arXiv subjects

Anthony Scemama

Publications and source records attributed to Anthony Scemama.

At least 37 records · Page 2Linked to original sources

arXiv2023

TREXIO: A File Format and Library for Quantum Chemistry

TREXIO is an open-source file format and library developed for the storage and manipulation of data produced by quantum chemistry calculations. It is designed with the goal of providing a reliable and efficient method of storing and exchanging wave function parameters and matrix elements, making it an important tool for researchers in the field of quantum chemistry. In this work, we present an overview of the TREXIO file format and library. The library consists of a front-end implemented in the C programming language and two different back-ends: a text back-end and a binary back-end utilizing the HDF5 library which enables fast read and write operations. It is compatible with a variety of platforms and has interfaces for the Fortran, Python, and OCaml programming languages. In addition, a suite of tools has been developed to facilitate the use of the TREXIO format and library, including converters for popular quantum chemistry codes and utilities for validating and manipulating data stored in TREXIO files. The simplicity, versatility, and ease of use of TREXIO make it a valuable resource for researchers working with quantum chemistry data.

physics.chem-ph↗

arXiv2023

Bi-orthonormal orbital optimization with a cheap core-electron free three-body correlation factor for Quantum Monte Carlo and Transcorrelation

We introduce a novel three-body correlation factor that is designed to vanish in the core region around each nucleus and approach a universal two-body correlation factor for valence electrons. The Transcorrelated Hamiltonian is used to optimize the orbitals of a single Slater determinant within a biorthonormal framework. The Slater-Jastrow wave function is optimized on a set of atomic and molecular systems containing both second-row elements and $3d$ transition metal elements. The optimization of the correlation factor and the orbitals, along with increasing the basis set, results in a systematic lowering of the Variational Monte Carlo energy for all systems tested. Importantly, the optimal parameters of the correlation factor obtained for atomic systems are transferable to molecules. Additionally, the present correlation factor is computationally efficient, using a mixed analytical-numerical integration scheme that reduces the costly numerical integration from $\mathbb{R}^6$ to $\mathbb{R}^3$.

physics.chem-ph↗

arXiv2022

Diffusion Monte Carlo using domains in configuration space

The sampling of the configuration space in diffusion Monte Carlo (DMC) is done using walkers moving randomly. In a previous work on the Hubbard model [\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B \textbf{60}, 2299 (1999)}], it was shown that the probability for a walker to stay a certain amount of time in the same state obeys a Poisson law and that the on-state dynamics can be integrated out exactly, leading to an effective dynamics connecting only different states. Here, we extend this idea to the general case of a walker trapped within domains of arbitrary shape and size. The equations of the resulting effective stochastic dynamics are derived. The larger the average (trapping) time spent by the walker within the domains, the greater the reduction in statistical fluctuations. A numerical application to the Hubbard model is presented. Although this work presents the method for finite linear spaces, it can be generalized without fundamental difficulties to continuous configuration spaces.

cond-mat.str-el↗

arXiv2022

Ground- and Excited-State Dipole Moments and Oscillator Strengths of Full Configuration Interaction Quality

We report ground- and excited-state dipole moments and oscillator strengths (computed in different ``gauges'' or representations) of full configuration interaction (FCI) quality using the selected configuration interaction method known as \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI). Thanks to a set encompassing 35 ground- and excited-state properties computed in 11 small molecules, the present near-FCI estimates allow us to assess the accuracy of high-order coupled-cluster (CC) calculations including up to quadruple excitations. In particular, we show that incrementing the excitation degree of the CC expansion (from CCSD to CCSDT or from CCSDT to CCSDTQ) reduces the average error with respect to the near-FCI reference values by approximately one order of magnitude.

physics.chem-ph↗

arXiv2022

Double excitation energies from quantum Monte Carlo using state-specific energy optimization

We show that recently developed quantum Monte Carlo methods, which provide accurate vertical transition energies for single excitations, also successfully treat double excitations. We study the double excitations in medium-sized molecules, some of which are challenging for high level coupled-cluster calculations to model accurately. Our fixed-node diffusion Monte Carlo excitation energies are in very good agreement with reliable benchmarks, when available, and provide accurate predictions for excitation energies of difficult systems where reference values are lacking.

