P. Bultinck

Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods

D.R. Alcoba, A. Torre, L. Lain, G. Massaccesi, O.B. Ona, P.W. Ayers, M. Van Raemdonck, P. Bultinck, D. Van Neck
Theoretical Chemistry Accounts
135 (6), 153
2016
A1

Abstract

The coefficients of full configuration interaction wave functions (FCI) for N-electron systems expanded in N-electron Slater determinants depend on the orthonormal one-particle basis chosen although the total energy remains invariant. Some bases result in more compact wave functions, i.e. result in fewer determinants with significant expansion coefficients. In this work, the Shannon entropy, as a measure of information content, is evaluated for such wave functions to examine whether there is a relationship between the FCI Shannon entropy of a given basis and the performance of that basis in truncated CI approaches. The results obtained for a set of randomly picked bases are compared to those obtained using the traditional canonical molecular orbitals, natural orbitals, seniority minimising orbitals and a basis that derives from direct minimisation of the Shannon entropy. FCI calculations for selected atomic and molecular systems clearly reflect the influence of the chosen basis. However, it is found that there is no direct relationship between the entropy computed for each basis and truncated CI energies.

When is the Fukui Function Not Normalized?

F. Heidar-Zadeh, R.A. Miranda-Quintana, T. Verstraelen, P. Bultinck, P.W. Ayers, A. Buekenhoudt
Journal of Chemical Theory and Computation (JCTC)
2016
A1

Maximum probability domains for Hubbard models

G. Acke, S. De Baerdemacker, P. Claeys, M. Van Raemdonck, W. Poelmans, D. Van Neck, P. Bultinck
Molecular Physics
114 (7-8), 1392-1405
2016
A1

Abstract

The theory of maximum probability domains (MPDs) is formulated for the Hubbard model in terms of projection operators and generating functions for both exact eigenstates as well as Slater determinants. A fast MPD analysis procedure is proposed, which is subsequently used to analyse numerical results for the Hubbard model. It is shown that the essential physics behind the considered Hubbard models can be exposed using MPDs. Furthermore, the MPDs appear to be in line with what is expected from Valence Bond (VB) Theory-based knowledge.

Open Access version available at UGent repository

Polynomial scaling approximations and Dynamic Correlation Corrections to Doubly Occupied Configuration Interaction wave functions

M. Van Raemdonck, D. Alcoba, W. Poelmans, S. De Baerdemacker, A. Torre, L. Lain, G. Massaccesi, D. Van Neck, P. Bultinck
Journal of Chemical Physics
143 (10), 104106
2015
A1

Abstract

A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.

Open Access version available at UGent repository

Variational optimization of the second order density matrix corresponding to a seniority-zero configuration interaction wave function

W. Poelmans, M. Van Raemdonck, B. Verstichel, S. De Baerdemacker, A. Torre, L. Lain, G. Massaccesi, D. Alcoba, P. Bultinck, D. Van Neck
Journal of Chemical Theory and Computation (JCTC)
11 (9), 4064–4076
2015
A1

Abstract

We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index $N$-representability $\mathcal{P}$-, $\mathcal{Q}$-, and $\mathcal{G}$-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly-occupied many-electron wave function, i.e.\ a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index $N$-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, $\text{N}_2$ and $\text{CN}^-$). This work is motivated by the fact that a doubly-occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly-occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as $L^3$, where $L$ is the number of spatial orbitals. Since the doubly-occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly-occupied framework.

A hybrid configuration interaction treatment based on seniority number and excitation schemes

D.R. Alcoba, A. Torre, L. Lain, O.B. Ona, P. Capuzzi, M. Van Raemdonck, P. Bultinck, D. Van Neck
Journal of Chemical Physics
141 (24), 244118
2014
A1

Abstract

We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method. (c) 2014 AIP Publishing LLC.

