Transferability of the electronic structure characteristics of saturated molecules

The common quantum mechanical problem for the total class of saturated hydrocarbons has been stated and solved within the framework of the effective Hamiltonian method. A quantum mechanical substantiation of the transferability of the electronic structure characteristics (bond dipole moments, bond energies, and bond force constants) as well as the investigation of the origin of transferability have been considered for the stated class of chemical compounds.     

Density matrix,superconductivity and molecular structure

Starting from Yang's offdiagonal long-range order concept and the macroscopic occupation condition for the second order density matrix as the basis for condensation phenomena we develop the notion that the extremal wave function (EWF), which is related to these conditions, leads to superconductivity in monatomic systems. We prove that the BCS model and the version where it is projected onto a fixed number of particles posesses EWF properties, differs negligibly from the EWF, and conserves offdiagonal ong-range order. The condition for the EWF to be energetically favored is the presence of macroscopic degenerate one-electron energy levels in the system, partial occupation of this degenerate region, and also an effective attraction among the electrons. Considerations are advanced indicating that these conditions are satisfied in the high temperature superconducting metal oxide ceramics, due to the presence of macroscopically degenerate diffuse orbitals distributed among the O^– ions in the CuO₂ layers, and with the effective screening of these layers by the metal-like La, Ba, Y, or O layers.L. M. Litvinenko Institute for Physical-Organic Chemistry and the Chemistry of Coal, Academy of Science of the Ukrainian SSR, Donetsk. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 4, pp. 395–413, July–August, 1991. Original article submitted February 25, 1991.     

Density matrix equation for crystals

An idempotent density matrix in which the orbitals are expanded in Bloch sums is used in the density matrix equation for ρ₁(1,1′) to obtain an equation appropriate for a crystal. The general equation is presented as well as its simplification for the single-cell approximation and the nearest-neighbor approximation.     

Density matrix renormalisation group Lagrangians

We introduce a Lagrangian formulation of the density matrix renormalisation group (DMRG). We present Lagrangians which, when minimised, yield the optimal DMRG wavefunction in a variational sense, both within the general matrix product ansatz and within the canonical form of the matrix product that is constructed within the DMRG sweep algorithm. Some of the results obtained are similar to elementary expressions in Hartree-Fock theory, and we draw attention to such analogies. The Lagrangians introduced here will be useful in developing theories of analytic response and derivatives in the DMRG.     

Density matrix methods in orbital optimization for MCSCF calculations

The problem considered is that of selecting the finite orbital basis which will minimize the energy in a given size CI calculation. (1) A one-body operator is defined which has as eigenfunctions the desired optimal basis. The operator is defined in terms of the basis which leads to a self-consistency problem of Hartree-Fock type. (2) A method of successive orbital rotations is defined which is shown to have desirable convergence properties.     

Density matrix method and ultrafast processes

When femto-second (fs) time-resolved experiments are used to study ultrafast processes, quantum beat phenomena are often observed. In this paper, to analyze the fs time-resolved spectra, we will present the density matrix method, a powerful theoretical technique, which describes the dynamics of population and coherence of the system. How to employ it to study the pump-probe experiments and fs ultrafast processes is described. The ππ*→nπ* transition of pyrazine is used as an example to demonstrate the application of the density matrix method. Recently, Suzuki’s group have employed the 22 fs time resolution laser to study the dynamics of the ππ* state of pyrazine. In this case, conical intersection is commonly believed to play an important role in this non-adiabatic process. How to treat the effect of conical intersection on non-adiabatic processes and fs time-resolved spectra is presented. Another important ultrafast process, vibrational relaxation, which takes place in sub-ps and ps range and has never been carefully studied, is treated in this paper. The vibrational relaxation in water dimer is chosen to demonstrate the calculation. It should be noted that the vibrational relaxation of (H2O)2 has not been experimentally studied but it can be accomplished by the pump-probe experiments.     

Density matrix purification with rigorous error control

Density matrix purification, although being a powerful tool for linear scaling construction of the density matrix in electronic structure calculations, has been limited by uncontrolled error accumulation. In this article, a strategy for the removal of small matrix elements in density matrix purification is proposed with which the forward error can be rigorously controlled. The total forward error is separated into two parts, the error in eigenvalues and the error in the occupied invariant subspace. We use the concept of canonical angles to measure and control differences between exact and approximate occupied subspaces. We also analyze the conditioning of the density matrix construction problem and propose a method for calculation of interior eigenvalues to be used together with density matrix purification.     

Density matrix in the open shell theory

All the second-order density matrix spin components for the spin-projected Slater determinant are presented as expansions in direct products of powers of unprojected spin- and residual electron density matrices. Spin components of the second-order transition density matrices between spin-projected Slater determinants built of orthogonal orbitals are also obtained.     

Density of levels in vibrational spectra of molecules

Density distribution of the discrete spectrum of a Hamiltonian which represents a system of N-coupled oscillators and, hence may describe molecular vibrations in the local mode approximation, is analyzed. The spectral density moments are expressed as linear combinations of products of coefficients which depend on the molecular topology (analogs of the propagation coefficients in the statistical theory of nuclear and atomic spectra) and of one-particle moments describing individual bonds and interactions between them. The dependence of the first three moments of the energy-level density on the structural parameters of the molecule is discussed. Detailed expressions for several special cases are derived. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63 : 835–842, 1997     

193-nm Photodissociation of ions from saturated and unsaturated aliphatic molecules

To determine the analytical utility of photodissociation as a general fragmentation technique for tandem mass spectrometry of organic ions, the ability to fragment those ions considered least likely to absorb photons efficiently was investigated. To this end, the ability to photodissociate ions of aliphatic compounds by using 193-nm photons has been studied. Three fragment ions, the C₄H ₉ ⁺ ion from n-hexane, the C₄H ₇ ⁺ ion from 2-hexene, and C₄H ₅ ⁺ from 2-hexyne, have been photodissociated. The fragmentation efficiencies for all three ions studied were between 25 and 45%. The photofragment ion spectrum for each precursor ion studied is made up of characteristic fragments. These spectra demonstrate the ability to photodissociate aliphatic ions that originate from both saturated and unsaturated molecules. This provides substantial hope that virtually all organic ions will be able to be photodissociated by using 193-nm photons.     

