This work proposes to describe open-shell molecules or radicals using the framework of the doubly... more This work proposes to describe open-shell molecules or radicals using the framework of the doubly occupied configuration interaction (DOCI) treatments, so far limited to closed-shell system studies. The proposal is based on considering molecular systems in singlet states generated by adding extra hydrogen atoms located at infinite distance from the target radical system. The energy of this radical is obtained by subtracting the energies of the dissociated hydrogen atoms from that provided by the two-electron reduced density matrix corresponding to the singlet state system in the DOCI space, which is variationally calculated by imposing a set of N-representability conditions. This method is numerically assessed by describing potential energy curves and reduced density matrices in selected ionic and neutral open-shell systems in the doublet spin symmetry ground state.
The spin-adapted reduced Hamiltonian theory has been applied to calculate the energies and the fi... more The spin-adapted reduced Hamiltonian theory has been applied to calculate the energies and the firstand second-order reduced density matrices for the isoelectronic sequence of beryllium up to argon in the singlet symmetry. The projection on the spin symmetry has been performed in two ways: by considering the space spanned by the eigenfunctions of S~and S, or by considering the space spanned by the S, eigenfunctions. Several approximations for calculating the reduced density matrices are analyzed and discussed in detail. The results obtained with two of the approximations considered are highly encouraging when compared both to experimental data and to the total energy values obtained with the full configuration-interaction method. 'The conversion factor used was 1 eV =0.036 750 272 a.u. consistent with the value R "=1. 097 373 & 10' cm ' and the data given in Ref. 12.
By means of the isolobality concept between a hydrogen atom and the radical dianion [B6H5 ] 2... more By means of the isolobality concept between a hydrogen atom and the radical dianion [B6H5 ] 2 derived from an extraction of a hydrogen atom in the dianion [B6H6] 2 , forming part of the K2(B6H6) structure, we rationalize the 3D boron skeleton architecture in the solids CaB6 and KB6. The above statement is supported by electronic structure computations based on the Electron Localisation Function (ELF) in the dianion [B6H6] 2 and radical anion [B6H5 ] 2. Valence-Bond (VB) theory is also used in the study of the B-B sigma bond connecting the octahedra in the CaB6 structure, with the model dimer [(H5B5)B-B(B5H5)] 4. Quantum-chemical geometry optimizations of clusters extracted from the CaB6 solid structure show the analogies between molecular chemistry and solid-state chemistry: In the same way as benzene is the building block of graphene and graphite, the anion [B6H6] 2 is the building block of CaB6 provided every H atom in [B6H6] 2 is connected to a further [(B )6] 2 octahedron in the three directions of the 3D space, and every void at the Ca positions is embedded with two electrons.
Journal of Statistical Mechanics: Theory and Experiment, 2021
This work incorporates translational and reflection symmetry reductions to the variational determ... more This work incorporates translational and reflection symmetry reductions to the variational determination of the two-particle reduced density matrix (2-RDM) corresponding to the ground state of N-particle systems, within the doubly occupied configuration interaction (DOCI) space. By exploiting these symmetries within this lower-bound variational methodology it is possible to treat larger systems than those previously studied. The 2-RDM matrix elements are calculated by imposing up to four-particle N-representability constraint conditions using standard semidefinite programing algorithms. The method is applied to the one- and two-dimensional XXZ spin 1/2 model of quantum magnetism. Several observables including the energy and the spin–spin correlation functions are obtained to assess the physical content of the variationally determined 2-RDM. Comparison with quantum-Monte Carlo and matrix product state simulations shows that in most cases only requiring up to three-particle positivity conditions is enough to correctly describe the ground-state properties of these one- and two-dimensional models.
