Andreas Savin

Andreas Savin
Sorbonne University | UPMC

About

275
Publications
23,180
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
28,534
Citations

Publications

Publications (275)
Preprint
Full-text available
Short-range corrections to long-range selected configuration interaction calculations are derived from perturbation theory considerations and applied to harmonium (with two to six electrons for some low-lying states). No fitting to reference data is used, and the method is applicable to ground and excited states. The formulas derived are rigorous w...
Chapter
Full-text available
Properties of erfonium, a Hooke atom with the Coulomb interaction potential 1/r replaced by a non-singular erf(μ r)/r potential are investigated. The structure of the Hooke atom potential and properties of its energy spectrum, relative to the ones of the spherical harmonic oscillator and of harmonium, are analyzed. It is shown, that at a certain va...
Preprint
Full-text available
The expectation value of the Hamiltonian using a model wave function is widely used to estimate the eigenvalues of electronic Hamiltonians. We explore here a modified formula for models based on long-range interaction. It scales differently the singlet and triplet component of the repulsion between electrons not present in the model (its short-rang...
Article
Full-text available
In this article, we explore the construction of Hamiltonians with long-range interactions and their corrections using the short-range behavior of the wave function. A key aspect of our investigation is the examination of the one-particle potential, kept constant in our previous work, and the effects of its optimization on the adiabatic connection....
Article
Full-text available
The adiabatic connection formalism, usually based on the first-order perturbation theory, has been generalized to an arbitrary order. The generalization stems from the observation that the formalism can be derived from a properly arranged Taylor expansion. The second-order theory is developed in detail and applied to the description of two electron...
Preprint
Full-text available
Properties of erfonium, a Hooke atom with the Coulomb interaction potential $1/r$ replaced by a non-singular $\text{erf}(\mu r)/r$ potential are investigated. The structure of the Hooke atom potential and properties of its energy spectrum, relative to the ones of the spherical harmonic oscillator and of harmonium, are analyzed. It is shown, that at...
Article
Full-text available
Sources of energy errors resulting from the replacement of the physical Coulomb interaction by its long-range erfc(μr)/r approximation are explored. It is demonstrated that the results can be dramatically improved and the range of μ giving energies within chemical accuracy limits significantly extended if the generalized cusp conditions are used to...
Preprint
Full-text available
Sources of energy errors resulting from the replacement of the physical Coulomb interaction by its long-range $\mathrm{erfc}(\mu r)/r$ approximation are explored. It is demonstrated that the results can be dramatically improved and the range of $\mu$ giving energies within chemical accuracy limits significantly extended, if the generalized cusp con...
Chapter
Full-text available
Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by the vagueness of the argumentation for using spin densities. Questioning the foundations of density functional...
Article
Full-text available
In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchan...
Preprint
Full-text available
In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchan...
Presentation
Full-text available
The generalized cusp condition for the radial part of the wave function describing two interacting particles is derived from the requirement that at the coalescence point the local energies generated by the consecutive powers of the Hamiltonian are non-singular and the ratios of the local energies of consecutive orders are order-independent. It is...
Article
Full-text available
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 formula...
Preprint
Full-text available
In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchan...
Preprint
Full-text available
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 dom...
Article
Full-text available
The notion of the nth order local energy, generated by the nth power of the Hamiltonian, has been introduced. The nth order two-particle coalescence conditions have been derived from the requirements that the nth order local energy at the coalescence point is non-singular and equal to the nth power of the Hamiltonian eigenvalue. The first condition...
Preprint
Full-text available
The notion of the n-th order local energy, generated by the n-th power of the Hamiltonian, has been introduced. The n-th order two-particle coalescence conditions have been derived from the requirements that the n-th order local energy at the coalescence point is non-singular and equal to the n-th power of the Hamiltonian eigenvalue. The first cond...
Preprint
Full-text available
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 formula...
Article
Full-text available
Confirming the result of a calculation by a calculation with a different method is often seen as a validity check. However, when the methods considered are all subject to the same (systematic) errors, this practice fails. Using a statistical approach, we define measures for reliability and similarity, and we explore the extent to which the similari...
