A unitary group approach based on the so-called bonded tableaux (VB) states is described. Several different realizations of the bonded tableaux are discussed and their relations are pointed out. From a viewpoint of th...A unitary group approach based on the so-called bonded tableaux (VB) states is described. Several different realizations of the bonded tableaux are discussed and their relations are pointed out. From a viewpoint of the symmetric group we reveal a simple structure of the matrix elements of unitary group generators and generator products. This structure makes an efficient approach to the matrix element evaluation.展开更多
We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin(LS)eigenspaces within the n-fold antisymmetrized tensor product∧^(n)V_(u),where n is the number of electrons and ...We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin(LS)eigenspaces within the n-fold antisymmetrized tensor product∧^(n)V_(u),where n is the number of electrons and u=s,p,d,…denotes the atomic subshell.This is an essential step for dimension reduction in configurationinteraction(CI)methods applied to atomic many-electron quantum systems.The algorithm relies on the observation that each Lz eigenstate with maximal eigenvalue is also an L2 eigenstate(equivalently for Sz and S2),as well as the traversal of LS eigenstates using the lowering operators L−and S−.Iterative application to the remaining states in∧^(n)V_(u)leads to an implicit simultaneous diagonalization.A detailed complexity analysis for fixed n and increasing subshell number u yields run time O(u^(3n−2)).A symbolic computer algebra implementation is available online.展开更多
Simple analytical expressions for one- and two-body matrix elements in the unitary group approach to the configuration interaction problems of many-electron systems are obtained based on the previous results for gener...Simple analytical expressions for one- and two-body matrix elements in the unitary group approach to the configuration interaction problems of many-electron systems are obtained based on the previous results for general irreps.展开更多
A strict universal method of calculating the electronic structure of condensed matter from the Hartree-Fock equation is proposed.It is based on a partial differential equation(PDE)strictly equivalent to the Hartree-Fo...A strict universal method of calculating the electronic structure of condensed matter from the Hartree-Fock equation is proposed.It is based on a partial differential equation(PDE)strictly equivalent to the Hartree-Fock equation,which is an integral-differential equation of fermion single-body wavefunctions.Although the maximum order of the differential operator in the Hartree-Fock equation is 2,the mathematical property of its integral kernel function can warrant the equation to be strictly equivalent to a 4 th-order nonlinear partial differential equation of fermion single-body wavefunctions.This allows the electronic structure calculation to eliminate empirical and random choices of the starting trial wavefunction(which is inevitable for achieving rapid convergence with respect to iterative times,in the iterative method of studying integral-differential equations),and strictly relates the electronic structure to the space boundary conditions of the singlebody wavefunction.展开更多
We have calculated the ground-state energy of the symmetric quantum-dot pattern by the ab initio calculation method, i.e. unrestricted Hartree-Fock-Roothaan (UHFR) method based on the Gaussian basis, and studied their...We have calculated the ground-state energy of the symmetric quantum-dot pattern by the ab initio calculation method, i.e. unrestricted Hartree-Fock-Roothaan (UHFR) method based on the Gaussian basis, and studied their electric capacitance spectra, assuming each quantum dot of quantum-dot pattern to be confined in a three-dimensional spherical potential well of finite depth. For the systems in question, our results show that our method and theoretical model not only give the electric capacitance peaks similar to s-shell and p-shell atom-like quantum dot, but also show some new fine-structure of electric capacitance in the symmetric quantum-dot pattern system. This method might be a feasible tool to study few-electron problems on the symmetric quantum-dot pattern system.展开更多
An irreducible tensor method based on M. O. theory for solving many-body Schrodinger equation of valence-electron system of metal complexes has been proposed. Electronic structures of several typical octahedral transi...An irreducible tensor method based on M. O. theory for solving many-body Schrodinger equation of valence-electron system of metal complexes has been proposed. Electronic structures of several typical octahedral transition metal complexes have been studied by means of this method. Calculated excitation energies agree with observed ones within several kcm-1.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘A unitary group approach based on the so-called bonded tableaux (VB) states is described. Several different realizations of the bonded tableaux are discussed and their relations are pointed out. From a viewpoint of the symmetric group we reveal a simple structure of the matrix elements of unitary group generators and generator products. This structure makes an efficient approach to the matrix element evaluation.
基金The author would like to thank Gero Friesecke for many helpful discussions,and DFG for financial support under project FR 1275/3-1.
文摘We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin(LS)eigenspaces within the n-fold antisymmetrized tensor product∧^(n)V_(u),where n is the number of electrons and u=s,p,d,…denotes the atomic subshell.This is an essential step for dimension reduction in configurationinteraction(CI)methods applied to atomic many-electron quantum systems.The algorithm relies on the observation that each Lz eigenstate with maximal eigenvalue is also an L2 eigenstate(equivalently for Sz and S2),as well as the traversal of LS eigenstates using the lowering operators L−and S−.Iterative application to the remaining states in∧^(n)V_(u)leads to an implicit simultaneous diagonalization.A detailed complexity analysis for fixed n and increasing subshell number u yields run time O(u^(3n−2)).A symbolic computer algebra implementation is available online.
文摘Simple analytical expressions for one- and two-body matrix elements in the unitary group approach to the configuration interaction problems of many-electron systems are obtained based on the previous results for general irreps.
文摘A strict universal method of calculating the electronic structure of condensed matter from the Hartree-Fock equation is proposed.It is based on a partial differential equation(PDE)strictly equivalent to the Hartree-Fock equation,which is an integral-differential equation of fermion single-body wavefunctions.Although the maximum order of the differential operator in the Hartree-Fock equation is 2,the mathematical property of its integral kernel function can warrant the equation to be strictly equivalent to a 4 th-order nonlinear partial differential equation of fermion single-body wavefunctions.This allows the electronic structure calculation to eliminate empirical and random choices of the starting trial wavefunction(which is inevitable for achieving rapid convergence with respect to iterative times,in the iterative method of studying integral-differential equations),and strictly relates the electronic structure to the space boundary conditions of the singlebody wavefunction.
基金the National Natural Seience Foundation of China(Grant No10074064)Youth Foundarion of Yantai Universiry(Grant No WL02Z7)
文摘We have calculated the ground-state energy of the symmetric quantum-dot pattern by the ab initio calculation method, i.e. unrestricted Hartree-Fock-Roothaan (UHFR) method based on the Gaussian basis, and studied their electric capacitance spectra, assuming each quantum dot of quantum-dot pattern to be confined in a three-dimensional spherical potential well of finite depth. For the systems in question, our results show that our method and theoretical model not only give the electric capacitance peaks similar to s-shell and p-shell atom-like quantum dot, but also show some new fine-structure of electric capacitance in the symmetric quantum-dot pattern system. This method might be a feasible tool to study few-electron problems on the symmetric quantum-dot pattern system.
基金Project supported by the National Natural Science Foundation of China.
文摘An irreducible tensor method based on M. O. theory for solving many-body Schrodinger equation of valence-electron system of metal complexes has been proposed. Electronic structures of several typical octahedral transition metal complexes have been studied by means of this method. Calculated excitation energies agree with observed ones within several kcm-1.