It is proposed that by evaluating pth-order spin-adapted reduced Hamiltonians and applying a mode... more It is proposed that by evaluating pth-order spin-adapted reduced Hamiltonians and applying a model of independent groups of p electrons we can approximate the pth-order reduced density matrix (p-RDM). Subsequently this pth-order matrix is contracted to the corresponding 2-RDM. As a test example we calculate the total energy of the beryllium-atom isoelectronic sequence using an independent-trio model. The results, as
This work extends to the unrestricted orbital approach the procedure described in our previous re... more This work extends to the unrestricted orbital approach the procedure described in our previous report [Alcoba et al., J. Chem. Phys. 148, 024105 (2018)] for determining variationally the two-electron reduced density matrix arising from doubly occupied-configuration-interaction wave functions by imposing two-and three-index N-representability conditions. An analysis of the numerical results obtained in selected systems, from both restricted and unrestricted treatments, allows one to assess the performance of these methodologies as well as to show the influence of the P, Q, G, T1, and T2 positivity conditions. We highlight the satisfactory results obtained within the unrestricted scheme.
This paper describes the determination of the energy averaged over the atomic states, with a defi... more This paper describes the determination of the energy averaged over the atomic states, with a definite spin, derived from a general configuration composed of equivalent and nonequivalent electrons. Using a simpler approach, we extend previous determinations which were limited to the equivalent electron case. The procedure, which is based on our method for calculating traces of replacement operators over model spaces, leads to a formula which is appropriate for computer evaluations.
A simple algorithm to derive the Brillouin-Wigner and the Rayleigh-Schrodinger series in time-ind... more A simple algorithm to derive the Brillouin-Wigner and the Rayleigh-Schrodinger series in time-independent perturbation theory is presented. The method provides a better understanding of the normalisation treatment of the perturbed wavefunctions and it establishes a clear relationship between the Brillouin-Wigner and Rayleigh-Schrodinger series.
Abstract The removal of I2(D1Σ+u) by CH3Cl, following optical excitation at 193 and 185 nm has be... more Abstract The removal of I2(D1Σ+u) by CH3Cl, following optical excitation at 193 and 185 nm has been studied by monitoring flourescence throughout the region 200–500 nm. It is observed that quenching of this state occurs both by reaction to form CH3I and CH2ClI and by inelastic collisions to the lowest ion-pair state (3Π2g).
This paper describes a procedure for determining the spectroscopic terms arising from an atomic o... more This paper describes a procedure for determining the spectroscopic terms arising from an atomic or a linear molecular configuration. The method, based on a simple calculation of the dimensions of (i', iz)-and (?! &)-adapted full configuration interaction spaces, reduces the conventional situations of equivalent, non-equivalent (or both) electron configurations to one unique case. Some practical examples are considered.
In this work, we analyze the effectiveness of different sets of well-known necessary N-representa... more In this work, we analyze the effectiveness of different sets of well-known necessary N-representability conditions that are imposed on the variational determination of two-electron reduced density matrices corresponding to the ground and excited states of N-electron Hamiltonians within doubly occupied configuration interaction subspaces. The two-electron reduced density matrix elements are determined so that they are suitably related to those of higher-order reduced density matrices and other associated matrices, up to a given order, constituting positive semidefinite matrices. These conditions up to two-, three-, and four-order have been sequentially imposed on the variational calculation of the expectation values of the dispersion operator corresponding to several Hamiltonian models, obtaining the electronic spectra. These results have been contrasted with those arising from the full configuration interaction method, illuminating the sufficiency/insufficiency of the variational N-representability conditions applied.
This work deals with the variational determination of the two-particle reduced density matrix (2-... more This work deals with the variational determination of the two-particle reduced density matrix (2-RDM) and the energy corresponding to the ground state of N-particle systems within the doubly occupied configuration interaction (DOCI) space. Here, we impose for the first time up to four-particle N-representability constraint conditions in the variational determination of the 2-RDM matrix elements using the standard semidefinite programming algorithms. The energies and 2-RDMs obtained from this treatment and the corresponding computational costs are compared with those arisen from previously reported less restrictive variational methods [D. R. Alcoba et al., J. Chem. Phys. 149, 194105 (2018)] as well as with the exact DOCI values. We apply the different approximations to the one-dimensional XXZ model of quantum magnetism, which has a rich phase diagram with one critical phase and constitutes a stringent test for the method. The numerical results show the usefulness of our treatment to achieve a high degree of accuracy.
