MSThE50
Mathematical and Numerical Aspects of Electronic Structure Theory  Part III of V
For Part I, see MSThBC50
For Part II, see MSThD50
For Part IV, see MSFrD50
For Part V, see MSFrE50
Date: August 13
Time: 16:0018:30
Room: 207
(Note: Click title to show the abstract.)
Organizer:
Lin, Lin (Univ. of California at Berkeley)
Lu, Jianfeng (Duke Univ.)
Abstract: Electronic structure theory and first principle calculations are among the most challenging and computationally demanding science and engineering problems. This minisymposium aims at presenting and discussing new developments of mathematical analysis, and numerical methods for achieving ever higher level of accuracy and efficiency in electronic structure theory. This includes ground state and excited state density functional theory calculations, wavefunction methods, together with some of their applications in computational materials science and quantum chemistry. We propose to bring together experts on electronic structure theory, which include not only mathematicians, but also physicists working actively in the field.
MSThE501
16:0016:30
Efficient spectralelement methods for electronic Schrodinger equation
Shen, Jie (Purdue Univ.)
Abstract: We present efficient spectralelement methods, based
on Legendre and Laguerre polynomials, for direct approximation of
the electronic Schrodinger equation in one spatial dimension. A
spectralelement approach is used to treat the singularity in
nucleuselectron Coulomb potential, and with the help of Slater
determinant, we construct special basis functions to obey the
antisymmetric property of the fermionic wavefunctions. Numerical
tests are presented to show the efficiency and accuracy of the
proposed methods.
MSThE502
16:3017:00
Numeric atomcentered orbital based allelectron electronic structure theory for accurate, large simulations
Blum, Volker (Duke Univ.)
Abstract: We describe recent methodological progress and applications of electronic structure theory methods implemented in a numeric atomcentered orbital framework (FHIaims). This basis choice enables simulations of materials and molecules (periodic and nonperiodic) from light to numerically converged accuracy, for DFT including hybrid functionals and manybody perturbation theory. Recent developments include a massively parallel dense eigenvalue solver "ELPA" and a localized "resolution of identity" that enables exactexchange for hybrid DFT up to thousands of atoms.
MSThE503
17:0017:30
Hierarchical tensors and tensor networks for quantum chemistry
Schneider, Reinhold (Inst. for Mathematics)
Abstract: n 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 constraint 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.
MSThE504
17:3018:00
A Mathematical Aspect of HohenbergKohn Theorem
Zhou, Aihui (Acad. of Mathematics & Sys. Sci., Chinese Acad. of Sci.)
Abstract: HohenbergKohn theorem plays a fundamental role in density functional theory ,
which has become a basic tool for the
study of electronic structure of matter.
In this presentation, we shall talk about the HohenbergKohn theorem
for a class of external potentials and present a mathematical rigorous proof.
MSThE505
18:0018:30
Compressed Modes and Compressed Density Matrices
Lai, Rongjie (Rensselaer Polytechnic Inst.)
Abstract: I will discuss our recent work on a new use of sparsitypromoting techniques to produce ˇ°compressed modes"  modes that are sparse and localized in space  for efficient solutions of L1 regularized variational Schrodinger equations in mathematics and physics. As lifted versions of compress modes, I will also discuss our recent work on compressed density matrices and their linear scaling algorithms.
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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
