Treatment Of Electron Correlation Research Articles

Improving the accuracy of Møller-Plesset perturbation theory with neural networks.

Noncovalent interactions are of fundamental importance across the disciplines of chemistry, materials science, and biology. Quantum chemical calculations on noncovalently bound complexes, which allow for the quantification of properties such as binding energies and geometries, play an essential role in advancing our understanding of, and building models for, a vast array of complex processes involving molecular association or self-assembly. Because of its relatively modest computational cost, second-order Møller-Plesset perturbation (MP2) theory is one of the most widely used methods in quantum chemistry for studying noncovalent interactions. MP2 is, however, plagued by serious errors due to its incomplete treatment of electron correlation, especially when modeling van der Waals interactions and π-stacked complexes. Here we present spin-network-scaled MP2 (SNS-MP2), a new semi-empirical MP2-based method for dimer interaction-energy calculations. To correct for errors in MP2, SNS-MP2 uses quantum chemical features of the complex under study in conjunction with a neural network to reweight terms appearing in the total MP2 interaction energy. The method has been trained on a new data set consisting of over 200 000 complete basis set (CBS)-extrapolated coupled-cluster interaction energies, which are considered the gold standard for chemical accuracy. SNS-MP2 predicts gold-standard binding energies of unseen test compounds with a mean absolute error of 0.04 kcal mol-1 (root-mean-square error 0.09 kcal mol-1), a 6- to 7-fold improvement over MP2. To the best of our knowledge, its accuracy exceeds that of all extant density functional theory- and wavefunction-based methods of similar computational cost, and is very close to the intrinsic accuracy of our benchmark coupled-cluster methodology itself. Furthermore, SNS-MP2 provides reliable per-conformation confidence intervals on the predicted interaction energies, a feature not available from any alternative method.

Relativistic Approximations to Paramagnetic NMR Chemical Shift and Shielding Anisotropy in Transition Metal Systems.

We apply approximate relativistic methods to calculate the magnetic property tensors, i.e., the g-tensor, zero-field splitting (ZFS) tensor (D), and hyperfine coupling (HFC) tensors, for the purpose of constructing paramagnetic nuclear magnetic resonance (pNMR) shielding tensors. The chemical shift and shielding anisotropy are calculated by applying a modern implementation of the classic Kurland-McGarvey theory ( J. Magn. Reson. 1970 , 2 , 286 ), which formulates the shielding tensor in terms of the g- and HFC tensors obtained for the ground multiplet, in the case of higher than doublet multiplicity defined by the ZFS interaction. The g- and ZFS tensors are calculated by ab initio complete active space self-consistent field and N-electron valence-state perturbation theory methods with spin-orbit (SO) effects treated via quasidegenerate perturbation theory. Results obtained with the scalar relativistic (SR) Douglas-Kroll-Hess Hamiltonian used for the g- and ZFS tensor calculations are compared with nonrelativistically based computations. The HFC tensors computed using the fully relativistic four-component matrix Dirac-Kohn-Sham approach are contrasted against perturbationally SO-corrected nonrelativistic results in the density functional theory framework. These approximations are applied on paramagnetic metallocenes (MCp2) (M = Ni, Cr, V, Mn, Co, Rh, Ir), a Co(II) pyrazolylborate complex, and a Cr(III) complex. SR effects are found to be small for g and D in these systems. The HFCs are found to be more influenced by relativistic effects for the 3d systems. However, for some of the 3d complexes, nonrelativistic calculations give a reasonable agreement with the experimental chemical shift and shielding anisotropy. The influence of scalar relativity is strong for the 5d IrCp2 system. This mixed ab initio/DFT technique, with a fully relativistic method used for the critical HFC tensor, should be useful for the treatment of both electron correlation and relativistic effects at a reasonable computational cost to compute the pNMR shielding tensors in transition metal systems.

Facing the challenge of predicting the standard formation enthalpies of n-butyl-phosphate species with ab initio methods.

