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A virtual vibrational spectrometer HF Spectrodyn, based on efficient software exploring unrestricted Hartree–Fock approximation, was used to perform computational spectrometry of C60, C66 and C70 carbon clusters as well as C60 dimers. All the species are presented as digital twins, the structure and properties of which were discussed. The obtained IR absorption and Raman scattering spectra are analyzed to point out strengths, limitations and ongoing developments of the virtual spectrometry. [ABSTRACT FROM AUTHOR]

We investigate variational principles for the approximation of quantum dynamics that apply for approximation manifolds that do not have complex linear tangent spaces. The first one, dating back to McLachlan [Mol. Phys. 8, 39–44 (1964)], minimizes the residuum of the time-dependent Schrödinger equation, while the second one, originating from the lecture notes of Kramer and Saraceno [Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics Vol. 140 (Springer, Berlin, 1981)], imposes the stationarity of an action functional. We characterize both principles in terms of metric and symplectic orthogonality conditions, consider their conservation properties, and derive an elementary a posteriori error estimate. As an application, we revisit the time-dependent Hartree approximation and frozen Gaussian wave packets. [ABSTRACT FROM AUTHOR]

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A virtual vibrational spectrometer HF Spectrodyn, based on efficient software exploring unrestricted Hartree–Fock approximation, was used to perform computational spectrometry of C60, C66 and C70 carbon clusters as well as C60 dimers. All the species are presented as digital twins, the structure and properties of which were discussed. The obtained IR absorption and Raman scattering spectra are analyzed to point out strengths, limitations and ongoing developments of the virtual spectrometry. [ABSTRACT FROM AUTHOR]

A new set of radiative parameters for spectral lines in La  v – x ions is reported in this paper. These data were determined through the use of a multiplatform approach involving three independent theoretical methods, i.e. the relativistic Hartree–Fock method including core-polarization corrections (HFR + CPOL), the multiconfiguration Dirac–Hartree–Fock (MCDHF) method, and the particle-hole configuration-interaction (PH-CI) method implemented in the AMBiT program. Based on cross-comparisons between the results obtained with these three methods, and from comparisons with the few previously published experimental and theoretical data, the most complete and reliable set of wavelengths, transition probabilities, and oscillator strengths was then used to determine the necessary opacities for the analysis of the spectra emitted in the early phases of kilonovae following neutron star mergers, i.e. for typical conditions corresponding to temperatures |$T \gt 20\,000 $|  K, a density ρ = 10−10 g cm−3, and a time after the merger t  = 0.1 d. [ABSTRACT FROM AUTHOR]

Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant error estimates were formally described in our previous work Burghardt et al (2021 J. Phys. A: Math. Theor. 54 414002). Specifically, we consider a representative two-dimensional tunneling system where a double well and a harmonic coordinate are cubically coupled. The time-dependent Hartree approximation is compared with a fully correlated solution, for different parameter regimes. The impact of the coupling and the resulting correlations are quantitatively assessed in terms of a time-dependent reaction probability along the tunneling coordinate. We show that the numerical error is correctly predicted on moderate time scales by a theoretically derived error estimate. [ABSTRACT FROM AUTHOR]

The recent source and sink potential approach by Pickup et al. [J. Chem. Phys. 143, 194105 (2015)] is extended to Hartree-Fock and density functional theory, allowing the calculation of the transmission and the visualization of ballistic currents through molecules at these levels of theory. This visualization allows the study of the transmission process in real-space, providing an important tool to better understand the conduction process. [ABSTRACT FROM AUTHOR]

Coupled cluster (CC) theory is widely accepted as the most accurate and generally applicable approach in quantum chemistry. CC calculations are usually performed with single Slater-determinant references, e.g., canonical Hartree-Fock (HF) wavefunctions, though any single determinant can be used. This is an attractive feature because typical CC calculations are straightforward to apply, as there is no potentially ambiguous user input required. On the other hand, there can be concern that CC approximations give unreliable results when the reference determinant provides a poor description of the system of interest, i.e., when the HF or any other single determinant ground state has a relatively low weight in the full CI expansion. However, in many cases, the reported "failures" of CC can be attributed to an unfortunate choice of reference determinant, rather than intrinsic shortcomings of CC itself. This is connected to well-known effects like spin-contamination, wavefunction instability, and symmetry-breaking. In this contribution, a particularly difficult singlet/triplet splitting problem in two phenyldinitrene molecules is investigated, where CC with singles, doubles and perturbative triples [CCSD(T)] was reported to give poor results. This is analyzed by using different reference determinants for CCSD(T), as well as performing higher level CCSDT-3 and CCSDT calculations. We show that doubly electron attached and doubly ionized equation-of-motion (DEA/DIP-EOM) approaches are powerful alternatives for treating such systems. These are operationally single-determinant methods that adequately take the multi-reference nature of these molecules into account. Our results indicate that CC remains a powerful tool for describing systems with both static correlation and dynamic correlation, when pitfalls associated with the choice of the reference determinant are avoided. [ABSTRACT FROM AUTHOR]

