LEADER 04298nam 2200553 450 001 9910466703203321 005 20200520144314.0 010 $a3-11-039137-6 010 $a3-11-036583-9 024 7 $a10.1515/9783110365832 035 $a(CKB)4100000005043687 035 $a(MiAaPQ)EBC5156280 035 $a(DE-B1597)428238 035 $a(OCoLC)1041994386 035 $a(DE-B1597)9783110365832 035 $a(Au-PeEL)EBL5156280 035 $a(CaPaEBR)ebr11605082 035 $a(OCoLC)1051138953 035 $a(EXLCZ)994100000005043687 100 $a20180921d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTensor numerical methods in quantum chemistry /$fVenera Khoromskaia, Boris N. Khoromskij 210 1$aBerlin ;$aBoston :$cDe Gruyter,$d[2018] 210 4$dİ2018 215 $a1 online resource (298 pages) 311 $a3-11-037015-8 327 $tFrontmatter -- $tContents -- $t1. Introduction -- $t2. Rank-structured formats for multidimensional tensors -- $t3. Rank-structured grid-based representations of functions in ?d -- $t4. Multiplicative tensor formats in ?d -- $t5. Multidimensional tensor-product convolution -- $t6. Tensor decomposition for analytic potentials -- $t7. The Hartree-Fock equation -- $t8. Multilevel grid-based tensor-structured HF solver -- $t9. Grid-based core Hamiltonian -- $t10. Tensor factorization of grid-based two-electron integrals -- $t11. Fast grid-based Hartree-Fock solver by factorized TEI -- $t12. Calculation of excitation energies of molecules -- $t13. Density of states for a class of rank-structured matrices -- $t14. Tensor-based summation of long-range potentials on finite 3D lattices -- $t15. Range-separated tensor format for many-particle systems -- $tBibliography -- $tIndex 330 $aThe conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results? from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 1015. Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. Tensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. This research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing. 606 $aCalculus of tensors 606 $aTensor algebra 606 $aQuantum chemistry 608 $aElectronic books. 615 0$aCalculus of tensors. 615 0$aTensor algebra. 615 0$aQuantum chemistry. 676 $a515.63 700 $aKhoromskaia$b Venera$01049872 702 $aKhoromskij$b Boris 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910466703203321 996 $aTensor numerical methods in quantum chemistry$92479212 997 $aUNINA