Tributyl-phosphate (TBP), a ligand used in the PUREX liquid-liquid separation process of spent nuclear fuel, can form an explosive mixture in contact with nitric acid that might lead to a violent explosive thermal runaway. In the context of safety of a nuclear reprocessing plant facility, it is crucial to predict the stability of TBP at elevated temperatures. So far, only the enthalpies of formation of TBP are available in the literature with rather large uncertainties, while those of its degradation products, di-(HDBP) and mono-(H2MBP), are unknown. In this goal, we have used state-of-the art quantum chemical methods to compute the formation enthalpies and entropies of TBP and its degradation products di-(HDBP) and mono-(H2MBP) in gas and liquid phases. Comparisons of levels of quantum chemical theory revealed that there are significant effects of correlation on their electronic structures, pushing for the need of not only high level of electronic correlation treatment, namely, local coupled cluster with single and double excitation operators and perturbative treatment of triple excitations, but also extrapolations to the complete basis to produce reliable and accurate thermodynamics data. Solvation enthalpies were computed with the conductor-like screening model for real solvents [COSMO-RS], for which we observe errors not exceeding 22 kJ mol-1. We thus propose with final uncertainty of about 20 kJ mol-1 standard enthalpies of formation of TBP, HDBP, and H2MBP which amounts to -1281.7 ± 24.4, -1229.4 ± 19.6, and -1176.7 ± 14.8 kJ mol-1, respectively, in the gas phase. In the liquid phase, the predicted values are -1367.3 ± 24.4, -1348.7 ± 19.6, and -1323.8± 14.8 kJ mol-1, to which we may add about -22 kJ mol-1 error from the COSMO-RS solvent model. From these data, the complete hydrolysis of TBP is predicted as an exothermic phenomena but showing a slightly endergonic process.

Local Electron Correlation Treatment in Extended Multireference Calculations: Effect of Acceptor-Donor Substituents on the Biradical Character of the Polycyclic Aromatic Hydrocarbon Heptazethrene.

The implementation of a local correlation (LC) treatment of multireference (MR) configuration interaction approaches within the COLUMBUS program system is reported. The LC treatment is based on the weak pairs approximation of Sæbø and Pulay (Ann. Rev. Phys. Chem. 1993, 44, 213) and a geometrical analysis of Walter et al. (Chem. Phys. Lett. 2001, 346, 177). The removal of simultaneous single excitations out of the weak pairs is based on the reference doubly occupied space only, leading to a straightforward program implementation and a conceptual simplicity in terms of well-defined localized orbitals. Reductions of up to an order of magnitude in the configuration space expansion and in computer time for the Davidson diagonalization step are found. The selection of the active and the virtual orbital spaces is not affected by this procedure. This treatment is successfully applied to the singlet biradical heptazethrene and its different acceptor-donor substituents: 4,12-dicyanoheptazethrene, 4,12-diaminoheptazethrene, and 4-amino-12-cyanoheptazethrene. Simultaneous insertion of pairs of donor and acceptor groups increases the biradical character; for push-pull substitution, this effect is significantly smaller. In addition, results obtained from spin-corrected unrestricted density functional theory calculations are supported by our MR calculations.

Localization of open-shell molecular orbitals via least change from fragments to molecule.

Both top-down and bottom-up localization schemes are proposed for constructing localized molecular orbitals (LMOs) of open-shell systems, via least change from fragments to molecule. The success of both schemes stems from (1) the primitive fragment LMOs that are local not only in space but also in energy and (2) the "conquer step" that allows arbitrary assignment of the unpaired electrons to fragments. Moreover, integral occupations are retained, so as to facilitate subsequent treatment of electron correlation and excitation.

Enhanced effect of CP -violating nuclear magnetic quadrupole moment in a HfF+ molecule

