Electron Correlation Corrections Research Articles

Accurate ab initio spectroscopic studies of promising interstellar ethanolamine iminic precursors

Context. The detection of NH2CH2CH2OH (ethanolamine) in molecular cloud G+0.693-0.027 adds an additional player to the pre-biotic molecules discovered so far in the interstellar medium (ISM). As this molecule might be formed through condensed-phase hydrogenation steps, detecting one or more of the molecules involved might help to elucidate the chemical pathway leading to its production. Aims. The chemical path involves the formation of four chemical species. In this work, we study the energies of the isomers involved, indicate the best candidates for detection purposes, and provide the distortion constants of the most energetically favoured isomers undetected so far. Methods. We used highly accurate CCSD(T)-F12/cc-pCVTZ-F12 computations to predict the lowest energy isomers as well as their spectroscopic constants, taking corrections for core electron correlation and scalar relativity into account. Results. We studied 14 isomers. We find that the lowest energy isomer proposed in previous studies is not the actual minimum. We provide a set of rotational and distortion constants of the two new most stable isomers together with their fundamental vibrational frequencies in order to guide the search for these important astrochemical precursors of prebiotic molecules in the ISM.

CoN4C2 : Two-dimensional cobalt carbonitride with a flat-band feature

Based on the first-principles simulations within the framework of density functional theory, we predict that ${\mathrm{CoN}}_{4}{\mathrm{C}}_{2}$ is a single-atom-thick two-dimensional material, which is composed of ${\mathrm{CoN}}_{4}$ unit and ${\mathrm{C}}_{2}$ dimer. The cohesive energy and phonon dispersion calculations of ${\mathrm{CoN}}_{4}{\mathrm{C}}_{2}$ monolayer, as well as molecular dynamics simulation, have been carried out and its stability is confirmed. The electronic states near the Fermi energy are dominated by Co $3d$ orbital states and the $2p$ orbitals of C and N atoms make a small contribution. The unusual electronic feature of ${\mathrm{CoN}}_{4}{\mathrm{C}}_{2}$ is the flat band state close to the Fermi energy, which is derived from Co ${\mathrm{d}}_{{z}^{2}}$ partial orbital. With the tensile strain increasing, a phase transition from nonmagnetic state to magnetic state is induced. At the biaxial tensile strain of 8.6%, the flat band is pushed to the Fermi energy. Moreover, the effect of electron correlation correction on the electronic structure of ${\mathrm{CoN}}_{4}{\mathrm{C}}_{2}$ is also discussed by the SCAN meta-GGA method and $\mathrm{GGA}+U$ method. Our results demonstrate that tensile strain is another knob to realize the flat band state at the Fermi level, similar to the twist angle in twisted bilayer graphene reported recently.

Solvent effects on Stokes shifts, and NLO response of thieno[3,4-b]pyrazine: A comprehensive QM/MM investigation

The analysis of solvent effects on the fluorescence and nonlinear optical (NLO) response of thieno[3,4-b]pyrazine was performed using the sequential Monte Carlo/Quantum Mechanics (s-MC/QM) approach. For this, the theoretical analysis was based on time-dependent density functional methods considering several implicit and explicit solvent models. Explicit solvent models include either electrostatic or non-electrostatic intermolecular forces like Keeson, London, and Debye interactions. The first absorption transition occurs with a charge transfer from the pyrazine to the thieno ring leading to a decrease in the molecular dipole moment by changing the average number of hydrogen-bonds on nitrogen and sulfur atoms. Including the solvent effects, this leads to a strong Stokes shift (~110 nm), showing that the title compound and its derivatives are promising for solar cells or even as a biological marker. Regarding the NLO response of the chromophore, the results indicate that the electronic-correlation (EC) plays a fundamental role for the first hyperpolarizability (β) but the solvent effect is negligible. The second-order Møller-Plesset perturbation theory and the long-range and dispersion corrected DFT-based methods show that EC corrections can improve the description of β by ca. 150% when compared with the Hartree–Fock approximation.