Preprint
Full-text available
The Kohn-Sham method uses a single model system, and corrects it by a density functional the exact user friendly expression of which is not known and is replaced by an approximated, usable, model. We propose to use instead more than one model system, and use a greedy extrapolation method to correct the results of the model systems. Evidently, there...
Article
Full-text available
Pauling described metallic bonds using resonance. The maximum probability domains in the Kronig–Penney model can show a picture of it. When the walls are opaque (and the band gap is large) the maximum probability domain for an electron pair essentially corresponds to the region between the walls: the electron pairs are localized within two consecut...
Article
Full-text available
The distribution of errors is a central object in the assessment and benchmarking of computational chemistry methods. The popular and often blind use of the mean unsigned error as a benchmarking statistic leads to ignore distributions features that impact the reliability of the tested methods. We explore how the Gini coefficient offers a global rep...
Preprint
Full-text available
The distribution of errors is a central object in the assesment and benchmarking of computational chemistry methods. The popular and often blind use of the mean unsigned error as a benchmarking statistic leads to ignore distributions features that impact the reliability of the tested methods. We explore how the Gini coefficient offers a global repr...
Preprint
Full-text available
Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by the vagueness of the argumentation for using spin densities. Questioning the foundations of density functional...
Article
The present contribution tries to succinctly review the progress presented during the Faraday Discussions New horizons in density functional theory that have taken place online, 2-4 September 2020.
Article
Model Hamiltonians with long-range interaction yield energies are corrected taking into account the universal behavior of the electron-electron interaction at a short range. Although the intention of this paper is to explore the foundations of using density functionals combined with range separation, the approximations presented can be used without...
Preprint
Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the foundations of using density functionals combined with range separation, the approximations presented can be used witho...
Article
Full-text available
Quantum machine learning models have been gaining significant traction within atomistic simulation communities. Conventionally, relative model performances are being assessed and compared using learning curves (prediction error vs. training set size). This article illustrates the limitations of using the Mean Absolute Error (MAE) for benchmarking,...
Article
In Paper I [P. Pernot and A. Savin, J. Chem. Phys. 152, 164108 (2020)], we introduced the systematic improvement probability as a tool to assess the level of improvement on absolute errors to be expected when switching between two computational chemistry methods. We also developed two indicators based on robust statistics to address the uncertainty...
Article
The comparison of benchmark error sets is an essential tool for the evaluation of theories in computational chemistry. The standard ranking of methods by their mean unsigned error is unsatisfactory for several reasons linked to the non-normality of the error distributions and the presence of underlying trends. Complementary statistics have recently...
Article
Full-text available
Preprint
Quantum machine learning models have been gaining significant traction within atomistic simulation communities. Conventionally, relative model performances are being assessed and compared using learning curves (prediction error vs. training set size). This article illustrates the limitations of using the Mean Absolute Error (MAE) for benchmarking,...
Article
Full-text available
Computational chemistry has become an important complement to experimental measurements. In order to choose among the multitude of the existing approximations, it is common to use benchmark data sets, and to issue recommendations based on numbers such as mean absolute errors. We argue, using as an example band gaps calculated with density functiona...
Preprint
Computational chemistry has become an important complement to experimental measurements. In order to choose among the multitude of the existing approximations, it is common to use benchmark data sets, and to issue recommendations based on numbers such as mean absolute errors. We argue, using as an example band gaps calculated with density functiona...
Preprint
In the first part of this study (Paper I), we introduced the systematic improvement probability (SIP) as a tool to assess the level of improvement on absolute errors to be expected when switching between two computational chemistry methods. We developed also two indicators based on robust statistics to address the uncertainty of ranking in computat...
Preprint
Full-text available
The comparison of benchmark error sets is an essential tool for the evaluation of theories in computational chemistry. The standard ranking of methods by their Mean Unsigned Error is unsatisfactory for several reasons linked to the non-normality of the error distributions and the presence of underlying trends. Complementary statistics have recently...