The ${\mathrm{HfF}}^{+}$ cation is a very promising system to use in the search for the electron electric dipole moment (EDM), and a corresponding experiment is carried out by JILA group [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science 342, 1220 (2013); K.-K. Ni, H. Loh, M. Grau, K. C. Cossel, J. Ye, and E. A. Cornell, J. Mol. Spectrosc. 300, 12 (2014). Here we theoretically investigate the cation to search for another effect which violates time-reversal ($T$) and spatial parity ($P$) symmetries---the nuclear magnetic quadrupole moment (MQM) interaction with electrons. We report an accurate ab initio relativistic electronic structure calculations of the molecular parameter ${W}_{M}=0.494 \frac{{10}^{33}\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}}{e\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}}$ that is required to interpret the experimental data in terms of the MQM of the Hf nucleus. For this we have implemented and applied the combined Dirac-Coulomb(-Gaunt) and relativistic effective core potential approaches to treat electron correlation effects from all of the electrons and to take into account high-order correlation effects using the coupled cluster method with single, double, triple and noniterative quadruple cluster amplitudes. We discuss interpretation of the MQM effect in terms of the strength constants of $T,P$-odd nuclear forces, proton and neutron EDMs, the QCD parameter $\ensuremath{\theta}$, and quark chromo-EDMs.

Quantifying the delocalization of surface and bulk F-centers

Electrons trapped in ionic crystal defects form color centers (F-centers) important in surface science, catalysis, and optoelectronic devices. We apply the electron delocalization range function (EDR) to quantify the delocalization of surface and bulk F-centers. The EDR uses computed one-particle density matrices to quantify “delocalization lengths” capturing the characteristic size of orbital lobes. Ab initio cluster model calculations confirm that the delocalization lengths of bulk alkali halide F-centers scale with the size of the anion vacancy. Calculations on magnesium oxide surface Fs and Fs+ centers, as well as other anionic surface defects, show how the trapped electrons' delocalization depends on the defect morphology, defect occupancy, and the approximate treatment of electron correlation. Application to N2 activation by anionic surface defects illustrate how the trapped electron localizes into the adsorbed molecule's unoccupied orbitals. The results confirm that the EDR provides a useful tool for understanding the chemistry of surface- and bulk-trapped electrons.

Ab initio Study of Anharmonic Force Field and Spectroscopic Constants for Germanium Dichloride

Ab initio study of the equilibrium structure, spectroscopy constants, and anharmonic force field for several isotopomers of germanium dichloride (70GeCl2, 72GeCl2, and 76GeCl2) have been carried out at the MP2 and CCSD(T) levels of theory using cc-pVTZ basis set. The calculated geometries, rotational constants, vibration-rotation interaction constants, harmonic frequencies, anharmonic constants, quartic and sextic centrifugal distortion constants, cubic and quartic force constants are compared with experimental data. For small mass differences of the Ge isotopes, the isotopic effects for germanium dichloride are much weaker. The agreements are satisfactory for these two methods, but the deviations of CCSD(T) results are slightly larger than that of MP2, because of CCSD(T)'s inadequate treatment of electron correlation in hypervalent Cl atom.

Beyond Kohn-Sham Approximation: Hybrid Multistate Wave Function and Density Functional Theory.

A multistate density functional theory (MSDFT) is presented in which the energies and densities for the ground and excited states are treated on the same footing using multiconfigurational approaches. The method can be applied to systems with strong correlation and to correctly describe the dimensionality of the conical intersections between strongly coupled dissociative potential energy surfaces. A dynamic-then-static framework for treating electron correlation is developed to first incorporate dynamic correlation into contracted state functions through block-localized Kohn-Sham density functional theory (KSDFT), followed by diagonalization of the effective Hamiltonian to include static correlation. MSDFT can be regarded as a hybrid of wave function and density functional theory. The method is built on and makes use of the current approximate density functional developed in KSDFT, yet it retains its computational efficiency to treat strongly correlated systems that are problematic for KSDFT but too large for accurate WFT. The results presented in this work show that MSDFT can be applied to photochemical processes involving conical intersections.

Spin-Adapted Formulation and Implementation of Density Cumulant Functional Theory with Density-Fitting Approximation: Application to Transition Metal Compounds.