physics.comp-ph↗

arXiv2022

Extension of selected configuration interaction for transcorrelated methods

In this work we present an extension of the popular selected configuration interaction (SCI) algorithms to the Transcorrelated (TC) framework. Although we used in this work the recently introduced one-parameter correlation factor [E. Giner, J. Chem. Phys., 154, 084119 (2021)], the theory presented here is valid for any correlation factor. Thanks to the formalization of the non Hermitian TC eigenvalue problem as a search of stationary points for a specific functional depending both on left-and right-functions, we obtain a general framework allowing different choices for both the selection criterion in SCI and the second order perturbative correction to the energy. After numerical investigations on different second-row atomic and molecular systems in increasingly large basis sets, we found that taking into account the non Hermitian character of the TC Hamiltonian in the selection criterion is mandatory to obtain a fast convergence of the TC energy. Also, selection criteria based on either the first order coefficient or the second order energy lead to significantly different convergence rates, which is typically not the case in the usual Hermitian SCI. Regarding the convergence of the total second order perturbation energy, we find that the quality of the left-function used in the equations strongly affects the quality of the results. Within the near-optimal algorithm proposed here we find that the SCI expansion in the TC framework converges faster than the usual SCI both in terms of basis set and number of Slater determinants.

cond-mat.str-el↗

arXiv2022

Reference Energies for Cyclobutadiene: Automerization and Excited States

Cyclobutadiene is a well-known playground for theoretical chemists and is particularly suitable to test ground- and excited-state methods. Indeed, due to its high spatial symmetry, especially at the $D_{4h}$ square geometry but also in the $D_{2h}$ rectangular arrangement, the ground and excited states of cyclobutadiene exhibit multi-configurational characters and single-reference methods, such as adiabatic time-dependent density-functional theory (TD-DFT) or equation-of-motion coupled cluster (EOM-CC), are notoriously known to struggle in such situations. In this work, using a large panel of methods and basis sets, we provide an extensive computational study of the automerization barrier (defined as the difference between the square and rectangular ground-state energies) and the vertical excitation energies at $D_{2h}$ and $D_{4h}$ equilibrium structures. In particular, selected configuration interaction (SCI), multi-reference perturbation theory (CASSCF, CASPT2, and NEVPT2), and coupled-cluster (CCSD, CC3, CCSDT, CC4, and CCSDTQ) calculations are performed. The spin-flip formalism, which is known to provide a qualitatively correct description of these diradical states, is also tested within TD-DFT (combined with numerous exchange-correlation functionals) and the algebraic diagrammatic construction [ADC(2)-s, ADC(2)-x, and ADC(3)] schemes. A theoretical best estimate is defined for the automerization barrier and for each vertical transition energy.

physics.chem-ph↗

arXiv2022

Optimization of large determinant expansions in quantum Monte Carlo

We present a new method for the optimization of large configuration interaction (CI) expansions in the quantum Monte Carlo (QMC) framework. The central idea here is to replace the non-orthogonal variational optimization of CI coefficients performed in usual QMC calculations by an orthogonal non-Hermitian optimization thanks to the so-called transcorrelated (TC) framework, the two methods yielding the same results in the limit of a complete basis set. By rewriting the TC equations as an effective self-consistent Hermitian problem, our approach requires the sampling of a single quantity per Slater determinant, leading to minimal memory requirements in the QMC code. Using analytical quantities obtained from both the TC framework and the usual CI-type calculations, we also propose improved estimators which reduce the statistical fluctuations of the sampled quantities by more than an order of magnitude. We demonstrate the efficiency of this method on wave functions containing $10^5-10^6$ Slater determinants, using effective core potentials or all-electron calculations. In all the cases, a sub-milliHartree convergence is reached within only two or three iterations of optimization.

physics.chem-ph↗

arXiv2022

What is the number of electrons in a spatial domain?

We like to attribute a number of electrons to spatial domains (atoms, bonds, ...). However, as a rule, the number of electrons in a spatial domain is not a sharp number. We thus study probabilities for having any number of electrons (between 0 and the total number of electrons in the system) in a given spatial domain. We show that by choosing a domain that maximizes a chosen probability (or is close to it), one obtains higher probabilities for chemically relevant regions. The probability to have a given electronic arrangement, - for example, by attributing a number of electrons to an atomic shell - can be low. It remains so even in the "best" case, i.e, if the spatial domain is chosen to maximize the chosen probability. In other words, the number of electrons in a spatial region significantly fluctuates. The freedom of choosing the number of electrons we are interested in shows that a "chemical" question is not always well-posed. We show it using as an example the KrF2 molecule.

physics.chem-ph↗

arXiv2022

The effect of uncertainty on building blocks in molecules

Probabilities to find a chosen number of electrons in flexible domains of space are calculated for highly correlated wave functions. Quantum mechanics can produce higher probabilities for chemically relevant arrangements of electrons in these regions. However, the probability to have a given arrangement, e.g., that corresponding to chemical formulas (bonds or atoms), is low although being often maximal. Like in valence bond theory, it is useful to consider alternative distributions of the electrons. Exchanges of electrons should be considered not only between atoms, but also between other types of regions, like those attributed to lone pairs. It is useful to have definitions flexible enough to allow the user to find the reference representations he considers most relevant. We tentatively suggest a tool (the effective number of parties) to help one make the choice.

