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The interacting quantum atoms (IQA) method offers a rigorous and minimal route to calculate atomic electron correlation energies from the two-particle density matrix (2PDM). The price paid is that this method is very time-consuming. However, employing CCSD and CCSD(T), we explore several approaches to speed up such calculations. We make the pivotal observation that the removal, from the true 2PDM, of both the Hartree–Fock part of the 2PDM and an approximate 2PDM (Müller) dramatically reduces the size of the quadrature grid needed to obtain accurate energies. [ABSTRACT FROM AUTHOR]

In this work, it is presented an approach to the local electron energy of the first thirty-six atoms in their ground state using Rényi's entropy is defined in terms of the electron density in position and momentum spaces. To carry out our study, we calculated and compared the trends obtained from the local functionals of kinetic, exchange, and Coulomb energy, with Rényi's entropy. Our results suggest that Rényi's entropy could be a good option to perform studies on the local behavior of the energy in atoms and also in studies on the electron correlation phenomenon. [ABSTRACT FROM AUTHOR]

Singlet and triplet spin state energies for three‐dimensional Hooke atoms, that is, electrons in a quadratic confinement, with even number of electrons (2, 4, 6, 8, 10) is discussed using Full‐CI and CASSCF type wavefunctions with a variety of basis sets and considering perturbative corrections up to second order. The effect of the screening of the electron–electron interaction is also discussed by using a Yukawa‐type potential with different values of the Yukawa screening parameter (λee = 0.2, 0.4, 0.6, 0.8, 1.0). Our results show that the singlet state is the ground state for two and eight electron Hooke atoms, whereas the triplet is the ground spin state for 4‐, 6‐, and 10‐electron systems. This suggests the following Aufbau structure 1s < 1p < 1d with singlet ground spin states for systems in which the generation of the triplet implies an inter‐shell one‐electron promotion, and triplet ground states in cases when there is a partial filling of electrons of a given shell. It is also observed that the screening of electron–electron interactions has a sizable quantitative effect on the relative energies of both spin states, specially in the case of two‐ and eight‐electron systems, favoring the singlet state over the triplet. However, the screening of the electron–electron interaction does not provoke a change in the nature of the ground spin state of these systems. By analyzing the different components of the energy, we have gained a deeper understanding of the effects of the kinetic, confinement and electron–electron interaction components of the energy. [ABSTRACT FROM AUTHOR]

The single-reference coupled-cluster (CC) method is one of the most efficient approaches for describing electron correlation effects in atoms and molecules but its successful application is limited to states dominated by a single Slater determinant. In cases where several determinants dominate the wave function expansion, the multi-reference (MR) CC formulations are required. They usually use the effective Hamiltonian formalism which allows dealing with two types of electron correlation appearing in the MR cases: nondynamic and dynamic. There are two MR-CC formulations of this type: the Hilbert space CC method and the Fock-space (FS) one. In the paper, a version of the FS-CC method designated for the description of systems with three-valence electrons is being considered. The idea of the intermediate Hamiltonian (IH) reformulation of the standard FS-CC method, which simplifies the calculations and avoids the intruder state problem, is discussed in this context. A new IH-FS-CC approach is presented which takes advantage of the redefinition of the normal ordering of the FS cluster expansion introduced by Lindgren. The redefinition significantly simplifies the IH-FS-CC formalism and lowers the computational cost of the calculations. The advantages of the new IH formulation are discussed in detail for the case of the FS-CC method in which the lowest-order cluster operators are included in all sectors of the Fock-space, including the three-valence one. [ABSTRACT FROM AUTHOR]

In this work, we presented a generalization of Rényi's entropy using Jackson's integral to obtain an expression linked to the electronic correlation; as study cases, we analyzed the first thirty-six atoms in their ground state and a set of 1842 molecules. The results obtained in this work show that our proposal of q-Rényi's entropy is directly related to the electron correlation. [ABSTRACT FROM AUTHOR]

In the linear‐scaling divide‐and‐conquer (DC) electronic structure method, each subsystem is calculated together with the neighboring buffer region, the size of which affects the energy error introduced by the fragmentation in the DC method. The DC self‐consistent field calculation utilizes a scheme to automatically determine the appropriate buffer region that is as compact as possible for reducing the computational time while maintaining acceptable accuracy (J. Comput. Chem. 2018, 39, 909). To extend the automatic determination scheme of the buffer region to the DC second‐order Møller–Plesset perturbation (MP2) calculation, a scheme for estimating the subsystem MP2 correlation energy contribution from each atom in the buffer region is proposed. The estimation is based on the atomic orbital Laplace MP2 formalism. Based on this, an automatic buffer determination scheme for the DC‐MP2 calculation is constructed and its performance for several types of systems is assessed. [ABSTRACT FROM AUTHOR]