Density cumulant functional theory (DCT) has recently emerged as an attractive ab initio approach for the treatment of electron correlation. In its orbital-optimized formulation (ODC-12) [J. Chem. Phys. 139, 204110 (2013)], DCT has been shown to provide reliable results for a variety of challenging chemical systems. Among the attractive properties of DCT are its size-consistency and size-extensivity, as well as the efficient computation of the molecular properties and analytic gradients. In this work, we present a new formulation and implementation of DCT that takes advantage of spin adaptation and the density-fitting approximation (DF-ODC-12). Our new spin-adapted DF-ODC-12 implementation is more efficient than the previous ODC-12 implementation with up to a ∼12-fold speed-up. We demonstrate the capabilities of DF-ODC-12 with a study of transition metal compounds, which require high levels of electron correlation treatment. For transition metal carbonyl complexes [Fe(CO)5, Cr(CO)6] and the ferrocene molecule [Fe(Cp)2], the DF-ODC-12 equilibrium parameters and bond dissociation energies extrapolated to the complete basis set limit are in very good agreement with reference data derived from experiment.

Bootstrap embedding: An internally consistent fragment-based method.

Strong correlation poses a difficult problem for electronic structure theory, with computational cost scaling quickly with system size. Fragment embedding is an attractive approach to this problem. By dividing a large complicated system into smaller manageable fragments "embedded" in an approximate description of the rest of the system, we can hope to ameliorate the steep cost of correlated calculations. While appealing, these methods often converge slowly with fragment size because of small errors at the boundary between fragment and bath. We describe a new electronic embedding method, dubbed "Bootstrap Embedding," a self-consistent wavefunction-in-wavefunction embedding theory that uses overlapping fragments to improve the description of fragment edges. We apply this method to the one dimensional Hubbard model and a translationally asymmetric variant, and find that it performs very well for energies and populations. We find Bootstrap Embedding converges rapidly with embedded fragment size, overcoming the surface-area-to-volume-ratio error typical of many embedding methods. We anticipate that this method may lead to a low-scaling, high accuracy treatment of electron correlation in large molecular systems.

Second hyperpolarizability of the calcium-doped lithium salt of pyridazine Li–H3C4N2 ⋯ Ca

In this work we report results of coupled cluster calculations for the second hyperpolarizability of the calcium-doped lithium salt of pyridazine (Li–H3C4N2⋯Ca) molecule. In the static limit an unusual value of 4.34×106au was obtained at the CCSD level of calculation. Results obtained for the dc-Kerr effect through SCF, CCS and CCSD methods show that γ(-ω;ω,0,0) is strongly dependent of the electron correlation treatment. Dynamic results obtained at the CCSD level are also reported for the IDRI, dc-SHG and THG nonlinear optical processes.

Beyond Time-Dependent Density Functional Theory Using Only Single Excitations: Methods for Computational Studies of Excited States in Complex Systems.

Single-excitation methods, namely, configuration interaction singles and time-dependent density functional theory (TDDFT), along with semiempirical versions thereof, represent the most computationally affordable electronic structure methods for describing electronically excited states, scaling as [Formula: see text] absent further approximations. This relatively low cost, combined with a treatment of electron correlation, has made TDDFT the most widely used excited-state quantum chemistry method over the past 20+ years. Nevertheless, certain inherent problems (beyond just the accuracy of this or that exchange-correlation functional) limit the utility of traditional TDDFT. For one, it affords potential energy surfaces whose topology is incorrect in the vicinity of any conical intersection (CI) that involves the ground state. Since CIs are the conduits for transitions between electronic states, the TDDFT description of photochemistry (internal conversion and intersystem crossing) is therefore suspect. Second, the [Formula: see text] cost can become prohibitive in large systems, especially those that involve multiple electronically coupled chromophores, for example, the antennae structures of light-harvesting complexes or the conjugated polymers used in organic photovoltaics. In such cases, the smallest realistic mimics might already be quite large from the standpoint of ab initio quantum chemistry. This Account describes several new computational methods that address these problems. Topology around a CI can be rigorously corrected using a "spin-flip" version of TDDFT, which involves an α → β spin-flipping transition in addition to occupied → virtual excitation of one electron. Within this formalism, singlet states are generated via excitation from a high-spin triplet reference state, doublets from a quartet, etc. This provides a more balanced treatment of electron correlation between ground and excited states. Spin contamination is problematic away from the Franck-Condon region, but we describe a "spin-complete" version of the theory in which proper spin eigenstates are obtained by construction. For systems of coupled chromophores, we have developed an ab initio version of the Frenkel-Davydov exciton model in which collective excitations of the system are expanded in a basis of excited states computed for individual chromophores. The monomer calculations are trivially parallelizable, as is computation of the coupling matrix elements needed to construct the exciton Hamiltonian, and systems containing hundreds of chromophores can be tackled on commodity hardware. This enables calculations on organic semiconductors, where even small model systems exhibit a semicontinuum of excited states that renders traditional TDDFT computationally challenging. Despite including only single excitations on each monomer, the exciton model can describe entangled spins on two or more monomers, an effect that is responsible for excitation energy transfer between chromophores, for example, in singlet fission. Excitonic approximations can also be applied to the TDDFT equations themselves, and a particularly promising application is to describe the effects of environment on an excitation that is localized on a single chromophore. This "local excitation approximation" to TDDFT allows an essentially arbitrary number of solvent molecules to be included in the calculation in a highly parallelizable way such that the time-to-solution increases only very slowly as additional solvent molecules are added. It is therefore possible to converge the calculation with respect to describing an ever-larger portion of the environment at a quantum-mechanical level.