International Journal of Quantum Chemistry, Apr 30, 2020
The variational determination of the second-order reduced density matrices arising from N-electro... more The variational determination of the second-order reduced density matrices arising from N-electron doubly occupied configuration interaction wave functions has recently been proposed as a method to describe systems possessing static correlation in their ground states. In this work, we propose to combine this approach with the on-top pair density functional theory in order to incorporate dynamic correlations and improve the description of systems possessing both types of electron correlation. The procedure requires ensuring that the second-order reduced density matrix elements satisfy determined N-representability variational conditions, as well as other constraints arising from the doubly-occupied configuration interaction wave function features. An analysis of the results obtained through this method, in studies of strongly correlated many-electron systems, shows the usefulness of our proposals.
The one-to-one structural correspondence between any conjugated hydrocarbon CnHm and the borane B... more The one-to-one structural correspondence between any conjugated hydrocarbon CnHm and the borane BnHm+n is extended here, with the B3LYP/cc-pVDZ model, to pure conjugated carbon systems with the example of buckminsterfullerene C60 with the corresponding icosahedral isoelectronic system closo-borane B60H60, and the fluorine substituted systems B60F30H30 and B60F60 , all with icosahedral Ih symmetry. All systems correspond to energy minima in the potential energy hypersurface, except for B60(F30)in(H30)out . Selected electronic structure methods are used to characterize all systems: molecular electrostatic potentials (MEP), atomic charges, bond orders, and topological properties of the electron density within quantum theory of atoms-in-molecules (QTAIM) and electron-localization function (ELF) theory. In the particular case of B60H60 we use the recently developed Hückeloid model to characterize this system. The stability of the energy minimum icosahedral structure B60F60 could have an ...
This work proposes to describe open-shell molecules or radicals using the framework of the doubly... more This work proposes to describe open-shell molecules or radicals using the framework of the doubly occupied configuration interaction (DOCI) treatments, so far limited to closed-shell system studies. The proposal is based on considering molecular systems in singlet states generated by adding extra hydrogen atoms located at infinite distance from the target radical system. The energy of this radical is obtained by subtracting the energies of the dissociated hydrogen atoms from that provided by the two-electron reduced density matrix corresponding to the singlet state system in the DOCI space, which is variationally calculated by imposing a set of N-representability conditions. This method is numerically assessed by describing potential energy curves and reduced density matrices in selected ionic and neutral open-shell systems in the doublet spin symmetry ground state.
The spin-adapted reduced Hamiltonian theory has been applied to calculate the energies and the fi... more The spin-adapted reduced Hamiltonian theory has been applied to calculate the energies and the firstand second-order reduced density matrices for the isoelectronic sequence of beryllium up to argon in the singlet symmetry. The projection on the spin symmetry has been performed in two ways: by considering the space spanned by the eigenfunctions of S~and S, or by considering the space spanned by the S, eigenfunctions. Several approximations for calculating the reduced density matrices are analyzed and discussed in detail. The results obtained with two of the approximations considered are highly encouraging when compared both to experimental data and to the total energy values obtained with the full configuration-interaction method. 'The conversion factor used was 1 eV =0.036 750 272 a.u. consistent with the value R "=1. 097 373 & 10' cm ' and the data given in Ref. 12.
