Méthode du cluster couplé

La méthode du cluster couplé, ou théorie du cluster couplé (expression souvent abrégée en « cluster couplé », en anglais coupled cluster) est une technique numérique de description des systèmes à plusieurs corps. Son utilisation la plus répandue est comme méthode ab initio de chimie quantique post-Hartree-Fock en chimie numérique. Il est basé sur la méthode d'orbitale moléculaire Hartree-Fock et lui ajoute un terme de correction afin de prendre en compte la corrélation électronique. Certains des calculs les plus précis pour des molécules de petite ou de taille moyenne utilisent cette méthode. La méthode fut développée initialement par Fritz Coester et Hermann Kümmel dans les années 1950 afin d'étudier les phénomènes de physique nucléaire, mais devint plus fréquemment utilisée après que Jiři Čížek et Josef Paldus eurent reformulé la méthode pour l'adapter à la corrélation électronique dans les atomes et molécules dans les années 1960. Elle constitue à ce jour une des méthodes les plus

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"Gold standard" coupled-cluster study of acetylene pentamers and hexamers via molecular tailoring approach

Brijesh Kumar Mishra

Due to high scaling order of MP2 and CCSD(T) methods, it is either difficult or at times even impossible to treat even moderately sized molecular systems with elaborate basis sets such as aug-cc-pVXZ (X = D, T, Q). In the present work, several structures of acetylene pentamers and hexamers are explored at MP2 and CCSD(T) levels of theory as prototypical examples of clusters bound by CH center dot center dot center dot pi interactions. To enable this investigation, fragment-based method Molecular Tailoring Approach (MTA) is employed. It is shown that these acetylene assemblies can be treated with substantial reduction in computational resources and time, yet retaining a sub-millihartree accuracy in the energy. Further, using standard extrapolation methodologies, stabilization energies at the complete basis set limit of the acetylene clusters under consideration are determined at MP2 and CCSD(T) levels of theory. To test out the feasibility of treating a large cluster at MP2 level, a demonstrative calculation on a dodecamer of acetylene is reported.

2011

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Machine learning models of the energy curvature vs particle number for optimal tuning of long-range corrected functionals

Alberto Fabrizio, Benjamin André René Meyer

The average energy curvature as a function of the particle number is a molecule-specific quantity, which measures the deviation of a given functional from the exact conditions of density functional theory. Related to the lack of derivative discontinuity in approximate exchange-correlation potentials, the information about the curvature has been successfully used to restore the physical meaning of Kohn-Sham orbital eigenvalues and to develop non-empirical tuning and correction schemes for density functional approximations. In this work, we propose the construction of a machine-learning framework targeting the average energy curvature between the neutral and the radical cation state of thousands of small organic molecules (QM7 database). The applicability of the model is demonstrated in the context of system-specific gamma-tuning of the LC-omega PBE functional and validated against the molecular first ionization potentials at equation-of-motion coupled-cluster references. In addition, we propose a local version of the non-linear regression model and demonstrate its transferability and predictive power by determining the optimal range-separation parameter for two large molecules relevant to the field of hole-transporting materials. Finally, we explore the underlying structure of the QM7 database with the t-SNE dimensionality-reduction algorithm and identify structural and compositional patterns that promote the deviation from the piecewise linearity condition.

AMER INST PHYSICS2020

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Geometries and vibrational frequencies of small radicals: Performance of Coupled Cluster and more approximate methods

Jeremy Samuel Arey, Peter Rudolf Tentscher

We generated a new set of reference geometries of small radicals using experimental equilibrium structures, as well as a benchmark-quality coupled cluster additivity scheme including up to quadruples excitations (CCSDTQ). Using these geometries and a set of experimental vibrational frequencies of open shell diatomics, we evaluated the performance of various coupled cluster methods based mainly on unrestricted references, using Dunning basis sets both with and without core correlation. Contrary to previous results, we found that UCCSD(T) and ROCCSD(T) perform equally well for geometries, better than CCSD, and close to their performances for closed shell systems. No improvement over CCSD(T) was achieved by using a Brueckner reference (BD(T)) or full triples (CCSDT). For frequencies, ROCCSD(T), BD(T), and CCSDT improve upon UCCSD(T), especially for the troublesome NO and CO+ cases. EOMIP-CCSD yields geometries and harmonic frequencies similar to CCSD, and qualitatively correct anharmonic (VPT2) contributions in all cases, like the RO-CC methods. The double hybrid DFT functional B2PLYP-D yields geometries and frequencies of similar quality to that of CCSD but at a much reduced cost. The meta hybrid functionals M06-2X, M06-HF, and BMK perform worse than CCSD, and worse than B3LYP, on average.

2012

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Chimie numérique

La chimie numérique ou chimie informatique, parfois aussi chimie computationnelle, est une branche de la chimie et de la physico-chimie qui utilise les lois de la chimie théorique exploitées dans de

Interaction de configuration

L'interaction de configuration (configuration interaction en anglais - CI) est une méthode post-Hartree-Fock linéaire variationnelle pour la résolution de l'équation de Schrödinger non relativiste dan

Méthode de Hartree-Fock

En physique et chimie numérique, la méthode de Hartree-Fock est une méthode de résolution approchée de l'équation de Schrödinger d'un système quantique à plusieurs corps utilisant le principe variatio

CH-353: Introduction to electronic structure methods

Repetition of the basic concepts of quantum mechanics and main numerical algorithms used for practical implementions. Basic principles of electronic structure methods:Hartree-Fock, many body perturbation theory, configuration interaction, coupled-cluster theory, density functional theory.

CH-431: Physical and computational organic chemistry

This course introduces modern computational electronic structure methods and their broad applications to organic chemistry. It also discusses physical organic concepts to illustrate the stability and reactivity of organic molecules.