Rh chemistry through the eyes of theory

We discuss the properties of Rh and its compounds from a theoretical chemistry perspective. Like its neighbors in the platinum metal group, this element exhibits a remarkable spectrum of catalytic activity both as an elemental metal and as the central ion of transition metal complexes. This property is reflected in a comparatively weak chemical bond dominated by d–p interactions, varying oxidation states and a highly flexible coordination shell. In turn, theoretical methods and their generalization as empirical concepts have to be able to deal with a multitude of binding situations and the strong electron–electron interaction within the Rh valence orbitals. Whereas density functional theory has greatly enhanced the computational accessibility of Rh compounds, quantitative models of catalytic cycles require a more explicit treatment of static electron correlation, such as integrated density functional‐coupled cluster schemes. WIREs Comput Mol Sci 2016, 6:311–320. doi: 10.1002/wcms.1250This article is categorized under: Structure and Mechanism > Molecular Structures Structure and Mechanism > Reaction Mechanisms and Catalysis

The Role of Spin-Orbit Coupling in the Double-Ionization Photoelectron Spectra of XCN(2+) (X = Cl, Br, and I).

The photoelectron spectra of XCN(2+) (X = Cl, Br, and I) were calculated employing ab initio electronic structure methods with high-level electron correlation and explicit treatment of spin-orbit coupling. Twelve scalar-relativistic excited states of the dicationic systems, calculated from state-averaged CASSCF/MRCI calculations, were used as the electronic basis to evaluate spin-orbit eigenstates. While the spin-orbit effects in ClCN(2+) are found to be negligible, the electronic spectroscopy of BrCN(2+) and ICN(2+) is significantly influenced by interstate spin-orbit coupling. Several electronic degeneracies are lifted, and many unexpected accidental degeneracies occurred due to the spin-orbit coupling. In particular, the spin-orbit interactions between X̃ (3)Σ(-)-b̃ (1)Σ(+), Ã (3)Π-c̃ (1)Π, B̃ (3)Δ-ã (1)Δ, and C̃ (3)Σ(+)-d̃ (1)Σ(-) are found to be strong in BrCN(2+) and ICN(2+). By careful analysis of the effect of spin-orbit coupling parameters and the spin-orbit eigenstate composition, an assignment of the hitherto unidentified experimental photoelectron bands of BrCN(2+) and ICN(2+) is presented.

CCSD(T)/CBS fragment-based calculations of lattice energy of molecular crystals.

A comparative study of the lattice energy calculations for a data set of 25 molecular crystals is performed using an additive scheme based on the individual energies of up to four-body interactions calculated using the coupled clusters with iterative treatment of single and double excitations and perturbative triples correction (CCSD(T)) with an estimated complete basis set (CBS) description. The CCSD(T)/CBS values on lattice energies are used to estimate sublimation enthalpies which are compared with critically assessed and thermodynamically consistent experimental values. The average absolute percentage deviation of calculated sublimation enthalpies from experimental values amounts to 13% (corresponding to 4.8 kJ mol(-1) on absolute scale) with unbiased distribution of positive to negative deviations. As pair interaction energies present a dominant contribution to the lattice energy and CCSD(T)/CBS calculations still remain computationally costly, benchmark calculations of pair interaction energies defined by crystal parameters involving 17 levels of theory, including recently developed methods with local and explicit treatment of electronic correlation, such as LCC and LCC-F12, are also presented. Locally and explicitly correlated methods are found to be computationally effective and reliable methods enabling the application of fragment-based methods for larger systems.