By means of the isolobality concept between a hydrogen atom and the radical dianion [B6H5 ] 2... more By means of the isolobality concept between a hydrogen atom and the radical dianion [B6H5 ] 2 derived from an extraction of a hydrogen atom in the dianion [B6H6] 2 , forming part of the K2(B6H6) structure, we rationalize the 3D boron skeleton architecture in the solids CaB6 and KB6. The above statement is supported by electronic structure computations based on the Electron Localisation Function (ELF) in the dianion [B6H6] 2 and radical anion [B6H5 ] 2. Valence-Bond (VB) theory is also used in the study of the B-B sigma bond connecting the octahedra in the CaB6 structure, with the model dimer [(H5B5)B-B(B5H5)] 4. Quantum-chemical geometry optimizations of clusters extracted from the CaB6 solid structure show the analogies between molecular chemistry and solid-state chemistry: In the same way as benzene is the building block of graphene and graphite, the anion [B6H6] 2 is the building block of CaB6 provided every H atom in [B6H6] 2 is connected to a further [(B )6] 2 octahedron in the three directions of the 3D space, and every void at the Ca positions is embedded with two electrons.
Journal of Statistical Mechanics: Theory and Experiment, 2021
This work incorporates translational and reflection symmetry reductions to the variational determ... more This work incorporates translational and reflection symmetry reductions to the variational determination of the two-particle reduced density matrix (2-RDM) corresponding to the ground state of N-particle systems, within the doubly occupied configuration interaction (DOCI) space. By exploiting these symmetries within this lower-bound variational methodology it is possible to treat larger systems than those previously studied. The 2-RDM matrix elements are calculated by imposing up to four-particle N-representability constraint conditions using standard semidefinite programing algorithms. The method is applied to the one- and two-dimensional XXZ spin 1/2 model of quantum magnetism. Several observables including the energy and the spin–spin correlation functions are obtained to assess the physical content of the variationally determined 2-RDM. Comparison with quantum-Monte Carlo and matrix product state simulations shows that in most cases only requiring up to three-particle positivity conditions is enough to correctly describe the ground-state properties of these one- and two-dimensional models.
It is proposed that by evaluating pth-order spin-adapted reduced Hamiltonians and applying a mode... more It is proposed that by evaluating pth-order spin-adapted reduced Hamiltonians and applying a model of independent groups of p electrons we can approximate the pth-order reduced density matrix (p-RDM). Subsequently this pth-order matrix is contracted to the corresponding 2-RDM. As a test example we calculate the total energy of the beryllium-atom isoelectronic sequence using an independent-trio model. The results, as
This work extends to the unrestricted orbital approach the procedure described in our previous re... more This work extends to the unrestricted orbital approach the procedure described in our previous report [Alcoba et al., J. Chem. Phys. 148, 024105 (2018)] for determining variationally the two-electron reduced density matrix arising from doubly occupied-configuration-interaction wave functions by imposing two-and three-index N-representability conditions. An analysis of the numerical results obtained in selected systems, from both restricted and unrestricted treatments, allows one to assess the performance of these methodologies as well as to show the influence of the P, Q, G, T1, and T2 positivity conditions. We highlight the satisfactory results obtained within the unrestricted scheme.
This paper describes the determination of the energy averaged over the atomic states, with a defi... more This paper describes the determination of the energy averaged over the atomic states, with a definite spin, derived from a general configuration composed of equivalent and nonequivalent electrons. Using a simpler approach, we extend previous determinations which were limited to the equivalent electron case. The procedure, which is based on our method for calculating traces of replacement operators over model spaces, leads to a formula which is appropriate for computer evaluations.
A simple algorithm to derive the Brillouin-Wigner and the Rayleigh-Schrodinger series in time-ind... more A simple algorithm to derive the Brillouin-Wigner and the Rayleigh-Schrodinger series in time-independent perturbation theory is presented. The method provides a better understanding of the normalisation treatment of the perturbed wavefunctions and it establishes a clear relationship between the Brillouin-Wigner and Rayleigh-Schrodinger series.
Abstract The removal of I2(D1Σ+u) by CH3Cl, following optical excitation at 193 and 185 nm has be... more Abstract The removal of I2(D1Σ+u) by CH3Cl, following optical excitation at 193 and 185 nm has been studied by monitoring flourescence throughout the region 200–500 nm. It is observed that quenching of this state occurs both by reaction to form CH3I and CH2ClI and by inelastic collisions to the lowest ion-pair state (3Π2g).