We introduce a mixed density fitting scheme that uses both a Gaussian and a plane-wave fitting basis to accurately evaluate electron repulsion integrals in crystalline systems. We use this scheme to enable efficient all-electron Gaussian based periodic density functional and Hartree-Fock calculations. [ABSTRACT FROM AUTHOR]

By solving the Bethe-Salpeter equation within the Hartree-Fock formalism, we study the optical spectra, optical gap, quasi-particle gap, exciton binding energy, and wave function of a closed-shell graphene system. With the excitonic effects fully taken into account, we find that all peaks of optical spectrum are blueshifted to higher photon energy with either the enhancement of the long-range Coulomb interactions or the suppression of the short-range Coulomb interactions but are redshifted to lower photon energy due to the increased size and decreased confinement. Remarkably, the region of a much higher relative probability for an electron resides mainly around the geometrical center of the structure, whereas the hole strongly localizes in the peripheral region of the geometric center. Our results are found to agree well with both recent experimental and theoretical works. [ABSTRACT FROM AUTHOR]

Full configuration interaction (FCI) restricted to a pairing space yields size-extensive correlation energies but its cost scales exponentially with molecular size. Restricting the variational two-electron reduced-density-matrix (2-RDM) method to represent the same pairing space yields an accurate lower bound to the pair FCI energy at a mean-field-like computational scaling of O(r3) where r is the number of orbitals. In this paper, we show that localized molecular orbitals can be employed to generate an efficient, approximately size-extensive pair 2-RDM method. The use of localized orbitals eliminates the substantial cost of optimizing iteratively the orbitals defining the pairing space without compromising accuracy. In contrast to the localized orbitals, the use of canonical Hartree-Fock molecular orbitals is shown to be both inaccurate and non-size-extensive. The pair 2-RDM has the flexibility to describe the spectra of one-electron RDM occupation numbers from all quantum states that are invariant to time-reversal symmetry. Applications are made to hydrogen chains and their dissociation, n-acene from naphthalene through octacene, and cadmium telluride 2-, 3-, and 4-unit polymers. For the hydrogen chains, the pair 2-RDM method recovers the majority of the energy obtained from similar calculations that iteratively optimize the orbitals. The localized-orbital pair 2-RDM method with its mean-field-like computational scaling and its ability to describe multireference correlation has important applications to a range of strongly correlated phenomena in chemistry and physics. [ABSTRACT FROM AUTHOR]

We propose an economical state-specific approach to evaluate electronic excitation energies based on the driven similarity renormalization group truncated to second order (DSRG-PT2). Starting from a closed-shell Hartree-Fock wave function, a model space is constructed that includes all single or single and double excitations within a given set of active orbitals. The resulting VCIS-DSRG-PT2 and VCISD-DSRG-PT2 methods are introduced and benchmarked on a set of 28 organic molecules [M. Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. Taking CC3 results as reference values, mean absolute deviations of 0.32 and 0.22 eV are observed for VCIS-DSRG-PT2 and VCISD-DSRG-PT2 excitation energies, respectively. Overall, VCIS-DSRG-PT2 yields results with accuracy comparable to those from time-dependent density functional theory using the B3LYP functional, while VCISDDSRG-PT2 gives excitation energies comparable to those from equation-of-motion coupled cluster with singles and doubles. [ABSTRACT FROM AUTHOR]

A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference. [ABSTRACT FROM AUTHOR]

Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock. [ABSTRACT FROM AUTHOR]

Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclearwave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus. [ABSTRACT FROM AUTHOR]

We propose a pruned multi-configuration time-dependent Hartree (MCTDH) method with systematically expanding nondirect product bases and use it to solve the time-independent Schrödinger equation. No pre-determined pruning condition is required to select the basis functions. Using about 65 000 basis functions, we calculate the first 69 vibrational eigenpairs of acetonitrile, CH3CN, to an accuracy better than that achieved in a previous pruned MCTDH calculation which required more than 100 000 basis functions. In addition, we compare the new pruned MCTDH method with the established multi-layer MCTDH (ML-MCTDH) scheme and determine that although ML-MCTDH is somewhat more efficient when low or intermediate accuracy is desired, pruned MCTDH is more efficient when high accuracy is required. In our largest calculation, the vast majority of the energies have errors smaller than 0.01 cm-1. [ABSTRACT FROM AUTHOR]

To study the scattering of CO off a movable Cu(100) surface, extensive multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) calculations are performed based on the SAP [R. Marquardt et al., J. Chem. Phys. 132, 074108 (2010)] potential energy surface in conjunction with a recently developed expansion model [Q. Meng and H.-D. Meyer, J. Chem. Phys. 143, 164310 (2015)] for including lattice motion. The surface vibration potential is constructed by a sum of Morse potentials where the parameters are determined by simulating the vibrational energies of a clean Cu(100) surface. Having constructed the total Hamiltonian, extensive dynamical calculations in both timeindependent and time-dependent schemes are performed. Two-layer MCTDH (i.e., normal MCTDH) block-improved-relaxations (time-independent scheme) show that increasing the number of included surface vibrational dimensions lets the vibrational energies of CO/Cu(100) decrease for the frustrated translation (T mode), which is of low energy but increase those of the frustrated rotation (R mode) and the CO-Cu stretch (S mode), whose vibrational energies are larger than the energies of the in-plane surface vibrations (~79 cm-1). This energy-shifting behavior was predicted and discussed by a simple model in our previous publication [Q. Meng and H.-D. Meyer, J. Chem. Phys. 143, 164310 (2015)]. By the flux analysis of the MCTDH/ML-MCTDH propagated wave packets, we calculated the sticking probabilities for the X + 0D, X + 1D, X + 3D, X + 5D, and X + 15D systems, where "X" stands for the used dimensionality of the CO/rigid-surface system and the second entry denotes the number of surface degrees of freedom included. From these sticking probabilities, the X + 5D/15D calculations predict a slower decrease of sticking with increasing energy as compared to the sticking of the X + 0D/1D/3D calculations. This is because the translational energy of CO is more easily transferred to surface vibrations, when the vibrational dimensionality of the surface is enlarged. [ABSTRACT FROM AUTHOR]

