arXiv subjects

Liqiang Wei

Publications and source records attributed to Liqiang Wei.

9 recordsLinked to original sources

arXiv2006

Quantum Chemistry at Finite Temperature

In this article, we present emerging fields of quantum chemistry at finite temperature. We discuss its recent developments on both experimental and theoretical fronts. First, we describe several experimental investigations related to the temperature effects on the structures, electronic spectra, or bond rupture forces for molecules. These include the analysis of the temperature impact on the pathway shifts for the protein unfolding by atomic force microscopy (AFM), the temperature dependence of the absorption spectra of electrons in solvents, and the temperature influence over the intermolecular forces measured by the AFM. On the theoretical side, we review advancements made by the author in the coming fields of quantum chemistry at finite temperature. Starting from the Bloch equation, we have derived the sets of hierarchy equations for the reduced density operators in both canonical and grand canonical ensembles. They provide a law according to which the reduced density operators vary in temperature for the identical and interacting many-body systems. By taking the independent particle approximation, we have solved the equations in the case of a grand canonical ensemble, and obtained an energy eigenequation for the molecular orbitals at finite temperature. The explicit expression for the temperature-dependent Fock operator is also given. They form a mathematical foundation for the examination of the molecular electronic structures and their interplay with finite temperature. Moreover, we clarify the physics concerning the temperature effects on the electronic structures or processes of the molecules, which is crucial for both theoretical understanding and computation. Finally, ....

cond-mat.soft↗

arXiv2006

Exploring Harmony between Theory and Computation - Toward a unified electronic structure theory

The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among matter with different levels of hierarchy is appreciated. It is shown that the generic perturbation theory can not only be used for understanding various electronic phenomena including the nature of chemical bonds but also serve as a $\it{unified}$ theme for developing $\it{general}$ electronic structure theories and calculation schemes. In particular, a $\it{standard}$ electron correlation approach is suggested and established according to this law.

physics.chem-ph↗

arXiv2005

On Emerging Fields of Quantum Chemistry at Finite Temperature

In this article, we present an emerging field of quantum chemistry at finite temperature. We discuss its recent developments on both theoretical and experimental fronts.We describe and analyze several experimental investigations related to the temperature effects on the structure, electronic spectra,or bond rupture forces for molecules. This includes the study of the temperature impact on the pathway shifts for the protein unfolding by atomic force microscopy, the temperature dependence of the absorption spectra of electrons in solvents, and temperature influence over the intermolecular forces measured by the AFM. On the theoretical side, we review a recent advancement made by the author in the coming fields of quantum chemistry at finite temperature. Starting from Bloch equation, we have derived the sets of hierarchy equations for the reduced density operators in both canonical and grand canonical ensembles. They provide a law according to which the reduced density operators vary in temperature for the identical and interacting many-body particles. By taking the independent particle approximation, we have solved the equation in the case of a grand canonical ensemble, and obtained an eigenequation for the molecular orbitals at finite temperature. The explicit expression for the temperature-dependent Fock operator is also given. They will form a foundation for the study of the molecular electronic structures and their interplay with the finite temperature. Furthermore, we clarify the physics concerning the temperature effect on the electronic structure or processes of molecules which is crucial for both theoretical understanding and computational study.Finally,we summarize our discussion and point out the theoretical and computational issues for the future explorations in the fields of quantum chemistry at finite temperature.

physics.chem-ph↗

arXiv2004

Single-Particle Green Function Approach and Correlated Atomic or Molecular Orbitals

In this paper, we propose a generic and systematic approach for study of the electronic structure for atoms or molecules. In particular, we address the issue of single particle states, or orbitals, which should be one of the most important aspects of a quantum many-body theory. We argue that the single-particle $\it{Green}$ function provides a most general scheme for generating these single particle states or orbitals. We call them the $\it{correlated}$ atomic or molecular orbitals to make a distinction from those determined from $\it{Hartree-Fock}$ equation. We present the calculation of the single particle properties (i.e., the electron affinities $(EA's)$ and ionization potentials $(IP's)$) for the $H_{2}O$ molecule using the correlated molecular orbitals in the context of quantum chemistry with a second-order self energy. We also calculate the total ground state energy with a single $Slater$ wavefunction determined only from the hole states. Comparisons are made with available experimental data as well as with those from the $\it{Hartree-Fock}$ or density functional theory $(DFT)$ calculations. We conclude that the correlated atomic or molecular orbital approach provides a strictest and most powerful method for studying the single-particle properties of atoms or molecules. It also gives a better total energy than do the $\it{Hartree-Fock}$ and $\it{DFT}$ even at the single $\it{Slater}$ determinant level. It promises that a correlation theory based on the correlated atomic or molecular orbitals will become an approach which possesses the advantages and also overcomes their shortcomings of current quantum chemistry methods based on either the conventional quantum many-body theory or the $DFT$.