Article
The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a given basis set. The derivation of the exact equations are based on the Levy-Lieb formulation of DFT, which h...
Article
Full-text available
The beryllium dimer and trimer are, despite their small number of electrons, excellent systems for assessing electronic-structure computational methods. With reference data provided by multi-reference averaged coupled-pair functional calculations, we assess several variants of range-separated density-functional theory, combining long-range second-o...
Preprint
The beryllium dimer and trimer are, despite their small number of electrons, excellent systems for assessing electronic-structure computational methods. With reference data provided by multi-reference averaged coupled-pair functional calculations, we assess several variants of range-separated density-functional theory, combining long-range second-o...
Preprint
The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a given basis set. The derivation of the exact equations are based on the Levy-Lieb formulation of DFT, which h...
Article
A Görling–Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh–Schrödinger (RS)-based perturbation theory this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct...
Article
Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform end-users on the expected amplitude of prediction errors attached to these methods. We show that, the distributions of...
Preprint
Benchmarking studies in computational chemistry use reference datasets to assess the accuracy of a method through error statistics. The commonly used error statistics, such as the mean signed and mean unsigned errors, do not inform end-users on the expected amplitude of prediction errors attached to these methods. We show that, the distributions of...
Preprint
A Görling-Levy (GL)-based perturbation theory along the range-separated adia-batic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schrödinger (RS)-based perturbation theory introduced in a previous work [E. Rebolini, J. Toulouse, A. M. Teale, T. Helgaker, A. Savin, Mol. Phys. 113, 1740...
Article
Full-text available
A G{\"o}rling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schr{\"o}dinger (RS)-based perturbation theory introduced in a previous work [E. Rebolini, J. Toulouse, A. M. Teale, T. Helgaker, A. Savin, Mol. Phys. 113...
Article
Full-text available
Tools have been designed obtain information about chemical bonds from quantum mechanical calculations. They work well for solutions of the stationary Schrödinger equation, but it is not clear whether Lewis electron pairs they aim to reproduce survive in time-dependent processes, in spite of the underlying Pauli principle being obeyed in this regime...
Article
Full-text available
Requiring that several properties are well reproduced is a severe test on density functional approximations. This can be assessed through the estimation of joint and conditional success probabilities. An example is provided for a small set of molecules, for properties characterizing the transition states (geometries and energies).
Article
Full-text available
Smooth model potentials with parameters selected to reproduce the spectrum of one-electron atoms are used to approximate the singular Coulomb potential. Even when the potentials do not mimic the Coulomb singularity, much of the spectrum is reproduced within the chemical accuracy. For the Hydrogen atom, the smooth approximations to the Coulomb poten...
Preprint
Full-text available
Smooth model potentials with parameters selected to reproduce the spectrum of one-electron atoms are used to approximate the singular Coulomb potential. Even when the potentials do not mimic the Coulomb singularity, much of the spectrum is reproduced within the chemical accuracy. For the Hydrogen atom, the smooth approximations to the Coulomb poten...
Article
We consider the zero-temperature van der Waals interaction between two molecules, each of which has a zero or near-zero electronic gap between a groundstate and the first excited state, using a toy model molecule ( equilateral H3) as an example. We show that the van der Waals energy between two groundstate molecules falls off as D^(-3) instead of t...
Preprint
We consider the zero-temperature van der Waals interaction between two molecules, each of which has a zero or near-zero electronic gap between a groundstate and the first excited state, using a toy model molecule ( equilateral H3) as an example. We show that the van der Waals energy between two groundstate molecules falls off as D^(-3) instead of t...
Article
The construction of density-functional approximations is explored by modeling the adiabatic connection locally, using energy densities defined in terms of the electrostatic potential of the exchange-correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this wo...
Article
The widespread idea that spin-density functional theory is based upon the extension of the Hohenberg–Kohn theorem to weak magnetic fields is contested. First, it is assumed that only the term linear in magnetic field can be kept in the Hamiltonian. Second, once this is done, two problems arise (1) not only the spin-dependent, but also the orbital-d...