Studies on the solid–liquid equilibria and intermolecular interactions Urea binary mixtures with Sulfanilamide and Sulfacetamide

The binary phase diagrams of Sulfanilamide-Urea (SN-U) and Sulfacetamide-Urea (SC-U) were measured using differential scanning calorimetry technique (DSC). Both examined mixtures were found to form simple binary eutectics. The limited miscibility in the solid state observed by DSC, proving inability of co-crystallization in new multi-molecular form, was also confirmed using PXRD and FTIR-ATR measurements of solid dispersions obtained via liquid assisted co-grinding. The lack of intermolecular complex formation in the crystals does not imply the lack of interactions in the liquid state. Detailed characteristics of potential homo- and hetero-molecular pairs were offered using ab initio and the first principle quantum chemistry computations. The obtained results happened to be strongly dependent on the applied level of theory. The importance of including the zero point energy contributions and electron correlation corrections was emphasized. It was found that the mole fraction of hetero-complexes with urea is the highest among all other constituents of studied systems at their eutectic points. Finally, the importance of intermolecular interaction leading to complexes formation in the liquid state at saturated position was documented by computed values of solvation Gibbs free energy. Based on computed trends it was inferred that the eutectic mixtures can be interpreted as such equilibria for which mutual solvation of all components is maximized.

Spectroscopic study of magnesium dinitrogen and sodium dinitrogen cation

ABSTRACT Despite its likely importance in astrochemistry, pure rotational spectra are not observable for gas-phase N2 since this molecule has no permanent dipole moment. Complexation of monomeric N2 with a cationic metal (MN2+) may be kinetically and thermodynamically favourable, and the detection of such MN2+ molecules could be useful tracers of N2 in order to probe its abundance and kinetics. Highly accurate quartic force field methods have been applied here to compute rotational and vibrational spectroscopic properties of the NaN2+ and MgN2+ molecules via a coupled cluster-based composite approach with additional corrections for post-CCSD(T) electron correlation and relativistic effects. The relative energies of various isomers have also been computed and show that both NaN2+ and MgN2+ have linear ground electronic states. At the highest level of theory, rotational constants (B0) of 4086.9 and 4106.0 MHz are predicted for NaN2+ and MgN2+, respectively, with dipole moments of 6.92 and 4.34 D, respectively, making them rotationally observable even at low concentrations. Post-CCSD(T) electron correlation corrections lower the N–N stretching frequency while relativistic corrections have a much smaller effect putting the fundamental frequencies at 2333.7 and 2313.6 cm−1, respective of NaN2+ and MgN2+ slightly above that in N2H+. Additive corrections do not significantly change the other two vibrational modes. An anharmonic, zero-point corrected N2 dissociation energy of 7.3 and 7.0 kcal mol−1 is, respectively, reported for NaN2+ and MgN2+ suggesting possible formation of these molecules in protoplanetary discs or planetary nebulae that are metal- and nitrogen-rich.

QED theory of the normal mass shift in few-electron atoms

The electron-electron interaction correction of first order in $1/Z$ to the one-electron part of the nuclear recoil effect on binding energies in atoms and ions is considered within the framework of the rigorous QED approach. The calculations to all orders in $\alpha Z$ are performed for the $1s^2$ state in heliumlike ions and the $1s^2 2s$ and $1s^2 2p_{1/2}$ states in lithiumlike ions in the range $Z=5$--$100$. The results obtained are compared with the Breit-approximation values. The performed calculations complete a systematic treatment of the QED nuclear recoil effect up to the first order in $1/Z$. The correction obtained is combined with the previously studied two-electron part as well as the higher-order electron-correlation corrections evaluated within the Breit approximation to get the total theoretical predictions for the mass shifts.

An adiabatic connection for doubly-occupied configuration interaction wave functions.

An adiabatic connection (AC) is developed as an electron correlation correction for doubly occupied configuration interaction (DOCI) wave functions. Following the work of Pernal [Phys. Rev. Lett. 120, 013001 (2018)], the working equations of the approach, termed AC-DOCI, are rooted in the extended random phase approximation (ERPA) and require knowledge of only the ground-state two-electron reduced density matrix (2RDM) from the DOCI. As such, the AC is naturally suited to modeling electron correlation in variational 2RDM (v2RDM)-based approximations to the DOCI. The v2RDM-driven AC-DOCI is applied to the dissociation of molecular nitrogen and the double dissociation of water; the approach yields energies that are similar in quality to those from second-order multireference perturbation theory near equilibrium, but the quality of the AC-DOCI energy degrades at stretched geometries. The exact adiabatic connection path suggests the assumption that the one-electron reduced-density matrix is constant along the AC path is invalid at stretched geometries, but this deficiency alone cannot explain the observed behavior. Rather, it appears that the ERPA's single-particle-transition ansatz cannot, in general, provide good approximations to the 2RDM along the AC path. The AC-DOCI is also applied to a set of 45 reaction energies; for these systems, the approach has an average accuracy that is comparable to that of single-reference second-order many-body perturbation theory.