physics.chem-ph↗

arXiv2003

Second Quantized Reduced Bloch Equations and the Exact Solutions for Pairing Hamiltonian

In this article, we present a set of hierarchy Bloch equations for the reduced density operators in either canonical or grand canonical ensembles in the occupation number representation. They provide a convenient tool for studying the equilibrium quantum statistical mechanics for some model systems. As an example of their applications, we solve the equations for the model system with a pairing Hamiltonian. With the aid of its symplectic group symmetry, we obtain the statistical reduced density matrices with different orders. As a special instance for the solutions, we also get the reduced density matrices of the ground state for a superconductor.

cond-mat.stat-mech↗

arXiv2003

Exploring the Harmony between Theory and Computation - Toward a unified electronic structure theory

The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among the matters with different levels of hierarchy is appreciated. It is shown that the general perturbation theory can not only be used for understanding the various electronic phenomena including the nature of chemical bonds but also serve as a unified theme for constructing general electronic structure theories and calculation schemes.

physics.chem-ph↗

arXiv2003

Orbital Approximation for the Reduced Bloch Equations: Fermi-Dirac Distribution for Interacting Fermions and Hartree-Fock Equation at Finite Temperature

In this paper, we solve a set of hierarchy equations for the reduced statistical density operator in a grand canonical ensemble for an identical many-body fermion system without or with two-body interaction. We take the single-particle approximation, and obtain an eigen-equation for the single-particle states. For the case of no interaction, it is an eigen-equation for the free particles, and solutions are therefore the plane waves. For the case with two-body interaction, however, it is an equation which is the extension of usual Hartre-Fock equation at zero temperature to the case of any finite temperature. The average occupation number for the single-particle states with mean field interaction is also obtained, which has the same Fermi-Dirac distribution from as that for the free fermion gas. The derivation demonstrates that even for an interacting fermion system, only the lowest $N$ orbitals, where $N$ is the number of particles, are occupied at zero temperature. In addition, their practical applications in such fields as studying the temperature effects on the average structure and electronic spectra for macromolecules are discussed.

cond-mat.stat-mech↗

arXiv2003

Hierarchy Bloch Equations for the Reduced Statistical Density Operators in Canonical and Grand canonical Ensembles

Starting from Bloch equation for a canonical ensemble, we deduce a set of hierarchy equations for the reduced statistical density operator for an identical many-body system with two-body interaction. They provide a law according to which the reduced density operator varies in temperature. By definition of the reduced density operator in Fock space for a grand canonical ensemble, we also obtain the analogous Bloch equation and the corresponding hierarchy reduced equations for the identical interacting many-body system. We discuss their possible solutions and applications.

cond-mat.stat-mech↗

arXiv2003

Universal Factorization of $3n-j (j > 2)$ Symbols of the First and Second Kinds for SU(2) Group and Their Direct and Exact Calculation and Tabulation

We show that general $3n-j (n>2)$ symbols of the first kind and the second kind for the group SU(2) can be reformulated in terms of binomial coefficients. The proof is based on the graphical technique established by Yutsis, et al. and through a definition of a reduced $6-j$ symbol. The resulting $3n-j$ symbols thereby take a combinatorial form which is simply the product of two factors. The one is an integer or polynomial which is the single sum over the products of reduced $6-j$ symbols. They are in the form of summing over the products of binomial coefficients. The other is a multiplication of all the triangle relations appearing in the symbols, which can also be rewritten using binomial coefficients. The new formulation indicates that the intrinsic structure for the general recoupling coefficients is much nicer and simpler, which might serves as a bridge for the study with other fields. Along with our newly developed algorithms, this also provides a basis for a direct, exact and efficient calculation or tabulation of all the $3n-j$ symbols of the SU(2) group for all range of quantum angular momentum arguments. As an illustration, we present teh results for the $12-j$ symbols of the first kind.

math-ph↗