Article
Full-text available
Benchmark calculations provide a large amount of information that can be very useful in assessing the performance of density functional approximations, and for choosing the one to use. In order to condense the information some indicators are provided. However, these indicators might be insufficient and a more careful analysis is needed, as shown by...
Preprint
The construction of density-functional approximations is explored by modeling the adiabatic connection em locally, using energy densities defined in terms of the electrostatic potential of the exchange-correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this...
Article
The adiabatic-connection framework has been widely used to explore the properties of the correlation energy in density-functional theory. The integrand in this formula may be expressed in terms of the electron–electron interactions directly, involving intrinsically two-particle expectation values. Alternatively, it may be expressed in terms of the...
Article
Full-text available
In this paper, an alternative method to range-separated linear-response time-dependent density-functional theory and perturbation theory is proposed to improve the estimation of the energies of a physical system from the energies of a partially interacting system. Starting from the analysis of the Taylor expansion of the energies of the partially i...
Article
Full-text available
Density-functional theory (DFT) methods have achieved widespread popularity for thermochemical predictions, which has lead to extensive benchmarking of functionals. While the use of statistics to judge the quality of various density-functional approximations is valuable and even seems unavoidable, the present chapter suggests some pitfalls of stati...
Data
This is a duplication of a paper with the tile: "Six questions on topology in theoretical chemistry" and following doi: 10.1016/j.comptc.2014.09.028
Data
Full-text available
This is a duplication of a paper with the title: "Six questions on topology in theoretical chemistry" and following doi: 10.1016/j.comptc.2014.09.028
Article
Connecting the accurate Quantum Mechanics to the chemical view is the first of foremost purposes of interpretative methods in general, and topological analysis in particular. In this field of methods, the Maximum Probability Domains (MPD) analysis, is conceptually appealing but has not been extensively applied yet. In this study we provide the gene...
Article
The performance of a method is generally measured by an assessment of the errors between the method's results and a set of reference data. The prediction uncertainty is a measure of the confidence that can be attached to a method's prediction. Its estimation is based on the random part of the errors which cannot be explained by reference data uncer...
Article
Full-text available
We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straight-forward perturbation theory, and an extension of th...
Article
Full-text available
We introduce the concept of maximum probability domains, developed in the context of the analysis of electronic densities, in the study of the microscopic spatial structures of liquids. The idea of locating a particle in a three dimensional region, by determining the domain where the probability of finding that, and only that, particle is maximum,...
Article
In spite of the usefulness of concepts related to reactivity, finding of a universally applicable recipe is hampered by the very nature of the problem, reactants behave differently under the influence of different reactants. Key elements in producing this diversity are degeneracy, and the irrelevance of asymptotic behavior for understanding equilib...
Article
Full-text available
We present a study of the variation of total energies and excitation energies along a range-separated adiabatic connection. This connection links the non-interacting Kohn-Sham electronic system to the physical interacting system by progressively switching on the electron-electron interactions whilst simultaneously adjusting a one-electron effective...
Article
Full-text available
Atom-localized molecular orbitals are defined and discussed for alternant hydrocarbons, in the HMO approximation
Chapter
The electron localization function (ELF) identifies regions of space that can be associated with electron pairs. It is usually obtained from quantum mechanical calculations, and helps in building a bridge between computational chemistry and the understanding of atomic interactions in crystals and molecules.
Article
Full-text available
In order to simulate the exact universal density functional, approximations are nowadays constructed by permitting more flexibility in its ansatz. In view of the difficulty of defining a systematically improvable form for it, this paper argues that an alternative way could be considered. It falls within the class of hybrid functionals with multi-de...
Article
The concepts of atoms and bonds in molecules which appeared in chemistry during the nineteenth century are unavoidable to explain the structure and the reactivity of the matter at a chemical level of understanding. Although they can be criticized from a strict reductionist point of view, because neither atoms nor bonds are observable in the sense o...