We calculate the high-harmonic generation (HHG) spectra, strong-field ionisation, and time-dependent dipole-moment of Ne using explicitly time-dependent optimised second-order many-body perturbation method (TD-OMP2) where both orbitals and amplitudes are time-dependent. We consider near-infrared (800 nm) and mid-infrared (1200 nm) laser pulses with very high intensities ( 5 × 10 14 , 8 × 10 14 , and 1 × 10 15 W / cm 2 ), required for strong-field experiments with the high-ionisation potential (21.6 eV) atom. We compare the result of the TD-OMP2 method with the time-dependent complete-active-space self-consistent field method and the time-dependent Hartree-Fock method. Further, we report the implementation of the TD-CC2 method within the chosen active space, which is also a second-order approximation to the TD-CCSD method, and present results of time-dependent dipole-moment and HHG spectra with an intensity of 5 × 10 13 W / cm 2 at a wavelength of 800 nm. It is found that the TD-CC2 method is not stable in the case with a higher laser intensity, and it does not provide a gauge-invariant description of the physical properties, which makes TD-OMP2 a superior choice to reach out to larger chemical systems, especially for the study of strong-field dynamics. The obtained results indicate that the TD-OMP2 method shows moderate performance, overestimating the response of Ne, while TDHF underestimates it.. [ABSTRACT FROM AUTHOR]

Within the quantum topological energy partitioning method called Interacting Quantum Atoms (IQA) we transition from Møller‐Plesset (MP4SDQ) to CCSD in calculating intra‐ and interatomic electron correlation energies for a set of hydrides, diatomics, a few simple molecules and non‐covalently bonded complexes, using the uncontracted basis set 6‐31++G(2d,2p). CCSD‐IQA allows a more rigorous analysis of atomic electron correlation than that offered by Møller‐Plesset, which returns IQA contributions that are identical to Hartree–Fock counterparts except for two‐electron terms. The CCSD‐IQA analysis returns bond and other interatomic correlation energies that are typically much larger in magnitude than the MP4SDQ values. Crisp patterns of energy transferability are detected in water clusters, both for intra‐atomic and interatomic correlation energies. CCSD determines that the intra‐atomic correlation energy of an oxygen drops by 15 kJ·mol–1 for donating a hydrogen and by 25 kJ·mol–1 for accepting a hydrogen. [ABSTRACT FROM AUTHOR]

Recently, the quantum topological energy partitioning method called interacting quantum atoms (IQA) has been extended to MPn (n = 2, 3, 4) wave functions. This enables the extraction of chemical insight related to dynamic electron correlation. The large computational expense of the IQA‐MPn approach is compensated by the advantages that IQA offers compared to older nontopological energy decomposition schemes. This expense is problematic in the construction of a machine learning training set to create kriging models for topological atoms. However, the algorithm presented here markedly accelerates the calculation of atomically partitioned electron correlation energies. Then again, the algorithm cannot calculate pairwise interatomic energies because it applies analytical integrals over whole space (rather than over atomic volumes). However, these pairwise energies are not needed in the quantum topological force field FFLUX, which only uses the energy of an atom interacting with all remaining atoms of the system that it is part of. Thus, it is now feasible to generate accurate and sizeable training sets at MPn level of theory. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

We analyze the Coulomb hole of Ne from highly‐accurate CISD wave functions obtained from optimized even‐tempered basis sets. Using a two‐fold extrapolation procedure we obtain highly accurate results that recover 97 % of the correlation energy. We confirm the existence of a shoulder in the short‐range region of the Coulomb hole of the Ne atom, which is due to an internal reorganization of the K‐shell caused by electron correlation of the core electrons. The feature is very sensitive to the quality of the basis set in the core region and it is not exclusive to Ne, being also present in most of second‐row atoms, thus confirming that it is due to K‐shell correlation effects. [ABSTRACT FROM AUTHOR]

Abstract: Undecacene, the largest member of the acene family, was photogenerated in a polymer matrix under cryogenic conditions from a precursor with two α‐diketone bridges. The electronic absorption of undecacene extends into the NIR region, but the spectrum is dominated by two strong absorptions in the UV/Vis range. The HOMO–LUMO transition is continuously shifted to lower energies as the number of rings of the acene increases (E vs. 1/N, N=number of rings), which is in line with the strong electron correlation calculated by DFT/MRCI. [ABSTRACT FROM AUTHOR]

In this letter, we applied the discrete and continuous Tsallis’ entropy, defined in terms of the occupation numbers and the electron density of atoms in their basal state. Our results show that only the discrete version of this entropy in the interval 0.0 < q < 2.0 gives a consistent behavior with respect to the electron correlation effects of the systems, while the continuous expression in some cases presents negative values, and in general decreases when the correlation effects increase. [ABSTRACT FROM AUTHOR]

An exact formula for the collective occupancy of natural orbitals with an angular momentum l is derived for the ground state of the two-electron harmonium atom. For confinement strengths ω that correspond to polynomial correlation factors as well as at the weak ( ω → ∞ ) and strong ( ω → 0 ) correlations limits, it reduces to closed-form expressions. At the former limit, a similar result obtains for the partial-wave contributions to the ground-state energy. Slow convergence of the collective occupancies to their leading large-l asymptotics provided by Hill's formula is uncovered. As the rate of convergence decreases strongly with ω , a complete breakdown of Hill's formula ensues upon the confinement strength becoming infinitesimally small. The relevance of these findings to the performance of the extrapolation schemes for the estimation of the complete-basis-set limits of quantum-mechanical observables is discussed. [ABSTRACT FROM AUTHOR]