Projected Hartree-Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. Coupled cluster theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and coupled cluster theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems. [ABSTRACT FROM AUTHOR]

The variational equations of motion of the multi-configuration time-dependent Hartree (MCTDH) approach contain the inverse of reduced density matrices which are typically ill-conditioned and therefore lead to small stepsizes for numerical time integration. This problem is usually dealt with via regularization of the density matrices, which works well in many cases but still calls for systematic improvement schemes. Recently this problem, its implications and possible solutions have become the subject of increased interest. Notably, a projector splitting integrator for the MCTDH approach that does not require the inversion of reduced density matrices has been proposed [C. Lubich, Appl. Math. Res. Express 2015, 311]. Here, we present the first implementation of this integration scheme. Results for low-dimensional benchmark systems are presented, and the case of initially unoccupied singleparticle functions is discussed. [ABSTRACT FROM AUTHOR]

The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e., those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM analysis. In this study, within the context of the MC-QTAIM, the formalism of including nuclear vibrational energy in the atomic basin energy is developed in detail and its contribution is derived analytically using the recently proposed non-adiabatic Hartree product nuclear wavefunction. It is demonstrated that within the context of this wavefunction, the quantum nuclei may be conceived pseudo-adiabatically as quantum oscillators and both isotropic harmonic and anisotropic anharmonic oscillator models are used to compute the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Inspired by the results gained within the context of the MC-QTAIM analysis, a heuristic approach is proposed within the context of the QTAIM to include nuclear vibrational energy in the basin energy from the vibrational wavefunction derived adiabatically. The explicit calculation of the basin contribution of the zero-point vibrational energy using the uncoupled harmonic oscillator model leads to results consistent with those derived from the MC-QTAIM. [ABSTRACT FROM AUTHOR]

The coupled-cluster approach with spin-orbit coupling (SOC) included in post-self-consistent field treatment (SOC-CC) using relativistic effective core potentials is extended to spatially non-degenerate open-shell systems in this work. The unrestricted Hartree-Fock determinant corresponding to the scalar relativistic Hamiltonian is employed as the reference and the open-shell SOC-CC approach is implemented at the CC singles and doubles (CCSD) level as well as at the CCSD level augmented by a perturbative treatment of triple excitations (CCSD(T)). Due to the breaking of time-reversal symmetry and spatial symmetry, this open-shell SOC-CC approach is rather expensive compared with the closedshell SOC-CC approach. The open-shell SOC-CC approach is applied to some open-shell atoms and diatomic molecules with s1, p3, σ¹, or π2 configuration. Our results indicate that rather accurate results can be achieved with the open-shell SOC-CCSD(T) approach for these systems. Dissociation energies for some closed-shell molecules containing heavy IIIA or VIIA atoms are also calculated using the closed-shell SOC-CC approach, where energies of the IIIA or VIIA atoms are obtained from those of the closed-shell ions and experimental ionization potentials or electron affinities. SOC-CCSD(T) approach affords reliable dissociation energies for these molecules. Furthermore, scalar-relativistic CCSD(T) approach with the same strategy can also provide reasonable dissociation energies for the 5th row IIIA or VIIA molecules, while the error becomes pronounced for the 6th row elements. [ABSTRACT FROM AUTHOR]

We develop a geometrical optimization technique for the projection-after-variation (PAV) scheme of the recently refined projected Hartree-Fock (PHF) as a fast alternative to the variation-after-projection (VAP) approach for optimizing the structures of molecules/clusters in symmetry-adapted electronic states at the mean-field computational cost. PHF handles the nondynamic correlation effects by restoring the symmetry of a broken-symmetry single referencewavefunction and moreover enables a black-box treatment of orbital selections. Using HF orbitals instead of PHF orbitals, our approach saves the computational cost for the orbital optimization, avoiding the convergence problem that sometimes emerges in the VAP scheme. We show that PAV-PHF provides geometries comparable to those of the complete active space self-consistent field and VAP-PHF for the tested systems, namely, CH2, O3, and the [Cu2O2]2+ core, where nondynamic correlation is abundant. The proposed approach is useful for large systems mainly dominated by nondynamic correlation to find stable structures in many symmetry-adapted states. [ABSTRACT FROM AUTHOR]

