MSTuE34
Mathematics and Algorithms in Quantum Chemistry  Part II of III
For Part I, see MSTuD34
For Part III, see MSWeD34
Date: August 11
Time: 16:0018:00
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.
MSTuE341
16:0016:30
Recent developments of adaptive local basis functions for electronic structure calculations
Lin, Lin (Univ. of California at Berkeley)
Abstract: The discontinuous Galerkin density functional theory (DGDFT) based on adaptive local basis functions can adaptively and systematically incorporates reduce the dimension of the discretized KohnSham equation. Recently, we validate the accuracy of the force calculation with single point calculation, molecular dynamics, and vibrational calculations. Together with the PEXSI technique, the DGDFT method is highly parallelizable to more than 100k processors.
MSTuE342
16:3017:00
Relativistic Wave Functions: Basic Structures, Coalescence Conditions and Explicit Representation
Shao, Sihong (Peking Univ.)
Abstract: We first show relativistic manybody Hamiltonians and wave functions can be expressed systematically with TracySingh products for partitioned matrices, and then derive the electronelectron coalescence conditions for the wave functions of the DiracCoulomb, DiracCoulombGaunt, and DiracCoulombBreit Hamiltonians by making use of the internal symmetries of the reduced twoelectron systems. These findings enrich our understandings of relativistic wave functions and may be useful to develop relativistic explicitly correlated wave function methods.
MSTuE343
17:0017:30
Hierarchical tensors and tensor networks for many particle quantum systems
Schneider, Reinhold (Inst. for Mathematics)
Abstract: In tensor product approximation,
Hierarchical Tucker tensor format (Hackbusch) and Tensor Trains (TT) (Tyrtyshnikov) have been introduced recently
offering stable and robust approximation by a low order cost . If $ \mathcal{V} = \bigotimes_{i=1}^d \mathbb{C}^2 $,
these formats are equivalent to tree tensor networks states and matrix product
states (MPS) originally introduced for the treatment of quantum spin systems.
Considering the electronic Schr\"odinger equation,
we use an occupation number labeling of Slater determinants, and show that the discrete Fock space becomes isometric to
dfold tensor product of a a twodimensional Hilbert space.
%We use hierarchical tensor representations, which are equivalent to tree tensor networks, in particularly in the form of matrix product states.
For the computation of an approximate ground solution this problem can be casted into an optimization
problem constrained by the restriction to tensors of
prescribed multilinear ranks $\mathbf{r} $. Dirac Frenkel variational principle developed in a similar fashion as for
MultiConfigurational Hartree (Fock) by observing the differential geometric structure of the novel tensor formats.
This provides a variational formulation of the QC (Quantum Chemistry) DMRG (Density Renormalization Group) algorithm
We propose a dynamical low rank approximation, corresponding to the DiracFrenkel variational principle, for solving a constraint optimization problem.
The approach can be applied to ground state calculations as well as to dynamical problems.
Convergence of (Riemannian) gradient algorithms can be shown.
A simple optimization methods is provided by alternating direction methods, which reveals the DMRG (density matrix renormalization group) algorithm.
This approach has been applied applied by G.C. Chan et al. and O. Legeza et al.
to analyse the dissociation of diatomic molecules and to transition metal complexes,
supporting that the presented approach has a certain potential to treat some strongly correlated electronic systems.
MSTuE344
17:3018:00
A Parallel OrbitalUpdating Approach for Electronic Structure Calculations
Xiaoying, Dai (Acad. of Mathematics & Sys. Sci., Chinese Acad. of Sci.))
Abstract: In this talk, we will talk about an orbital iteration based parallel approach for electronic structure calculations. With this new approach, the solution of the singleparticle equation is reduced to some solutions of independent linear algebraic systems and a small scale algebraic problem. It is demonstrated by our numerical experiments that this new approach is quite efficient for electronic structure calculations. This presentation is based on some joint works with X. Gong, A. Zhou, andJ.Zhu.
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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