physics.chem-ph↗

arXiv2021

Reference excitation energies of increasingly large molecules: a QMC study of cyanine dyes

We revisit here the lowest vertical excitations of cyanine dyes using quantum Monte Carlo and leverage on recent developments to systematically improve on previous results. In particular, we employ a protocol for the construction of compact and accurate multi-determinant Jastrow-Slater wave functions for multiple states, which we have recently validated on the excited-state properties of several small prototypical molecules. Here, we obtain quantum Monte Carlo excitation energies in excellent agreement with high-level coupled cluster for all the cyanines where the coupled cluster method is applicable. Furthermore, we push our protocol to longer chains, demonstrating that quantum Monte Carlo is a viable methodology to establish reference data at system sizes which are hard to reach with other high-end approaches of similar accuracy. Finally, we determine which ingredients are key to an accurate treatment of these challenging systems and rationalize why a description of the excitation based on only active $π$ orbitals lacks the desired accuracy for the shorter chains.

physics.chem-ph↗

arXiv2021

A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

We study beryllium dihydride (BeH$_2$) and acetylene (C$_2$H$_2$) molecules using real-space diffusion Monte Carlo (DMC) method. The molecules serve as perhaps the simplest prototypes that illustrate the difficulties with biases in the fixed-node DMC calculations that might appear with the use of effective core potentials (ECPs) or other nonlocal operators. This is especially relevant for the recently introduced correlation consistent ECPs (ccECPs) for $2s2p$ elements. Corresponding ccECPs exhibit deeper potential functions due to higher fidelity to all-electron counterparts, which could lead to larger local energy fluctuations. We point out that the difficulties stem from issues that are straightforward to address by upgrades of basis sets, use of T-moves for nonlocal terms, inclusion of a few configurations into the trial function and similar. The resulting accuracy corresponds to the ccECP target (chemical accuracy) and it is in consistent agreement with independent correlated calculations. Further possibilities for upgrading the reliability of the DMC algorithm and considerations for better adapted and more robust Jastrow factors are discussed as well.

physics.comp-ph↗

arXiv2021

Accurate full configuration interaction correlation energy estimates for five- and six-membered rings

Following our recent work on the benzene molecule [\href{https://doi.org/10.1063/5.0027617}{J.~Chem.~Phys.~\textbf{153}, 176101 (2020)}], itself motivated by the blind challenge of Eriksen \textit{et al.} [\href{https://doi.org/10.1021/acs.jpclett.0c02621}{J.~Phys.~Chem.~Lett.~\textbf{11}, 8922 (2020)}] on the same system, we report accurate full configuration interaction (FCI) frozen-core correlation energy estimates for twelve five- and six-membered ring molecules in the standard correlation-consistent double-$ζ$ Dunning basis set (cc-pVDZ). Our FCI correlation energy estimates, with estimated error smaller than 1 millihartree, are based on energetically optimized-orbital selected configuration interaction (SCI) calculations performed with the \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) algorithm. Having at our disposal these accurate reference energies, the respective performance and convergence properties of several popular and widely-used families of single-reference quantum chemistry methods are investigated. In particular, we study the convergence properties of i) the Møller-Plesset perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), ii) the iterative approximate coupled-cluster series CC2, CC3, and CC4, and iii) the coupled-cluster series CCSD, CCSDT, and CCSDTQ. The performance of the ground-state gold standard CCSD(T) as well as the completely renormalized CC model, CR-CC(2,3), are also investigated.

physics.chem-ph↗

arXiv2021

Excited States From State Specific Orbital Optimized Pair Coupled Cluster

The pair coupled cluster doubles (pCCD) method (where the excitation manifold is restricted to electron pairs) has a series of interesting features. Among others, it provides ground-state energies very close to what is obtained with doubly-occupied configuration interaction (DOCI), but with polynomial cost (compared with the exponential cost of the latter). Here, we address whether this similarity holds for excited states, by exploring the symmetric dissociation of the linear \ce{H4} molecule. When ground-state Hartree-Fock (HF) orbitals are employed, pCCD and DOCI excited-state energies do not match, a feature that is assigned to the poor HF reference. In contrast, by optimizing the orbitals at the pCCD level (oo-pCCD) specifically for each excited state, the discrepancies between pCCD and DOCI decrease by one or two orders of magnitude. Therefore, the pCCD and DOCI methodologies still provide comparable energies for excited states, but only if suitable, state-specific orbitals are adopted. We also assessed whether a pCCD approach could be used to directly target doubly-excited states, without having to resort to the equation-of-motion (EOM) formalism. In our $Δ$oo-pCCD model, excitation energies were extracted from the energy difference between separate oo-pCCD calculations for the ground state and the targeted excited state. For a set comprising the doubly-excited states of \ce{CH+}, \ce{BH}, nitroxyl, nitrosomethane, and formaldehyde, we found that $Δ$oo-pCCD provides quite accurate excitation energies, with root mean square deviations (with respect to full configuration interaction results) lower than CC3 and comparable to EOM-CCSDT, two methods with much higher computational cost.