Open Access version available at UGent repository

More insight in multiple bonding with valence bond theory

K. Hendrickx, B. Braida, P. Bultinck, P. C. Hiberty
Computational and Theoretical Chemistry
1053, pp. 180-188
2015
A1
Published while none of the authors were employed at the CMM

Abstract

An original procedure is proposed, based on valence bond theory, to calculate accurate dissociation energies for multiply bonded molecules, while always dealing with extremely compact wave functions involving three valence bond structures at most. The procedure consists of dividing the bond-breaking into sequential steps, thus breaking one by one the separate components of the multiple bond. By using the breathing-orbital valence bond method (Hiberty and Shaik, 2002), it is ensured that both static and dynamic differential electron correlations are taken into account in each step. The procedure is illustrated for typical examples of multiply bonded molecules, N2, C2 and CO. The so-calculated total dissociation energies are at par with accurate calculations by state-of-the-art standard methods in the same basis set. The procedure also allows one to get some deep insight into the properties of the individual bonds that constitute the multiple bond. A so-called quasi-classical state is defined, in which the electrons of the bond under study have only one spin arrangement pattern, αβ, thus disabling the exchange of the two spin arrangements that is necessary for a covalent bonding interaction to take place. Taking this quasi-classical state as a non-bonded reference, one may estimate the “in-situ bonding energy” of an individual bond, as calculated at the molecular equilibrium geometry and in the presence of the other electrons. The procedure may also be used to assess the preferred bond length of an individual bond, which is shown to amount to 1.33 Å for the σ bond of N2, while the π bonds get stronger and stronger as the interatomic distance is shortened. Another application is the calculation of the resonance energy arising from the mixing of the ionic components of an individual bond to its covalent component, and the comparison of this resonance energy with the in-situ bonding energy. This shows that the σ bond of N2 and C2 is a classical covalent bond. On the other hand, the π bonds have a substantial resonance energy that put them close to the category of charge-shift bonds.

Non-Variational Orbital Optimization Techniques for the AP1roG Wave Function

K. Boguslawski, P. Tecmer, P.W. Ayers, P. Bultinck, S. De Baerdemacker, D. Van Neck
Journal of Chemical Theory and Computation (JCTC)
10 (11), 4873-4882
2014
A1

Abstract

We introduce new nonvariational orbital optimization schemes for the antisymmetric product of one-reference orbital geminal (AP1roG) wave function (also known as pair-coupled cluster doubles) that are extensions to our recently proposed projected seniority-two (PS2-AP1roG) orbital optimization method [ J. Chem. Phys. 2014, 140, 214114)]. These approaches represent less stringent approximations to the PS2-AP1roG ansatz and prove to be more robust approximations to the variational orbital optimization scheme than PS2-AP1roG. The performance of the proposed orbital optimization techniques is illustrated for a number of well-known multireference problems: the insertion of Be into H2, the automerization process of cyclobutadiene, the stability of the monocyclic form of pyridyne, and the aromatic stability of benzene.

Efficient description of strongly correlated electrons with mean-field cost

K. Boguslawski, P. Tecmer, P.W. Ayers, P. Bultinck, S. De Baerdemacker, D. Van Neck
Physical Review B
89 (20), 201106
2014
A1

Abstract

We present an efficient approach to the electron correlation problem that is well suited for strongly interacting many-body systems, but requires only mean-field-like computational cost. The performance of our approach is illustrated for one-dimensional Hubbard rings with different numbers of sites, and for the nonrelativistic quantum-chemical Hamiltonian exploring the symmetric dissociation of the H-50 hydrogen chain.

Open Access version available at UGent repository

Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal

K. Boguslawski, P. Tecmer, P.A. Limacher, P.A. Johnson, P.W. Ayers, P. Bultinck, S. De Baerdemacker, D. Van Neck
Journal of Chemical Physics
140 (21), 214114
2014
A1

Abstract

We present a new, non-variational orbital-optimization scheme for the antisymmetric product of one-reference orbital geminal wave function. Our approach is motivated by the observation that an orbital-optimized seniority-zero configuration interaction (CI) expansion yields similar results to an orbital-optimized seniority-zero-plus-two CI expansion [L. Bytautas, T. M. Henderson, C. A. Jimenez-Hoyos, J. K. Ellis, and G. E. Scuseria, J. Chem. Phys. 135, 044119 (2011)]. A numerical analysis is performed for the C-2 and LiF molecules, for the CH2 singlet diradical as well as for the symmetric stretching of hypothetical (linear) hydrogen chains. For these test cases, the proposed orbital-optimization protocol yields similar results to its variational orbital optimization counterpart, but prevents symmetry-breaking of molecular orbitals in most cases. (C) 2014 AIP Publishing LLC.