Screened moments and absence of ferromagnetism in FeAl

While the stoichiometric intermetallic compound FeAl is found to be paramagnetic in experiment, standard band-theory approaches predict the material to be ferromagnetic. We show that this discrepancy can be overcome by a better treatment of electronic correlations with density functional plus dynamical mean field theory. Our results show no ferromagnetism down to 100 K and since the susceptibility is decreasing at the lowest temperatures studied we also do not expect ferromagnetism at even lower temperatures. This behavior is found to originate from temporal quantum fluctuations that screen short-lived local magnetic moments of 1.6 $\mu_B$ on Fe.

Insight into organic reactions from the direct random phase approximation and its corrections.

The performance of the random phase approximation (RPA) and beyond-RPA approximations for the treatment of electron correlation is benchmarked on three different molecular test sets. The test sets are chosen to represent three typical sources of error which can contribute to the failure of most density functional approximations in chemical reactions. The first test set (atomization and n-homodesmotic reactions) offers a gradually increasing balance of error from the chemical environment. The second test set (Diels-Alder reaction cycloaddition = DARC) reflects more the effect of weak dispersion interactions in chemical reactions. Finally, the third test set (self-interaction error 11 = SIE11) represents reactions which are exposed to noticeable self-interaction errors. This work seeks to answer whether any one of the many-body approximations considered here successfully addresses all these challenges.

An energy decomposition analysis for second-order Møller-Plesset perturbation theory based on absolutely localized molecular orbitals.

An energy decomposition analysis (EDA) of intermolecular interactions is proposed for second-order Møller-Plesset perturbation theory (MP2) based on absolutely localized molecular orbitals (ALMOs), as an extension to a previous ALMO-based EDA for self-consistent field methods. It decomposes the canonical MP2 binding energy by dividing the double excitations that contribute to the MP2 wave function into classes based on how the excitations involve different molecules. The MP2 contribution to the binding energy is decomposed into four components: frozen interaction, polarization, charge transfer, and dispersion. Charge transfer is defined by excitations that change the number of electrons on a molecule, dispersion by intermolecular excitations that do not transfer charge, and polarization and frozen interactions by intra-molecular excitations. The final two are separated by evaluations of the frozen, isolated wave functions in the presence of the other molecules, with adjustments for orbital response. Unlike previous EDAs for electron correlation methods, this one includes components for the electrostatics, which is vital as adjustment to the electrostatic behavior of the system is in some cases the dominant effect of the treatment of electron correlation. The proposed EDA is then applied to a variety of different systems to demonstrate that all proposed components behave correctly. This includes systems with one molecule and an external electric perturbation to test the separation between polarization and frozen interactions and various bimolecular systems in the equilibrium range and beyond to test the rest of the EDA. We find that it performs well on these tests. We then apply the EDA to a halogen bonded system to investigate the nature of the halogen bond.

Efficient and accurate treatment of electron correlations with Correlation Matrix Renormalization theory.

We present an efficient method for calculating the electronic structure and total energy of strongly correlated electron systems. The method extends the traditional Gutzwiller approximation for one-particle operators to the evaluation of the expectation values of two particle operators in the many-electron Hamiltonian. The method is free of adjustable Coulomb parameters, and has no double counting issues in the calculation of total energy, and has the correct atomic limit. We demonstrate that the method describes well the bonding and dissociation behaviors of the hydrogen and nitrogen clusters, as well as the ammonia composed of hydrogen and nitrogen atoms. We also show that the method can satisfactorily tackle great challenging problems faced by the density functional theory recently discussed in the literature. The computational workload of our method is similar to the Hartree-Fock approach while the results are comparable to high-level quantum chemistry calculations.