physics.chem-ph↗

arXiv2021

Spin-adapted selected configuration interaction in a determinant basis

Selected configuration interaction (SCI) methods, when complemented with a second-order perturbative correction, provide near full configuration interaction (FCI) quality energies with only a small fraction of the Slater determinants of the FCI space. However, a selection criterion based on determinants alone does not ensure a spin-pure wave function. In other words, such SCI wave functions are not eigenfunctions of the $S^2$ operator. In many situations (bond breaking, magnetic system, excited state, etc), having a spin-adapted wave function is essential for a quantitatively correct description of the system. Here, we propose an efficient algorithm which, given an arbitrary determinant space, generates all the missing Slater determinants allowing one to obtain spin-adapted wave functions while avoiding manipulations involving configuration state functions. For example, generating all the possible determinants with 6 spin-up and 6 spin-down electrons in 12 open shells takes 21 CPU cycles per generated Slater determinant. The selection is still done with individual determinants, and one can take advantage of the basis of configuration state functions in the diagonalization of the Hamiltonian to reduce significantly the memory footprint.

physics.chem-ph↗

arXiv2021

Tailoring CIPSI expansions for QMC calculations of electronic excitations: the case study of thiophene

The perturbatively selected configuration interaction scheme (CIPSI) is particularly effective in constructing determinantal expansions for quantum Monte Carlo (QMC) simulations with Jastrow-Slater wave functions: fast and smooth convergence of ground-state properties, as well as balanced descriptions of ground- and excited-states of different symmetries have been reported. In particular, accurate excitation energies have been obtained by the pivotal requirement of using CIPSI expansions with similar second-order perturbation corrections for each state, that is, similar estimated errors with respect to the full configuration interaction limit. Here we elaborate on the CIPSI selection criterion for excited states of the same symmetry as the ground state, generating expansions from a common orbital set. Using these expansions in QMC as determinantal components of Jastrow-Slater wave functions, we compute the lowest, bright excited state of thiophene, which is challenging due to its significant multireference character. The resulting vertical excitation energies are within 0.05~eV of the best theoretical estimates, already with expansions of only a few thousand determinants. Furthermore, we relax the ground- and excited-state structures following the corresponding root in variational Monte Carlo and obtain bond lengths which are accurate to better than 0.01~Å. Therefore, while the full treatment at the CIPSI level of this system would be quite demanding, in QMC we can compute high-quality excitation energies and excited-state structural parameters building on affordable CIPSI expansions with relatively few, well chosen determinants.

physics.class-ph↗

arXiv2021

QUESTDB: a database of highly-accurate excitation energies for the electronic structure community

We describe our efforts of the past few years to create a large set of more than 500 highly-accurate vertical excitation energies of various natures ($π\to π^*$, $n \to π^*$, double excitation, Rydberg, singlet, doublet, triplet, etc) in small- and medium-sized molecules. These values have been obtained using an incremental strategy which consists in combining high-order coupled cluster and selected configuration interaction calculations using increasingly large diffuse basis sets in order to reach high accuracy. One of the key aspect of the so-called QUEST database of vertical excitations is that it does not rely on any experimental values, avoiding potential biases inherently linked to experiments and facilitating theoretical cross comparisons. Following this composite protocol, we have been able to produce theoretical best estimate (TBEs) with the aug-cc-pVTZ basis set for each of these transitions, as well as basis set corrected TBEs (i.e., near the complete basis set limit) for some of them. The TBEs/aug-cc-pVTZ have been employed to benchmark a large number of (lower-order) wave function methods such as CIS(D), ADC(2), CC2, STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, ADC(3), CC3, NEVPT2, and others (including spin-scaled variants). In order to gather the huge amount of data produced during the QUEST project, we have created a website [https://lcpq.github.io/QUESTDB_website] where one can easily test and compare the accuracy of a given method with respect to various variables such as the molecule size or its family, the nature of the excited states, the type of basis set, etc. We hope that the present review will provide a useful summary of our effort so far and foster new developments around excited-state methods.

physics.chem-ph↗

arXiv2020

Towards a Systematic Improvement of the Fixed-Node Approximation in Diffusion Monte Carlo for Solids -- A Case Study In Diamond

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for \textit{ab initio} electronic structure calculations, in practice the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros) must be used. This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced.

physics.chem-ph↗