As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially ionized states [B. Militzer and K. P. Driver, Phys. Rev. Lett. 115, 176403 (2015)] at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide density-temperature range of 1.93-11.60 g/cm3 and 103-1.29×108 K.We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that are consistent with DFT-MD at intermediate temperatures of 2 × 106 K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to K-shell and L-shell ionization. Our Hugoniot curves provide a benchmark for widely used EOS models: SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 107 K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. We also compute the temperature-density dependence of thermal and pressure ionization processes. [ABSTRACT FROM AUTHOR]

In electronic structure theory, the availability of an analytical derivative is one of the desired features for a method to be useful in practical applications, as it allows for geometry optimization as well as computation of molecular properties. With the recent advances in the development of symmetryprojected Hartree-Fock (PHF) methods, we here aim at further extensions by devising the analytic gradients of post-PHF approaches with a special focus on spin-extended (spin-projected) configuration interaction with single and double substitutions (ECISD). Just like standard single-reference methods, the mean-field PHF part does not require the corresponding coupled-perturbed equation to be solved, while the correlation energy term needs the orbital relaxation effect to be accounted for, unless the underlying molecular orbitals are variationally optimized in the presence of the correlation energy. We present a general strategy for post-PHF analytical gradients, which closely parallels that for single-reference methods, yet addressing the major difference between them. The similarity between ECISD and multi-reference CI not only in the energy but also in the optimized geometry is clearly demonstrated by the numerical examples of ozone and cyclobutadiene. [ABSTRACT FROM AUTHOR]

Amulti-layer multi-configurational time-dependent Hartree(MCTDH)approach using a second quantization representation (SQR) based on optimized time-dependent orbitals is introduced. The approach combines elements of the multi-layer MCTDH-SQR approach ofWang and Thoss, which employs a preselected time-independent orbital basis, and the MCTDH for bosons and multi-configuration timedependent Hartree-Fock approaches, which do not use multi-layering but employ time-dependent orbital bases. In contrast to existing MCTDH-type approaches, the results of the present approach for a given number of configurations are not invariant with respect to unitary transformations of the time-dependent orbital basis. Thus a natural orbital representation is chosen to achieve fast convergence with respect to the number of configurations employed. Equations of motion for the present ansatz, called (multi-layer) MCTDH in optimized second quantization representation, are derived. Furthermore, a scheme for the calculation of optimized unoccupied single-particle functions is given which can be used to avoid singularities in the equations of motion. [ABSTRACT FROM AUTHOR]

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime. [ABSTRACT FROM AUTHOR]

Density functional approximations (DFAs) often suffer from self-repulsion and delocalization errors which are reduced by exact (Hartree-Fock-like) exchange admixture. Oyeyemi and co-workers recently showed that several DFAs with little exact exchange incorrectly predict bent alkynyl radical geometries, giving errors in ab initio composite methods using density functional theory geometries [V. B. Oyeyemi et al., J. Phys. Chem. Lett. 3, 289 (2012)]. We show that the simple Hartree-Fock-Slater and Xα DFAs, which have substantial delocalization error, predict linear alkynyl radical geometries without incorporating exact exchange. Our Rung 3.5 DFAs, and rescaled generalized gradient approximations, can give either linear σ, bent σ-πσ-π, or nearly linear π radicals, all without incorporating exact exchange. This highlights the complexity of delocalization error, the utility of accurate empirical DFA geometries for ab initio composite methods, and the insights to be gained from Rung 3.5 DFAs. [ABSTRACT FROM AUTHOR]

The 2E" state of NO3, a prototype for the Jahn-Teller effect, has been an enigma and a challenge for a long time for both experiment and theory. We present a detailed theoretical study of the vibronic quantum dynamics in this electronic state, uncovering the effects of tunnelling, geometric phase, and symmetry. To this end, 45 vibronic levels of NO3 in the 2E" state are determined accurately and analyzed thoroughly. The computation is based on a high quality diabatic potential representation of the two-sheeted surface of the 2E" state developed by us [W. Eisfeld et al., J. Chem. Phys. 140, 224109 (2014)] and on the multi-configuration time dependent Hartree approach. The vibrational eigenstates of the NO-3 anion are determined and analyzed as well to gain a deeper understanding of the symmetry properties of such D3h symmetric systems. To this end, 61 eigenstates of the NO-3 anion ground state are computed using the single sheeted potential surface of the 1A1 state published in the same reference quoted above. The assignments of both the vibrational and vibronic levels are discussed. A simple model is proposed to rationalize the computed NO3 spectrum strongly influenced by the Jahn-Teller couplings, the associated geometric phase effect, and the tunnelling. Comparison with the available spectroscopic data is also presented. [ABSTRACT FROM AUTHOR]

The 2E" state of NO3, a prototype for the Jahn-Teller effect, has been an enigma and a challenge for a long time for both experiment and theory. We present a detailed theoretical study of the vibronic quantum dynamics in this electronic state, uncovering the effects of tunnelling, geometric phase, and symmetry. To this end, 45 vibronic levels of NO3 in the 2E" state are determined accurately and analyzed thoroughly. The computation is based on a high quality diabatic potential representation of the two-sheeted surface of the 2E" state developed by us [W. Eisfeld et al., J. Chem. Phys. 140, 224109 (2014)] and on the multi-configuration time dependent Hartree approach. The vibrational eigenstates of the NO-3 anion are determined and analyzed as well to gain a deeper understanding of the symmetry properties of such D3h symmetric systems. To this end, 61 eigenstates of the NO-3 anion ground state are computed using the single sheeted potential surface of the 1A1 state published in the same reference quoted above. The assignments of both the vibrational and vibronic levels are discussed. A simple model is proposed to rationalize the computed NO3 spectrum strongly influenced by the Jahn-Teller couplings, the associated geometric phase effect, and the tunnelling. Comparison with the available spectroscopic data is also presented. [ABSTRACT FROM AUTHOR]

The analytic energy gradients with respect to nuclear motion are derived for the natural orbital functional (NOF) theory. The resulting equations do not require resorting to linear-response theory, so the computation of NOF energy gradients is analogous to gradient calculations at the Hartree-Fock level of theory. The structures of 15 spin-compensated systems, composed of first- and second-row atoms, are optimized employing the conjugate gradient algorithm. As functionals, two orbital-pairing approaches were used, namely, the fifth and sixth Piris NOFs (PNOF5 and PNOF6). For the latter, the obtained equilibrium geometries are compared with coupled cluster singles and doubles calculations and accurate empirical data. [ABSTRACT FROM AUTHOR]

The present study focuses on the Be2 +, Be2, Be2-, and Be3 species with the aim to unveil their bonding pattern. The ground states of the above molecules are examined mainly through multi reference configuration interaction methods using an aug-cc-pVQZ basis set. Previous work is scrutinized with an eye to the instability problems inherent in various Hartree-Fock schemes. Under this point of view, we rationalize previous findings and put them in a unified context of what and why should be done in similar hard to crack cases. In all the above species, the covalently bound ground states are formed just because the Be atom is found in its first excited ³P(2s¹2p¹) state. [ABSTRACT FROM AUTHOR]

The present study focuses on the Be2 +, Be2, Be2-, and Be3 species with the aim to unveil their bonding pattern. The ground states of the above molecules are examined mainly through multi reference configuration interaction methods using an aug-cc-pVQZ basis set. Previous work is scrutinized with an eye to the instability problems inherent in various Hartree-Fock schemes. Under this point of view, we rationalize previous findings and put them in a unified context of what and why should be done in similar hard to crack cases. In all the above species, the covalently bound ground states are formed just because the Be atom is found in its first excited ³P(2s¹2p¹) state. [ABSTRACT FROM AUTHOR]

• The type-II band alignment of CsSnCl 3 /Cs 2 SnCl 6 hetero-interface leads to significantly reduced bandgap, with its CBM and VBM states dominated by Cs 2 SnCl 6 and CsSnCl 3 , respectively. • Spontaneous spacial separation of photoexcited charge carriers and electron tunneling from valence band of CsSnCl 3 to conduction band of Cs 2 SnCl 6 are predicted. Both processes are benefitial to increases in carrier density and carrier lifetime. • The rather similar orbital hybridization characters of both frontier states result in parity-forbidden optical transition at the Г point. • The CBM state dominated by Cs 2 SnCl 6 shows high licalization owing to the zero-dimensional electronic structure, further leading to the strong Hartree-Fock exchange interaction and open-up of bandgap in CsSnCl 3 /Cs 2 SnCl 6 hetero-interface. Low-toxicity tin halide perovskites (ASnX 3) with excellent optoelectronic properties are attracting an increasing level of interest. Sn2+ oxidation to Sn4+ via forming Sn vacancies should promote the formation of A 2 SnX 6. The resulted Cs 2 SnCl 6 /CsSnCl 3 hetero-interfaces can have significant influence on the optoelectronic properties. Here, we performed first-principles calculations to explore the electronic and optical properties of Cs 2 SnCl 6 /CsSnCl 3 hetero-interfaces. Our results revealed that the bandgap of Cs 2 SnCl 6 /CsSnCl 3 is significantly reduced due to the type-II band alignment with the VBM and CBM states are respectively dominated by CsSnCl 3 and Cs 2 SnCl 6. Both frontier states are derived from antibonding states of Sn 5s and Cl 3p, thus exhibit rather similar orbital hybridization characters. Spontaneous spacial separation of photo-excited charge carriers and electron tunneling are expected to occur at Cs 2 SnCl 6 /CsSnCl 3 interfaces, which should be beneficial to increased carrier density and long carrier lifetime. The CBM state exhibits rather high localization due to the effective zero-dimensional electronic structure of Cs 2 SnCl 6. Moreover, Cs 2 SnCl 6 /CsSnCl 3 superlattices exhibit improved light absorption. The electronic and optical properties of Cs 2 SnCl 6 /CsSnCl 3 can be well modulated by varying the thickness of either perovskite layer. Our work provides theoretical insights into the optoelectronic properties of Cs 2 SnCl 6 /CsSnCl 3 heterostructures, shedding light on the regulation strategies for high-performance tin halide perovskite optoelectronics. [ABSTRACT FROM AUTHOR]

The structure and properties of three layered heterometallic quaternary sulfides SrLaCuS 3 , SrNdCuS 3 and SrTmCuS 3 were studied for the first time using ab initio calculations in the stoichiometric and nonstoichiometric approximation. [Display omitted] • Quaternary sulfides SrRECuS 3 (RE = La, Nd, Tm) were studied using ab initio calculations. • Calculations were performed in the stoichiometric and nonstoichiometric approximations. • The wavenumbers and types of Raman and "silent" modes at the Г-point were determined. • The elastic constants and elastic moduli of the reported sulfides were calculated. The structure and properties of three layered heterometallic quaternary sulfides SrLaCuS 3 , SrNdCuS 3 and SrTmCuS 3 were studied for the first time using first-principles calculations in the stoichiometric and nonstoichiometric approximations. The applied DFT-based computations were performed using a hybrid functional with the contribution of nonlocal exchange in the Hartree-Fock formalism. It was revealed that the nonstoichiometry of SrLaCuS 3 and SrNdCuS 3 must be considered for modeling phonon spectra, elastic properties and band gaps. The wavenumbers and types of the Raman and "silent" modes at the Г-point were determined. From the analysis of displacement vectors, the degree of participation of ions in each mode was determined. The elastic constants and elastic moduli of the reported sulfides were calculated. [ABSTRACT FROM AUTHOR]

The principal purpose of this topical review is to single out some of the universal features of high-temperature (high- T c) and related strongly-correlated systems, which can be compared with experiment in a quantitative manner. The description starts with the concept of exchange-interaction-mediated (real-space) pairing, combined with strong correlations among narrow band electrons, for which the reference state is that of the Mott–Hubbard insulator. The physical discussion of concrete properties relies on variational approach, starting from generalized renormalized mean-field theory (RMFT) in the form of statistically-consistent Gutzwiller approximation (SGA), and its subsequent generalization, i.e., a systematic Diagrammatic Expansion of the Variational (Gutzwiller-type) Wave Function (DE-GWF). The solution leads to the two energy scales, one involving unconventional quasiparticles close to the Fermi energy, and the other reflecting the fully correlated state, involving electrons deeper below the Fermi surface. Those two regimes are separated by a kink in the dispersion relation, which is observed in photoemission. As a result, one obtains both the doping dependent properties in the correlated state, and effective renormalized quasiparticles. The reviewed ground-state characteristics for high- T c systems encompass high- T c superconductivity, nematicity, charge- (and pair-) density-wave effects, as well as non-BCS kinetic energy gain in the paired state. The calculated dynamic properties are: the universal Fermi velocity, the Fermi wave-vector, the effective mass enhancement, the pseudogap; and the d -wave gap magnitude. We discuss that, within the variational approach, the minimal realistic model is represented by the so-called t - J - U Hamiltonian. Inadequacy of the t - J and Hubbard models, particularly of their RMFT versions, is discussed explicitly. For heavy fermion systems, modeled by the Anderson lattice model and with the DE-GWF approach, we discuss the phase diagram, encompassing superconducting, Kondo insulating, ferro- and anti-ferromagnetic states. The superconducting state is then a two- d -wave gap system. If the orbital degeneracy of f -electrons is included, the coexistent ferromagnetic- (spin–triplet) superconducting phases appear and match those observed for UGe 2 in a semiquantitative manner. Finally, in the second part, we generalize our approach to the collective spin and charge fluctuations in high- T c systems, starting from variational approach, defining the saddle-point state, and combining it with 1 / N expansion. The present scheme differs essentially from that starting from the saddle-point Hartree–Fock approximation, and incorporating the fluctuations in the random phase approximation (RPA). The spectrum of collective spin and charge excitations is determined for the Hubbard and t - J - U models, and subsequently compared quantitatively with recent experiments. The Appendices provide formal details to make this review self-contained. [ABSTRACT FROM AUTHOR]

A combined numerical-experiment investigation on the flow and acoustic field of an electronic expansion valve (EEV) is conducted in this paper. In an electronic expansion valve (EEV) under refrigeration condition, it is usually complex about internal flow. There are high pressure gradient and velocity gradient in the flow field, and it also involves the process of flashing phase change, physical property change, and heat transfer, which is difficult to simulate directly. After many explorations in this paper, the flow field of EEV under refrigeration condition is simulated by a four-step computational fluid dynamics (CFD). On this basis, the noise of EEV which is induced by the internal turbulent flow and propagates outward through the shell of EEV is simulated by a Hybrid Method. Numerical simulations of the mass flow rate (MFR) and sound pressure level (SPL) are verified by experimental data. Then, the characteristics of the internal flow field causing the external acoustic radiation are analyzed and used to create an improved design that can reduce the SPL while the MFR hardly changes. [ABSTRACT FROM AUTHOR]

