A general nonAbelian density matrix renormalization group algorithm with application to the C{sub 2} dimer
Abstract
We extend our previous work [S. Sharma and G. K.L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spinadapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general nonAbelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hardcoded for each symmetry group, but are instead generated on the fly using the appropriate ClebschGordan coefficients. This allows our single implementation to easily enable (or disable) any nonAbelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C{sub 2} dimer in the ccpVQZ basis set (with a frozencore), corresponding to a Hilbert space dimension of 10{sup 12} manybody states. While our calculated energy lies within the 0.3 mE{sub h} error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{submore »
 Authors:
 Department of Chemistry, Frick Laboratory, Princeton University, Princeton, New Jersey 08544 (United States)
 Publication Date:
 OSTI Identifier:
 22415820
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CLEBSCHGORDAN COEFFICIENTS; CONFIGURATION INTERACTION; DENSITY MATRIX; DIAGRAMS; DIMERS; ELECTRON CORRELATION; EXCITATION; EXCITED STATES; EXTRAPOLATION; GROUND STATES; HILBERT SPACE; IRREDUCIBLE REPRESENTATIONS; MANYBODY PROBLEM; MONTE CARLO METHOD; POTENTIAL ENERGY; RENORMALIZATION; SPIN; SU2 GROUPS; TENSORS
Citation Formats
Sharma, Sandeep, Email: sanshar@gmail.com. A general nonAbelian density matrix renormalization group algorithm with application to the C{sub 2} dimer. United States: N. p., 2015.
Web. doi:10.1063/1.4905237.
Sharma, Sandeep, Email: sanshar@gmail.com. A general nonAbelian density matrix renormalization group algorithm with application to the C{sub 2} dimer. United States. doi:10.1063/1.4905237.
Sharma, Sandeep, Email: sanshar@gmail.com. 2015.
"A general nonAbelian density matrix renormalization group algorithm with application to the C{sub 2} dimer". United States.
doi:10.1063/1.4905237.
@article{osti_22415820,
title = {A general nonAbelian density matrix renormalization group algorithm with application to the C{sub 2} dimer},
author = {Sharma, Sandeep, Email: sanshar@gmail.com},
abstractNote = {We extend our previous work [S. Sharma and G. K.L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spinadapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general nonAbelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hardcoded for each symmetry group, but are instead generated on the fly using the appropriate ClebschGordan coefficients. This allows our single implementation to easily enable (or disable) any nonAbelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C{sub 2} dimer in the ccpVQZ basis set (with a frozencore), corresponding to a Hilbert space dimension of 10{sup 12} manybody states. While our calculated energy lies within the 0.3 mE{sub h} error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{sub u}{sup +}, B{sup 1}Δ{sub g}, B{sup ′1}Σ{sub g}{sup +}, d{sup 3}Π{sub g}, and C{sup 1}Π{sub g} are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations {sup 1}Σ{sub g}{sup +}, {sup 1}Σ{sub u}{sup +}, {sup 1}Σ{sub g}{sup −}, and {sup 1}Σ{sub u}{sup −}, to an estimated accuracy of 0.1 mE{sub h} of the exact result in this basis.},
doi = {10.1063/1.4905237},
journal = {Journal of Chemical Physics},
number = 2,
volume = 142,
place = {United States},
year = 2015,
month = 1
}

Communication: Active space decomposition with multiple sites: Density matrix renormalization group algorithm
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted activespace wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps aremore » 
Spin orbit coupling for molecular ab initio density matrix renormalization group calculations: Application to gtensors
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the BornOppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spinadaptation of the algorithm, the total spin S is a good quantum number for these states. After the nonrelativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctionsmore »