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Patrick Cassam-Chenaï

Publications and source records attributed to Patrick Cassam-Chenaï.

15 recordsLinked to original sources

A Remarkable Application of Zassenhaus Formula to Strongly Correlated Electron Systems

We show that the Zassenhaus decomposition for the exponential of the sum of two non-commuting operators, simplifies drastically when these operators satisfy a simple condition, called the no-mixed adjoint property. An important application to a Unitary Coupled Cluster method for strongly correlated electron systems is presented. This ansatz requires no Trotterization and is exact on a quantum computer with a finite number of Givens gate equals to the number of free parameters. The formulas obtained in this work also shed light on why and when optimization after Trotterization gives exact solutions in disentangled forms of unitary coupled cluster.

math-ph↗

Singlet Geminal Wavefunctions

Wavefunction forms based on products of electron pairs are usually constructed as closed-shell singlets, which is insufficient when the molecular state has a nonzero spin or when the chemistry is determined by $d$- or $f-$electrons. A set of two-electron forms are considered as explicit couplings of second-quantized operators to open-shell singlets. Geminal wavefunctions are constructed and their structure is elaborated. Numerical results for small model systems clearly demonstrate improvement over closed-shell singlet pairs.

physics.chem-ph↗

A Conjecture on Antisymmetrized Geminal Power Wavefunctions

We conjecture that ``Antisymmetrized Geminal Power'' wave functions, and, in particular, those of extreme type in Coleman's terminology (i.e. with all geminal coefficients equal), can always be rewritten as antisymmetrized products of geminals orthogonal to each other. We prove this conjecture in simple cases and provide numerical evidence that it holds true in more complicated examples. Establishing the validity of this conjecture is important as it questions the physical interpretation of AGP wavefunctions.

cond-mat.supr-con↗

2D-Block Geminals: a non 1-orthogonal and non 0-seniority model with reduced computational complexity

We present a new geminal product wave function ansatz where the geminals are not constrained to be strongly orthogonal nor to be of seniority zero. Instead, we introduce weaker orthogonality constraints between geminals which significantly lower the computational effort, without sacrificing the indistinguishability of the electrons. That is to say, the electron pairs corresponding to the geminals are not fully distinguishable, and their product has still to be antisymmetrized according to the Pauli principle to form a \textit{bona fide} electronic wave function.Our geometrical constraints translate into simple equations involving the traces of products of our geminal matrices. In the simplest non-trivial model, a set of solutions is given by block-diagonal matrices where each block is of size 2x2 and consists of either a Pauli matrix or a normalized diagonal matrix, multiplied by a complex parameter to be optimized. With this simplified ansatz for geminals, the number of terms in the calculation of the matrix elements of quantum observables is considerably reduced. A proof of principle is reported and confirms that the ansatz is more accurate than strongly orthogonal geminal products while remaining computationally affordable.

physics.chem-ph↗

Electrons as an environment for nuclei within molecules: a quantitative assessment of their contribution to a classical-like molecular structure

Molecular structure is often considered as emerging from the decoherence effect of the environment. Electrons are part of the environment of the nuclei in a molecule. In this work, their contribution to the classical-like geometrical relationships often observed between nuclei in molecular systems is investigated. Reduced density matrix (RDM) elements are evaluated from electron-nucleus wave functions. The computational results show that the electrons play a role in the localization of the nuclei around specific geometries. Although the electronic environment alone cannot explain molecular symmetry-broken isomers, it can contribute to their dynamical stability by reducing off-diagonal RDM elements.

physics.chem-ph↗

Molien generating functions and integrity bases for the action of the SO(3) and O(3) groups on a set of vectors

The construction of integrity bases for invariant and covariant polynomials built from aset of three dimensional vectors under the SO(3) and O(3) symmetries is presented. Thispaper is a follow--up to our previous work that dealt with a set of two dimensional vectorsunder the action of the SO(2) and O(2) groups [G. Dhont and B. I. Zhilinskiı, J. Phys. A:Math. Theor., 46, 455202 (2013)]. The expressions of the Molien generating functions asone rational function are a useful guide to build integrity bases for the rings of invariantsand the free modules of covariants. The structure of the non--free modules of covariants ismore complex. In this case, we write the Molien generating function as a sum of rationalfunctions and show that its symbolic interpretation leads to the concept of generalizedintegrity basis. The integrity bases and generalized integrity bases for O(3) are deducedfrom the SO(3) ones. The results are useful in quantum chemistry to describe the potentialenergy or multipole moment hypersurfaces of molecules. In particular, the generalizedintegrity bases that are required for the description of the electric and magnetic quadrupolemoment hypersurfaces of tetratomic molecules are given for the first time.

math.AC↗

Theoretical Study of the Anisotropy Spectra of the Valine Zwitterion and Glyceraldehyde

The electronic absorption (EA), circular dichroism (ECD), and anisotropy spectra of the L-valine zwitterion and D-glyceraldehyde are calculated by time-dependent density functional theory (TDDFT) with the M06-2X and B3LYP functionals. It is found that the absorption and ECD spectra from TDDFT/M06-2X agree well with experimental results measured from amorphous film of L-valine. Moreover, the calculations reproduce all three major peaks observed in the experimental anisotropy spectra. For D-glyceraldehyde, the TDDFT/M06-2X calculations indicate that the excitation wavelengths of the first excited state of 32 stable conformers distribute from 288 to 322 nm, giving rise to two ECD peaks with opposite signs centered at 288 nm and 322 nm. The very weak absorption of the first excited state (S1) induces two high peaks in the anisotropy spectra of D-glyceraldehyde, which should be seen in future experimental works.

physics.chem-ph↗

Anharmonic vibrational spectroscopy of Polycyclic Aromatic Hydrocarbons (PAHs)

While powerful techniques exist to accurately account for anharmonicity in vibrational molecular spectroscopy, they are computationally very expensive and cannot be routinely employed for large species and/or at non- zero vibrational temperatures. Motivated by the study of Polycyclic Aromatic Hydrocarbon (PAH) emission in space, we developed a new code, which takes into account all modes and can describe all IR transitions including bands becoming active due to resonances as well as overtones, combination and difference bands. In this article, we describe the methodology that was implemented and discuss how the main difficulties were overcome, so as to keep the problem tractable. Benchmarking with high-level calculations was performed on a small molecule. We carried out specific convergence tests on two prototypical PAHs, pyrene (C$_{16}$H$_{10}$) and coronene (C$_{24}$H$_{12}$), aiming at optimising tunable parameters to achieve both acceptable accuracy and computational costs for this class of molecules. We then report the results obtained at 0 K for pyrene and coronene, comparing the calculated spectra with available experimental data. The theoretical band positions were found to be significantly improved compared to harmonic Density Functional Theory (DFT) calculations. The band intensities are in reasonable agreement with experiments, the main limitation being the accuracy of the underlying calculations of the quartic force field. This is a first step towards calculating moderately high-temperature spectra of PAHs and other similarly rigid molecules using Monte Carlo sampling.

physics.chem-ph↗

Smeared Coulomb potential orbitals for the electron-nucleus mean field configuration interaction method

We propose to use the eigenfunctions of a one-electron model Hamiltonian to perform electron-nucleus mean field configuration interaction (EN-MFCI) calculations. The potential energy of our model Hamiltonian corresponds to the Coulomb potential of an infinite wire with charge $Z$ distributed according to a Gaussian function. The time independent \sch equation for this Hamiltonian is solved perturbationally in the limit of small amplitude vibration (Gaussian function width close to zero).

physics.chem-ph↗

An improved lower bound for the maximal length of a multivector

A new lower bound for the maximal length of a multivector is obtained. It is much closer to the best known upper bound than previously reported lower bound estimates. The maximal length appears to be unexpectedly large for $n$-vectors, with n>2, since the few exactly known values seem to grow linearly with vector space dimension, whereas the new lower bound has a polynomial order equal to n-1 like the best known upper bound. This result has implications for quantum chemistry.

math.RA↗

Generalization of the concepts of seniority number and ionicity

We present generalized versions of the concepts of seniority number and ionicity. These generalized numbers count respectively the partially occupied and fully occupied shells for any partition of the orbital space into shells. The Hermitian operators whose eigenspaces correspond to wave functions of definite generalized seniority or ionicity values are introduced. The generalized seniority numbers (GSNs) afford to establish refined hierarchies of configuration interaction (CI) spaces within those of fixed ordinary seniority. Such a hierarchy is illustrated on the buckminsterfullerene molecule.

physics.chem-ph↗

Spin contamination and noncollinearity in general complex Hartree-Fock wave functions

An expression for the square of the spin operator expectation value, \textless{} S^2\textgreater{}, is obtained for a general complex Hartree-Fock (GCHF) wave function and decomposed into four contributions: The main one whose expression is formally identical to the restricted (open-shell) Hartree-Fock expression. A spin contamination one formally analogous to that found for spin unrestricted Hartree-Fock wave functions. A noncollinearity contribution related to the fact that the wave function is not an eigenfunction of the spin-S\_z operator. A perpendicularity contribution related to the fact that the spin density is not constrained to be zero in the xy-plane. All these contributions are evaluated and compared for the H\_2O^+ system. The optimization of the collinearity axis is also considered.

quant-ph↗

A Fast Algorithm for the Construction of Integrity Bases Associated to Symmetry-Adapted Polynomial Representations. Application to Tetrahedral XY4 Molecules

Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the construction of symmetry--adapted polynomials in the symmetry coordinates of a molecular system, because it is based on a finer description of the mathematical structure of the latter. The present article extends its use to the construction of polynomial bases which span possibly, non--totally symmetric irreducible representations of a molecular symmetry group. Electric or magnetic observables can carry such irreducible representations, a common example is given by the electric dipole moment surface. The elementary generating functions and their corresponding integrity bases, where both the initial and the final representations are irreducible, are the building blocks of the algorithm presented in this article, which is faster than algorithms based on projection operators only. The generating functions for the full initial representation of interest are built recursively from the elementary generating functions. Integrity bases which can be used to generate in the most economical way symmetry--adapted polynomial bases are constructed alongside in the same fashion. The method is illustrated in detail on XY4 type of molecules. Explicit integrity bases for all five possible final irreducible representations of the tetrahedral group have been calculated and are given in the supplemental material associated with this paper.

math-ph↗

Improving Guess Geminals for the Geminal Mean Field Configuration Interaction Method

The purpose of this letter is to show that a rotation of Hartree-Fock canonical orbitals which minimizes the lowest eigenvalues of a configuration interaction calculation limited to the mono-excitated configurations from a given orbital allows one to construct a better starting guess for the geminal mean field configuration interaction method.

physics.chem-ph↗

Geometric Measure of Indistinguishability for Groups of Identical Particles

The concept of p-orthogonality (1=< p =< n) between n-particle states is introduced. It generalizes common orthogonality, which is equivalent to n-orthogonality, and strong orthogonality between fermionic states, which is equivalent to 1-orthogonality. Within the class of non p-orthogonal states a finer measure of non p-orthogonality is provided by Araki's angles between p-internal spaces. The p-orthogonality concept is a geometric measure of indistinguishability that is independent of the representation chosen for the quantum states. It induces a new hierarchy of approximations for group function methods. The simplifications that occur in the calculation of matrix elements between p-orthogonal group functions are presented.

quant-ph↗