In SU(N) gluodynamics, above the de-confinement temperature, the effective potential has minima at non-zero A 0 -background fields in the two-loop approximation. Also, it has a minimum at non-zero chromomagnetic background field, known as 'Savvidy'-vacuum, which shows up on the one-loop level. In this paper, we join these two approaches. We formulate, at finite temperature, the effective action, or the free energy, in SU(2) gluodynamics on the two-loop level, with both, A 0 background and magnetic background present at the same time, which was not done so far. We provide the necessary representations for both, effective numerical calculation and high-temperature expansions. The results are represented as a 3D plot of the real part of the effective potential. Also, we reproduce for zero either, the A 0 -background or the magnetic background, the known minima and compare them. The imaginary part is, on the two-loop level, still present. We mention that, as is known from literature for the case without A 0 -background, the imaginary part is compensated by the ring ('daisy') diagrams. However, in our two-loop approximation, the results reveal an unnatural, singular behavior of the real part of the effective potential in the region, where the imaginary part sets in. Our conclusion is that one has to go beyond the two-loop approximation and its ring improved version, in order to investigate the minimum of the effective action as a function of A 0 and chromomagnetic field, and its stability, at least in the approximation of super daisy diagrams, i.e., the Hartree approximation in the CJT formalism. [ABSTRACT FROM AUTHOR]

Spin projected wave functions are generalizations of the Hartree–Fock wave function. Among them, the Half‐Projected Hartree–Fock (HPHF) wave function is a nearly pure wave function of spin and recovers a small part of the spin correlation energy. This paper reviews the history of the HPHF theory, not only from the conceptual point of view but also providing a compilation of the publications of this method over the years until now. In addition, the extension of the HPHF method to the calculation of excited states with the same symmetry as the ground state will be discussed. The possible variational collapse during the calculation of a singlet excited state of the same symmetry as the ground state is avoided by orthogonalizing a pair of corresponding orbitals, one occupied and one virtual orbital, at every step of the variational process. As an example, the potential energy surfaces of the S0 ground and 1S1(n, π*) first excited state of the formic acid HCOOH are calculated. [ABSTRACT FROM AUTHOR]

An experimental and theoretical study based on DFT/TD-DFT approximations is presented to understand the nature of electronic excitations, reactivity, and nonlinear optical (NLO) properties of reactive orange 16 dye (RO16), an azo chromophore widely used in textile and pharmacological industries. The results show that the solvent has a considerable influence on the electronic properties of the material. According to experimental results, the absorption spectrum is formed by four intense transitions, which have been identified as π → π ∗ states using TD-DFT calculations. However, the TD-DFT results reveal a weak n → π ∗ in the low-lying spectral region. Continuum models of solvation indicate that these states suffer from bathochromic (ca. 15 nm) and hypsochromic shifts (ca. 4 nm), respectively. However, the expected blue shift for the absorption n → π ∗ is only described using long-range or dispersion-corrected DFT methods. RO16 is classified as a strong electrophilic system, with electrophilicity ω > 1.5 eV. Concerning the nucleophilicity parameter (N), from vacuum to solvent, the environment is active and changes the nucleophilic status from strong to moderate nucleophile (2.0 ≤ N ≤ 3.0 eV). The results also suggest that all electrical constants are strongly dependent on long-range and Hartree-Fock exchange contributions, and the absence of these interactions gives results far from reality. In particular, the results for the NLO response show that the chromophore presents a potential application in this field with a low refractive index and first hyperpolarizability ca. 214 times bigger than the value usually reported for urea (β = 0.34 × 10− 30 esu), which is a standard NLO material. Concerning the solvent effects, the results indicate that the polarizability increases ∼ 20 × 1 0 − 24 esu from gas to solvent while the first hyperpolarizability is calculated as ∼ 45 × 1 0 − 30 esu, ca. 180%, regarding the vacuum. The results suggest RO16 is a potential compound in NLO applications. [ABSTRACT FROM AUTHOR]

We examine long-wavelength correlation functions of massive scalar fields in de Sitter spacetime. For the theory with a quartic self-interaction, the two-point function is calculated up to two loops. Comparing our results with the Hartree–Fock approximation and with the stochastic approach shows that the former resums only the cactus type diagrams, whereas the latter contains the sunset diagram as well and produces the correct result. We also demonstrate that the long-wavelength expectation value of the commutator of two fields is equal to zero both for spacelike and timelike separated points. [ABSTRACT FROM AUTHOR]

We investigate the existence and properties of ground state solutions for a class of nonlinear Choquard equations. Proofs are mainly based on the variational method. [ABSTRACT FROM AUTHOR]

In this paper we are interested in a class of semiclassical Schrödinger-Poisson system with Hartree-type nonlinearity. Firstly, we prove the existence of groundstate for autonomous system by using the subcritical approximation and the Pohozaev constraint method. Secondly, we prove the existence of semiclassical state solutions and multiplicity for system with critical frequency by using the genus. Finally, we study multiplicity and concentration behavior for solutions of system with general potential by using the Lusternik-Schnirelman theory. [ABSTRACT FROM AUTHOR]