Angular dependence of strong field ionization of N2 by time-dependent configuration interaction using density functional theory and the Tamm-Dancoff approximation

The ionization of N2 serves as an important test case for computational methods for strong field ionization. Because Koopmans’s theorem fails for Hartree-Fock calculations of N2, corrections for electron correlation are needed to obtain the proper ordering of ionization energies of N2. Lopata and co-workers found that real-time integration of time-dependent Hartree-Fock (rt-TD-HF) gave a ratio for strong field ionization parallel and perpendicular to the molecular axis that was too small compared to experiment, but real-time integration of time-dependent density functional theory (rt-TD-DFT) with an appropriately tuned long-range corrected functional, lc-ωPBE*, was in good agreement with experiment. The present study finds that time-dependent configuration interaction (TDCI) with single excitations based on a Hartree-Fock reference determinant (TD-CIS) has the same problems as rt-TD-HF. These problems can be overcome within the TDCI framework by calculating the excitation energies and transition dipole moments with density functional theory using linear response TD-DFT in the Tamm-Dancoff approximation (TDA) with suitably tuned long-range corrected functionals (TD-TDA). The correct angular dependence of the total ionization rate is obtained with TD-TDA using tuned lc-ωPBE*, lc-BLYP*, and ωB97XD* functionals. Partitioning of the total ionization rate into orbital components confirms that the larger ionization rate perpendicular to the molecular axis found for TD-CIS is due to greater π orbital contributions than those seen in TD-TDA. The use of density functional theory corrects this problem. At higher fields, both the TD-CIS and TD-TDA simulations show an increased ionization rate perpendicular to the molecular axis because of increased ionization from the π orbitals.

Do Dyson Orbitals resemble canonical Hartree–Fock orbitals?

ABSTRACTDyson orbitals are overlaps between states with N and N±1 electrons and provide conceptual links between transition probabilities of electron detachment or attachment, density matrices, total energies and general principles of chemical bonding. Canonical, Hartree–Fock orbitals are compared with Dyson orbitals obtained with electron–propagator calculations that retain all elements of the self–energy matrix, wherein all orbital–relaxation and electron–correlation corrections to Koopmans results reside. For valence ionization energies and electron affinities of representative closed–shell molecules, canonical, Hartree–Fock orbitals usually are excellent approximations to Dyson orbitals, although there are some notable cases where the resemblance is not as strong. Numerical relationships between pole strengths and the Koopmans contributions to Dyson orbitals also are inferred from the data.

Relative stability between the manganese hydroxide- and oxo-models for water oxidation by CCSD, DMRG CASCI, CASSCF, CASPT2 and CASDFT methods; Importance of static and dynamical electron correlation effects for OEC of PSII

Relative stability between manganese hydroxide (H2O)2(OH)4Mn(IV)OH (1) and manganese oxo (H2O)3(OH)3Mn(IV)O (2) species were investigated by coupled cluster (CC) SD and SD(T), DMRG CASCI, CASSCF, CASPT2 and CASDFT methods. The DMRG CASCI and DMRG CASSCF based on thirteen active orbitals and thirteen active electrons {13, 13} CAS space indicted the greater stability of 2 than 1. On the other hand, the relative stability between 1 and 2 was reversed by UCC SD, DLPNO-UCC SD, CASPT2 and CAS-DFT, indicating an important role of dynamical electron correlation corrections. Implications of present results are discussed to elucidate scope and applicability of hybrid DFT (HDFT) methods for 1 and 2.

Development of the Fragment Molecular Orbital Method for Calculating Nonlocal Excitations in Large Molecular Systems.

We developed the fragment-based method for calculating nonlocal excitations in large molecular systems. This method is based on the multilayer fragment molecular orbital method and the configuration interaction single (CIS) wave function using localized molecular orbitals. The excited-state wave function for the whole system is described as a superposition of configuration state functions (CSFs) for intrafragment excitations and for interfragment charge-transfer excitations. The formulation and calculations of singlet excited-state Hamiltonian matrix elements in the fragment CSFs are presented in detail. The efficient approximation schemes for calculating the matrix elements are also presented. The computational efficiency and the accuracy were evaluated using the molecular dimers and molecular aggregates. We confirmed that absolute errors of 50 meV (relative to the conventional calculations) are achievable for the molecular systems in their equilibrium geometries. The perturbative electron correlation correction to the CIS excitation energies is also demonstrated. The present theory can compute a large number of excited states in large molecular systems; in addition, it allows for the systematic derivation of a model exciton Hamiltonian. These features are useful for studying excited-state dynamics in condensed molecular systems based on the ab initio electronic structure theory.

