1,378 research outputs found
Approximation by Bernstein-Chlodowsky operators of max-product kind
We dene the max-product (nonlinear) Bernstein-Chlodowsky operators andobtain some upper estimates of approximation error for some subclasses of functions. Wealso investigate the shape-preserving properties for these operators
DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes
We have implemented internally contracted complete active space second order
perturbation theory (CASPT2) with the density matrix renormalization group
(DMRG) as active space solver [Y. Kurashige and T. Yanai, J. Chem. Phys. 135,
094104 (2011)]. Internally contracted CASPT2 requires to contract the
generalized Fock matrix with the 4-particle reduced density matrix (4-RDM) of
the reference wavefunction. The required 4-RDM elements can be obtained from
3-particle reduced density matrices (3-RDM) of different wavefunctions, formed
by symmetry-conserving single-particle excitations op top of the reference
wavefunction. In our spin-adapted DMRG code chemps2
[https://github.com/sebwouters/chemps2], we decompose these excited
wavefunctions as spin-adapted matrix product states, and calculate their 3-RDM
in order to obtain the required contraction of the generalized Fock matrix with
the 4-RDM of the reference wavefunction. In this work, we study the
longitudinal static second hyperpolarizability of all-trans polyenes
CH [n = 4 - 12] in the cc-pVDZ basis set. DMRG-SCF and
DMRG-CASPT2 yield substantially lower values and scaling with system size
compared to RHF and MP2, respectively.Comment: 9 pages, 4 figure
Benchmark of dynamic electron correlation models for seniority-zero wavefunctions and their application to thermochemistry
Wavefunctions restricted to electron-pair states are promising models to
describe static/nondynamic electron correlation effects encountered, for
instance, in bond-dissociation processes and transition-metal and actinide
chemistry. To reach spectroscopic accuracy, however, the missing dynamic
electron correlation effects that cannot be described by electron-pair states
need to be included \textit{a posteriori}. In this article, we extend the
previously presented perturbation theory models with an Antisymmetric Product
of 1-reference orbital Geminal (AP1roG) reference function that allow us to
describe both static/nondynamic and dynamic electron correlation effects.
Specifically, our perturbation theory models combine a diagonal and
off-diagonal zero-order Hamiltonian, a single-reference and multi-reference
dual state, and different excitation operators used to construct the projection
manifold. We benchmark all proposed models as well as an \textit{a posteriori}
linearized coupled cluster correction on top of AP1roG against CR-CCSD(T)
reference data for reaction energies of several closed-shell molecules that are
extrapolated to the basis set limit. Moreover, we test the performance of our
new methods for multiple bond breaking processes in the N, C, and BN
dimers against MRCI-SD and MRCI-SD+Q reference data. Our numerical results
indicate that the best performance is obtained from a linearized coupled
cluster correction as well as second-order perturbation theory corrections
employing a diagonal and off-diagonal zero-order Hamiltonian and a
single-determinant dual state. These dynamic corrections on top of AP1roG allow
us to reliably model molecular systems dominated by static/nondynamic as well
as dynamic electron correlation.Comment: 15 pages, 2 figure
Spatial and spin symmetry breaking in semidefinite-programming-based Hartree-Fock theory
The Hartree-Fock problem was recently recast as a semidefinite optimization
over the space of rank-constrained two-body reduced-density matrices (RDMs)
[Phys. Rev. A 89, 010502(R) (2014)]. This formulation of the problem transfers
the non-convexity of the Hartree-Fock energy functional to the rank constraint
on the two-body RDM. We consider an equivalent optimization over the space of
positive semidefinite one-electron RDMs (1-RDMs) that retains the non-convexity
of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble
-representability conditions, and ensemble spin-state conditions may be
imposed as well. The spin-state conditions place additional linear and
nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several
molecular systems and explore its spatial (point group) and spin ( and
) symmetry breaking properties. When imposing and symmetry but
relaxing point group symmetry, the procedure often locates
spatial-symmetry-broken solutions that are difficult to identify using standard
algorithms. For example, the RDM-based approach yields a smooth,
spatial-symmetry-broken potential energy curve for the well-known Be--H
insertion pathway. We also demonstrate numerically that, upon relaxation of
and symmetry constraints, the RDM-based approach is equivalent to
real-valued generalized Hartree-Fock theory.Comment: 9 pages, 6 figure
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