The correct understanding of the behavior of highly stripped ions immersed in a dense plasma environment is a hitherto challenge for theory and it is of importance in various applications. Here, we developed four kinds of novel theoretical models to the determination of the spectral properties and collision dynamics of H‐like ions in dense and hot plasmas by employing the analytical potential [Li et al., Phys. Plasmas2019, 26, 033301] to describe the interactions among the charged particles: (i) The electron photon processes in plasma model within the relativistic scheme; (ii) The multiconfiguration Dirac–Fock model within the framework of relativistic self‐consistent iteration approximation; (iii) The generalized pseudospectral method within the relativistic framework; and (iv) An analytic formula based on the Hartree–Fock method and the irreducible tensor theory within the non‐relativistic regime, derived from a solution of Schrödinger equation. As a typical example, energy eigenvalues, radiative transition properties, spectral line shifts, and electron impact excitation and ionization cross sections of the selected N6+ and Ne9+ ions are determined for several temperature‐density cases, characteristic of inertial confinement fusion plasmas. A comparison of these results with each other and the results from earlier calculations as well as with the available experimental data is provided. Systematic trend is determined for all the properties under study concerning increased screening. The present study not only extends our understanding of the dense plasma shielding effects, but also opens the way for future investigations allowing accurate predictions of spectral properties of ions in dense and hot plasmas aimed at providing precision data for various practical applications. [ABSTRACT FROM AUTHOR]

This review presents a critical and comprehensive overview of current experimental measurements of complete elastic constant tensors for molecular crystals. For a large fraction of these molecular crystals, detailed comparisons are made with elastic tensors obtained using the corrected small basis set Hartree–Fock method S‐HF‐3c, and these are shown to be competitive with many of those obtained from more sophisticated density functional theory plus dispersion (DFT‐D) approaches. These detailed comparisons between S‐HF‐3c, experimental and DFT‐D computed tensors make use of a novel rotation‐invariant spherical harmonic description of the Young's modulus, and identify outliers among sets of independent experimental results. The result is a curated database of experimental elastic tensors for molecular crystals, which we hope will stimulate more extensive use of elastic tensor information—experimental and computational—in studies aimed at correlating mechanical properties of molecular crystals with their underlying crystal structure. [ABSTRACT FROM AUTHOR]

The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green's function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0) of the ADG code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei. [ABSTRACT FROM AUTHOR]

The importance of the Density Functional Theory (DFT) calculation approach lies in their ability to provide a highly accurate prediction of structural and optoelectronic properties. However, the traditional methods of DFT failed to predict optoelectronic properties satisfactorily. Therefore, it will be necessary to examine methods containing different percentages of Hartree-Fock exchange and correlation in order to find the most suitable functionals. DFT and Time-Dependent-DFT (TD-DFT) calculations was carried out using four different functionals approximations incorporating a different amount of Hartree Fock exchange (B3LYP, BHandHLYP, CAM-B3LYP and LC-PBE), in order to evaluate their accuracies to predict the geometrical, optoelectronic and charge transfer properties of four triphenylamine-based dyes for Dye-Sensitized Solar Cells (DSSCs) applications. The functional hybrid B3LYP was the best among adopted functional that reproduced the geometrical, optoelectronic and charge transfer properties. On the other hand, it has been shown that the Hartree-Fock exchange percentage for BHandHLYP, significantly improved TD-DFT results in the case of organic dyes. Moreover, the corrected long-range functionals (CAM-B3LYP and LC-wPBE) present valuable tools for giving results of comparable precision with experimental optical data. In terms of the choice of the most appropriate functional for computational calculation, the obtained results can be useful for future DSSC applications. [ABSTRACT FROM AUTHOR]

In this work, we present two different methods for calculation of the atomic structure for atoms and ions. The first one is the Hartree‐Fock pseudo‐Relativistic method which can be ab initio where we calculate the atomic parameters theoretically by using, for example, the first three programs of the Cowan (CW) atomic structure code: RCN, RCN2, and RCG. We can also use it semi‐empirically by using the fourth CW program RCE and fitting the purely theoretical energy levels with experimental data taken for example from the NIST database. The second one is the Thomas‐Fermi‐Dirac‐Amaldi method which can be ab initio where we calculate the atomic parameters theoretically by using, for example, the SUPERSTRUCTURE (SS) or the AUTOSTRUCTURE (AS) atomic structure codes. We can also use it semi‐empirically by using the Term Energy Corrections in SS or the Level Energy Corrections in SS or AS atomic structure codes. As an application of using these methods, we calculate energy levels, oscillator strengths, and transition probabilities for the 5p‐6s transitions for the Mo II ion using ab initio and semi‐empirical methods with the CW and AS atomic structure codes. [ABSTRACT FROM AUTHOR]

In this work, energy levels, oscillator strengths, and transition probabilities for the Ti II ion are calculated by the Hartree–Fock pseudo‐Relativistic method using the Cowan (CW) atomic structure code and by the Thomas‐Fermi‐Dirac‐Amaldi method using the AUTOSTRUCTURE (AS) atomic structure code. We used the terms and levels generated by the 12 configurations: 3d2 ns (n = 4–6), 3d2 np (n = 4,5), 3d2 nd (n = 4,5), 3d2 4f, 3d 4s np (n = 4,5), 3d 4s2, 3d3. We improved our ab initio calculated data by using the semi‐empirical methods in the CW and AS atomic structure codes. We also compared them with other theoretical and experimental results and obtained new data for this ion. [ABSTRACT FROM AUTHOR]