinyl type copolymers whose monomer units both contain an asymmetric carbon atom in the chain, a method is proposed which relies on intersecting straight lines in a Σ_s versus Σ_p diagram. We define Σ_s = σ_AB + σ_AB and Σ_p = σ_AB·σ_BA, σ being the probability of forming an isotactic enchainment between the monomer units when B adds to a chain ending in A, or A adds to a chain ending in B, respectively. For these definitions it is assumed that σ_AB and σ_BA are not necessarily equal in their numerical values. The method described is applicable to triad probabilities obtained both from copolymers and such homopolymers which have been prepared from copolymers under retention of configuration by a polymer analogous reaction. In this work, triad data have been evaluated which were obtained by NMR from methyl methacrylate-methacrylic acid copolymers, wherein the methyl methacrylate units were pentadeuterated on the α? CH₃ and β? CH₂ groups, as well as from methyl methacrylate homopolymers, the latter being prepared from undeuterated methyl methacrylate-methacrylic acid copolymers by esterification. The approximate values Σ_s = 0.38, Σ_p = 0.02 were obtained for the deuterated copolymers, while Σ_s = 0.392 ± 0.003 and Σ_p = 0.037 ± 0.003 were found for the undeuterated homopolymers.     

A new and efficient method for conjugate addition of trialkylphosphites to 3-acylsubstituted coumarins

A new and efficient conjugate addition of trialkylphosphites to 3-ω-bromoacetylcoumarin 1 catalysed by p-toluenesulfonic acid (TsOH) has been studied. Under the same conditions, an enolphosphate gave the corresponding esters of 3-acetyl-4-phosphono-2-oxochromans in high yields. The use of TsOH in the reaction of 3-acetyl-, 3-benzoyl-, and 3-ethoxycarbonyl coumarins led mainly to 1,4-addition products—the corresponding 3-acyl-4-dialkylphosphono-2-oxochromans—in very good yields.