This paper describes a procedure for determining the spectroscopic terms arising from an atomic o... more This paper describes a procedure for determining the spectroscopic terms arising from an atomic or a linear molecular configuration. The method, based on a simple calculation of the dimensions of (i', iz)-and (?! &)-adapted full configuration interaction spaces, reduces the conventional situations of equivalent, non-equivalent (or both) electron configurations to one unique case. Some practical examples are considered.
In this work, we analyze the effectiveness of different sets of well-known necessary N-representa... more In this work, we analyze the effectiveness of different sets of well-known necessary N-representability conditions that are imposed on the variational determination of two-electron reduced density matrices corresponding to the ground and excited states of N-electron Hamiltonians within doubly occupied configuration interaction subspaces. The two-electron reduced density matrix elements are determined so that they are suitably related to those of higher-order reduced density matrices and other associated matrices, up to a given order, constituting positive semidefinite matrices. These conditions up to two-, three-, and four-order have been sequentially imposed on the variational calculation of the expectation values of the dispersion operator corresponding to several Hamiltonian models, obtaining the electronic spectra. These results have been contrasted with those arising from the full configuration interaction method, illuminating the sufficiency/insufficiency of the variational N-representability conditions applied.
This work deals with the variational determination of the two-particle reduced density matrix (2-... more This work deals with the variational determination of the two-particle reduced density matrix (2-RDM) and the energy corresponding to the ground state of N-particle systems within the doubly occupied configuration interaction (DOCI) space. Here, we impose for the first time up to four-particle N-representability constraint conditions in the variational determination of the 2-RDM matrix elements using the standard semidefinite programming algorithms. The energies and 2-RDMs obtained from this treatment and the corresponding computational costs are compared with those arisen from previously reported less restrictive variational methods [D. R. Alcoba et al., J. Chem. Phys. 149, 194105 (2018)] as well as with the exact DOCI values. We apply the different approximations to the one-dimensional XXZ model of quantum magnetism, which has a rich phase diagram with one critical phase and constitutes a stringent test for the method. The numerical results show the usefulness of our treatment to achieve a high degree of accuracy.
International Journal of Quantum Chemistry, Apr 30, 2020
The variational determination of the second-order reduced density matrices arising from N-electro... more The variational determination of the second-order reduced density matrices arising from N-electron doubly occupied configuration interaction wave functions has recently been proposed as a method to describe systems possessing static correlation in their ground states. In this work, we propose to combine this approach with the on-top pair density functional theory in order to incorporate dynamic correlations and improve the description of systems possessing both types of electron correlation. The procedure requires ensuring that the second-order reduced density matrix elements satisfy determined N-representability variational conditions, as well as other constraints arising from the doubly-occupied configuration interaction wave function features. An analysis of the results obtained through this method, in studies of strongly correlated many-electron systems, shows the usefulness of our proposals.
The one-to-one structural correspondence between any conjugated hydrocarbon CnHm and the borane B... more The one-to-one structural correspondence between any conjugated hydrocarbon CnHm and the borane BnHm+n is extended here, with the B3LYP/cc-pVDZ model, to pure conjugated carbon systems with the example of buckminsterfullerene C60 with the corresponding icosahedral isoelectronic system closo-borane B60H60, and the fluorine substituted systems B60F30H30 and B60F60 , all with icosahedral Ih symmetry. All systems correspond to energy minima in the potential energy hypersurface, except for B60(F30)in(H30)out . Selected electronic structure methods are used to characterize all systems: molecular electrostatic potentials (MEP), atomic charges, bond orders, and topological properties of the electron density within quantum theory of atoms-in-molecules (QTAIM) and electron-localization function (ELF) theory. In the particular case of B60H60 we use the recently developed Hückeloid model to characterize this system. The stability of the energy minimum icosahedral structure B60F60 could have an ...
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