Theoretical study of the NMR chemical shift of Xe in supercritical condition.

In this work we investigate the level of theory necessary for reproducing the non-linear variation of the 129Xe nuclear magnetic resonance (NMR) chemical shift with the density of Xe in supercritical conditions. In detail we study how the 129Xe chemical shift depends under supercritical conditions on electron correlation, relativistic and many-body effects. The latter are included using a sequential-QM/MM methodology, in which a classical MD simulation is performed first and the chemical shift is then obtained as an average of quantum calculations of 250 MD snapshots conformations carried out for Xe n clusters (n = 2 - 8 depending on the density). The analysis of the relativistic effects is made at the level of 4-component Hartree-Fock calculations (4c-HF) and electron correlation effects are considered using second order Møller-Plesset perturbation theory (MP2). To simplify the calculations of the relativistic and electron correlation effects we adopted an additive scheme, where the calculations on the Xe n clusters are carried out at the non-relativistic Hartree-Fock (HF) level, while electron correlation and relativistic corrections are added for all the pairs of Xe atoms in the clusters. Using this approach we obtain very good agreement with the experimental data, showing that the chemical shift of 129Xe in supercritical conditions is very well described by cluster calculations at the HF level, with small contributions from relativistic and electron correlation effects.

Towards a quantum chemical protocol for the prediction of rovibrational spectroscopic data for transition metal molecules: Exploration of CuCN, CuOH, and CuCCH.

High accuracy electronic structure computations for small transition metal-containing molecules have been a long term challenge. Due to coupling between electronic and nuclear wave functions, even experimental/theoretical identification of the ground electronic state requires tremendous efforts. Quartic force fields (QFFs) are effective ab initio tools for obtaining reliable anharmonic spectroscopic properties. However, the method that employs complete basis set limit extrapolation ("C"), consideration of core electron correlation ("cC"), and inclusion of scalar relativity ("R") to produce the energy points on the QFF, the composite CcCR methodology, has not yet been utilized to study inorganic spectroscopy. This work takes the CcCR methodology and adapts it to test whether such an approach is conducive for the closed-shell, copper-containing molecules CuCN, CuOH, and CuCCH. Gas phase rovibrational data are provided for all three species in their ground electronic states. Equilibrium geometries and many higher-order rovibrational properties show good agreement with earlier studies. However, there are notable differences, especially in computation of fundamental vibrational frequencies. Even with further additive corrections for the inner core electron correlation and coupled cluster with full single, double, and triple substitutions (CCSDT), the differences are still larger than expected indicating that more work should follow for predicting rovibrational properties of transition metal molecules.

Radiative transition rates of 1s2s(3S)3p levels for Li-like ions with [formula omitted

Energy and radiative transition rates of the 1s2s (1,3S) 3p levels of Li-like ions with 5⩽Z⩽10 are calculated using a multiconfiguration Dirac-Fock approach including quantum-electrodynamic and electronic correlation corrections. The importance of the electronic correlation on the radiative transition probabilities is assessed in detail.

Nucleophilic aromatic substitution in chlorinated aromatic systems with a glutathione thiolate model

The conjugation of glutathione with chlorobenzene and di-, tri-, tetra-, and hexa-chlorinated benzenes via nucleophilic aromatic substitution was modeled for isolated reacting species by ab initio molecular orbital theory to provide an understanding of the intrinsic reactivity of unactivated chloroaromatic systems. Computations at the HF/6-31+G(d,p) level were augmented with electron correlation corrections using MP2 theory and density functional theory at the B3LYP level. Features of the reaction hypersurface were elaborated using thiolate (thiomethoxide) as the model for an enzyme-activated glutathione molecule. Unlike the similar reaction with 1-chloro-2, 4-dinitrobenzene a known substrate with glutathione, no σ-complex or Meisenheimer complex was isolated as a true intermediate on the hypersurface. Instead, the σ-complex appears as a transition state, preceded and followed by two ion-molecule complexes in which the approaching and departing anions reside in the plane of the aromatic ring. Solvent calculations show a very similar hypersurface landscape with only one transition state and no intermediate. Activation energies are somewhat greater than for 1-chloro-2, 4-dinitrobenzene owing to the lack of nitro substituents, which provide stabilization in these systems. Nevertheless, activation energies calculated at correlated levels indicate that these reactions are still feasible and consistent with experiment. Transition states and activation energies for dichlorobenzenes and polychlorobenzenes are lower in energy than for chlorobenzene implying greater stability conferred to the transition state by ortho and para substituents.