The matrix theory of electron spin multiplets for atoms and molecules

In this article a matrix method for the construction of spin multiplets (spinconfigurations) is suggested in order to solve the multielectron problem for atoms and mulecules by means of configuration interaction.A simple graphical way is given to enumerate configurations and to break their set into subsets of configurations related to the given projection of the total spin of a system S _z . It is found that all matrices in the theory of spin multiplets are convex and in cases of two, three, and four electrons are broken into blocks of an order no higher than 3.The model of the solution of the multielectron Schrödinger equation, in which the total spin of core electrons is zero, is considered. In this model the construction of linear combinations of configurations is reduced to the construction of those for but valence electrons.     

A binary matrix for background suppression in MALDI-MS of small molecules

Application of matrix-assisted laser-desorption ionization mass spectrometry (MALDI-MS) to small-molecule detection is often limited, because of high matrix background signals in the low-mass region. We report here an approach in which a mixture of two conventional MALDI matrices with different proton affinity was used to suppress the formation of matrix clusters and fragments. Specifically, when acidic α-cyano-4-hydroxycinnamic acid (CHCA) and basic 9-aminoacridine (9-AA) were used as the binary matrix, fewer background matrix peaks were observed in both positive and negative-mode detection of small molecules. In addition, the presence of CHCA substantially reduced the laser fluence needed for analyte desorption and ionization; thus better signal-to-background ratios were observed for negatively charged inositol phosphates in complex plant extracts. The mixing of MALDI matrices of different protonaffinities leads to suppression of matrix clusterformation and subsequently yields cleaner MS spectraof fewer background peaks in both positive andnegative detection of small molecules     

Density functional based structure optimization for molecules containing heavy elements: analytical energy gradients for the Douglas-Kroll-Hess scalar relativistic approach to the LCGTO-DF method

The self-consistent scalar-relativistic linear combination of Gaussian-type orbitals density functional (LCGTO-DF) method has been extended to calculate analytical energy gradients. The method is based on the use of a unitary second order Douglas-Kroll-Hess (DKH) transformation for decoupling large and small components of the full four-component Dirac-Kohn-Sham equation. The approximate DKH transformation most common in molecular calculations has been implemented; this variant employs nuclear potential based projectors and it leaves the electron-electron interaction untransformed. Examples are provided for the geometry optimization of a series of heavy metal systems which feature a variety of metal-ligand bonds, like Au₂, AuCl, AuH, Mo(CO)₆ and W(CO)₆ as well as the d¹⁰ complexes [Pd(PH₃)₂O₂] and [Pt(PH₃)₂O₂]. The calculated results, obtained with several gradient-corrected exchange-correlation potentials, compare very well with experimental data and they are of similar or even better accuracy than those of other high quality relativistic calculations reported so far.     

Dihydrobenzoic acid modified nanoparticle as a MALDI-TOF MS matrix for soft ionization and structure determination of small molecules with diverse structures

Efficient structural characterization is important for quality control when developing novel materials. In this study, we demonstrated the soft ionization capability of the hybrid of immobilized silica and 2,5-dihydrobenzoic acid (DHB) on iron oxide magnetic nanoparticles in MALDI-TOF MS with a clean background. The ratio between SiO₂ and DHB was examined and was found to affect the surface immobilization of DHB on the nanoparticle, critically controlling the ionization efficiency and interference background. Compared with commercial DHB, the functionalized nanoparticle-assisted MALDI-TOF MS provided superior soft ionization with production of strong molecular ions within 5 ppm mass accuracy on a variety of new types of synthetic materials used for solar cells, light emitting devices, dendrimers, and glycolipids, including analytes with either thermally labile structures or poor protonation tendencies. In addition, the enhancements of the molecular ion signal also provided high-quality product-ion spectra allowing structural characterization and unambiguous small molecule identification. Using this technique, the structural differences among the isomers were distinguished through their characteristic fragment ions and comprehensive fragmentation patterns. With the advantages of long-term stability and simple sample preparation by deposition on a regular sample plate, the use of DHB-functionalized nanoparticles combined with high-resolution MALDI-TOF MS provides a generic platform for rapid and unambiguous structure determination of small molecules.     

Density functional theory study on anti-resonance in preresonance Raman scattering for naphthalene molecules

The anti-resonance phenomenon in preresonance Raman scattering is investigated on the basis of the direct Taylor expansion of the electric dipole transition moments in vibrational Raman tensors with respect to vibrational normal coordinates. A time-dependent density functional theory treatment is applied to compute the anti-resonance of a nontotally symmetric vibrational model for naphthalene molecules, and the model spectra agree favorably with experiment. This direct evaluation approach may provide a method of predicting anti-resonance and studying its origin.     

BCN-sequenced,valence saturated compounds. Synthesis and structure

The synthesis and characterization are presented of a series of compounds having the common structural features of four-coordinate BCN sequences. The discovery of a novel difunctionally substituted borohydride ion, (CH₃)₂NCH₂-BH₂CH₂N(CH₂)₂BH₂CH₂N(CH₃)₂^?, provides for a more complete understanding of the general synthesis mechanism.