MSWeD34
Mathematics and Algorithms in Quantum Chemistry  Part III of III
For Part I, see MSTuD34
For Part II, see MSTuE34
Date: August 12
Time: 13:3015:30
Room: 112
(Note: Click title to show the abstract.)
Organizer:
Melgaard, Michael (Univ. of Sussex)
Shao, Sihong (Peking Univ.)
Abstract: Ab initio models of electronic structures has had an immense impact in the physics and chemistry communities, as well as the materials science community, due to the capacity for carrying out realistic computations. The mathematical formulation and the efficient numerical simulation of such models is a notoriously difficult problem for several reasons, e.g., high dimensional configurations spaces, multiparticle interactions, multiple scales, nonlinear effects, and/or degeneracies of eigenspaces. Further developments in this area require the integration of physical modeling, mathematical analysis, and algorithm development in order to obtain reliable computational tools. The minisymposium aims to bring together quantum chemists, applied and computational mathematicians, physicists and materials scientists all of whom are working in quantum chemistry to exchange ideas and to share their recent progress on the frontiers of theory and numerical methods as well as applications in material science. The minisymposium will particularly focus on three topics: Timedependent problems and excited states; Wave function methods; Relativistic effects.
MSWeD341
13:3014:00
Critical point theory and variational methods with applications to electronic structure models within Quantum Chemistry
Melgaard, Michael (Univ. of Sussex)
Abstract: We report on a series of rigorous results on the existence of ground states and excited states for various weakly coupled, semilinear nonlinear elliptic PDEs arising in electronic structure models of molecular systems in quantum chemistry.
For wave function methods, we give results for HartreeFock type models taking into account relativistic effects and magnetic fields by using the LionsFangGhoussoub critical point approach to multiple solutions on a noncompact Riemannian manifold.
Within Density Functional Theory (DFT), we give rigorous results on the openshell, spinpolarized KohnSham models for nonrelativistic and quasirelativistic $N$electron Coulomb systems, that is, systems where the kinetic energy of the electrons is given by either the nonrelativistic operator $\Delta_{x_{n}}$ or the quasirelativistic operator (nonlocal, pseudodifferential operator of order one)
$\sqrt{ \alpha^{2} \Delta_{x_{n}} + \alpha^{4}} \alpha^{2}$; here $\alpha$ is Sommerfeld's fine structure constant. For standard and extended KohnSham models in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge $Z_{\rm tot}$ of $K$ nuclei is greater than $N1$. For the quasirelativistic setting we also need that $Z_{\rm tot}$ is smaller than a critical charge $Z_{\rm c}=2 \alpha^{1} \pi^{1}$.
This is joint work with C. Argaez (University of Iceland, Iceland), E. Chiumiento (IAM CONICET, Argentina) and M. Enstedt (Uppsala University, Sweden).
MSWeD342
14:0014:30
Nonadiabatic couplings within timedependent density functional theory
Li, Zhendong (princeton Univ.)
Abstract: Timedependent density functional theory (TDDFT) has emerged as a powerful tool for investigating electronic excitations of molecular systems. In this talk, I will show how the problem of calculating nonadiabatic couplings within TDDFT is solved by extending the standard response theory to include nuclear derivatives.
MSWeD343
14:3015:00
Electron correlation in a relativistic framework
SAUE, Trond (CNRS/Laboratoire de Chimie et Physique Quantiques)
Abstract: The proper and efficient inclusion of electron correlation is a major challenge in molecular quantum chemistry. In 1958 Löwdin defined the correlation energy as the difference between the exact eigenvalue of the electronic Hamiltonian and the HartreeFock energy. In relativistic theory a severe complication arises since the electronic Hamiltonian has no bound solutions. In the present contribution we shall explore the proper definition of correlation energy in a relativistic framework.
MSWeD344
15:0015:30
Relativistic scales for absolute nuclear magnetic shielding constant
Xiao, Yunlong (College of Chemistry & Molecular Engineering, Peking Univ.)
Abstract: The relativistic expression for nuclear magnetic shielding (NMS) constant and nuclear spinrotation (NSR) constant are studied base on the relativistic bodyfixed frame molecular Hamiltonian. Because of the closely connection of two properties (NMS and NSR constants), a relativistic scale for absolute nuclear magnetic shielding is proposed.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