Ground-state Landégfactors for selected ions along the boron isoelectronic sequence

Land\'e $g$ factors for the fine-structure $1{s}^{2}2{s}^{2}2p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2}$ and $^{2}P_{3/2}$ levels in the boron isoelectronic sequence for selected $Z$ values have been calculated using the multiconfiguration Dirac-Fock method with both quantum-electrodynamic and electronic correlation corrections included. All-order Breit and vacuum polarization corrections were included in the calculation, with a fully optimized active set wave function. The results are compared with the available theoretical data, showing a very good agreement.

Excited-states and spectroscopic properties of superoxide anion: a theoretical study including spin–orbit coupling

ABSTRACTThe potential energy curves (PECs) of 24 Λ–S electronic states of superoxide anion (O2−), which correlated with the first dissociation channel, were calculated using a high-accuracy internally contracted multireference configuration interaction (icMRCI) methodology with the Davidson correction in conjunction with the correlation-consistent basis sets. The core electron correlation and scalar relativistic corrections as well as basis set extrapolation were included. The spin–orbit coupling was also taken into account by using the state interaction approach with the Breit–Pauli Hamiltonian. The PECs of 54 Ω states generated from the 24 Λ–S states were constructed and described in detail. The spectroscopic constants of the seventeen Λ–S and 37 Ω bound states were evaluated and the vibrational properties of some weakly bound states were predicted. Comparing with the available experimental and theoretical data shows that the computational strategy employed is suitable and highly accurate for this system.

Assessing the performance of popular QM methods for calculation of conformational energies of trialanine

Accurate description of the conformational energies of the amino acids is essential for molecular dynamics simulation of protein structures. In this study, we compute the relative energies at 51 conformations for a trialanine tetrapeptide at different levels of theory. The computed energies at various theoretical levels, including the semiempirical DFTB method, HF, DFT, MP2 and CCSD(T), are compared with each other. The calculated energies from density-fitting local CCSD(T)/CBS (complete basis set) calculations are taken as the benchmark. The accuracy of the theoretical methods is highly dependent on the electronic correlation and dispersion corrections as well as the size of the basis sets. The involvement of the empirical dispersion energies in HF and DFT methods consistently improves their performance. Considering both the accuracy and computational efficiency, the Minnesota density functional M06-L-D and M06-2X-D are efficient and accurate for modeling of trialanine structures.

A note on the interaction-induced electric quadrupole moment of two xenon atoms

We have used flexible Gaussian-type basis sets and high-level ab initio methods to calculate the interaction-induced quadrupole (Θ) and hexadecapole (Φ) moment of the Xe⋯Xe pair in the region 4≤R/a0≤15. A very large [15s12p9d5f1g] basis set yields (at R/a0=4) Θint=−10.3709 and −10.4487 ea02 at the SCF and MP2 level, respectively. At the coupled cluster (CCSD) level the electron correlation correction is positive for both moments around the theoretical internuclear separation of 8.5 a0.

Importance of the Electron Correlation and Dispersion Corrections in Calculations Involving Enamines, Hemiaminals, and Aminals. Comparison of B3LYP, M06-2X, MP2, and CCSD Results with Experimental Data.

While B3LYP, M06-2X, and MP2 calculations predict the ΔG° values for exchange equilibria between enamines and ketones with similar acceptable accuracy, the M06-2X/6-311+G(d,p) and MP2/6-311+G(d,p) methods are required for enamine formation reactions (for example, for enamine 5a, arising from 3-methylbutanal and pyrrolidine). Stronger disagreement was observed when calculated energies of hemiaminals (N,O-acetals) and aminals (N,N-acetals) were compared with experimental equilibrium constants, which are reported here for the first time. Although it is known that the B3LYP method does not provide a good description of the London dispersion forces, while M06-2X and MP2 may overestimate them, it is shown here how large the gaps are and that at least single-point calculations at the CCSD(T)/6-31+G(d) level should be used for these reaction intermediates; CCSD(T)/6-31+G(d) and CCSD(T)/6-311+G(d,p) calculations afford ΔG° values in some cases quite close to MP2/6-311+G(d,p) while in others closer to M06-2X/6-311+G(d,p). The effect of solvents is similarly predicted by the SMD, CPCM, and IEFPCM approaches (with energy differences below 1 kcal/mol).