Recent Advances in Wave Function-Based Methods of Molecular-Property Calculations

NMR crystallography of molecular organics

Developments of NMR methodology to characterise the structures of molecular organic structures are reviewed, concentrating on the previous decade of research in which density functional theory-based calculations of NMR parameters in periodic solids have become widespread. With a focus on demonstrating the new structural insights provided, it is shown how "NMR crystallography" has been used in a spectrum of applications from resolving ambiguities in diffraction-derived structures (such as hydrogen atom positioning) to deriving complete structures in the absence of diffraction data. As well as comprehensively reviewing applications, the different aspects of the experimental and computational techniques used in NMR crystallography are surveyed. NMR crystallography is seen to be a rapidly maturing subject area that is increasingly appreciated by the wider crystallographic community.

eT 1.0: An open source electronic structure program with emphasis on coupled cluster and multilevel methods

The e^T program is an open source electronic structure package with emphasis on coupled cluster and multilevel methods. It includes efficient spin adapted implementations of ground and excited singlet states, as well as equation of motion oscillator strengths, for CCS, CC2, CCSD, and CC3. Furthermore, e^T provides unique capabilities such as multilevel Hartree-Fock and multilevel CC2, real-time propagation for CCS and CCSD, and efficient CC3 oscillator strengths. With a coupled cluster code based on an efficient Cholesky decomposition algorithm for the electronic repulsion integrals, e^T has similar advantages as codes using density fitting, but with strict error control. Here, we present the main features of the program and demonstrate its performance through example calculations. Because of its availability, performance, and unique capabilities, we expect e^T to become a valuable resource to the electronic structure community.

Computation of Electromagnetic Properties of Molecular Ensembles

We outline a methodology for efficiently computing the electromagnetic response of molecular ensembles. The methodology is based on the link that we establish between quantum‐chemical simulations and the transfer matrix (T‐matrix) approach, a common tool in physics and engineering. We exemplify and analyze the accuracy of the methodology by using the time‐dependent Hartree‐Fock theory simulation data of a single chiral molecule to compute the T‐matrix of a cross‐like arrangement of four copies of the molecule, and then computing the circular dichroism of the cross. The results are in very good agreement with full quantum‐mechanical calculations on the cross. Importantly, the choice of computing circular dichroism is arbitrary: Any kind of electromagnetic response of an object can be computed from its T‐matrix. We also show, by means of another example, how the methodology can be used to predict experimental measurements on a molecular material of macroscopic dimensions. This is possible because, once the T‐matrices of the individual components of an ensemble are known, the electromagnetic response of the ensemble can be efficiently computed. This holds for arbitrary arrangements of a large number of molecules, as well as for periodic or aperiodic molecular arrays. We identify areas of research for further improving the accuracy of the method, as well as new fundamental and technological research avenues based on the use of the T‐matrices of molecules and molecular ensembles for quantifying their degrees of symmetry breaking. We provide T‐matrix‐based formulas for computing traditional chiro‐optical properties like (oriented) circular dichroism, and also for quantifying electromagnetic duality and electromagnetic chirality. The formulas are valid for light‐matter interactions of arbitrarily‐high multipolar orders.

Performance of the LRESC Model on top of DFT Functionals for Relativistic NMR Shielding Calculations

The linear response within the elimination of the small component model (LRESC) is an insightful and computationally efficient method for including relativistic effects on molecular properties like the nuclear magnetic shielding constants, spin-rotation constant, g-tensor, and electric field gradient of heavy atom containing molecules with atoms belonging up to the sixth row of the periodic table. One of its main advantages is its capacity to analyze the electronic origin of the different relativistic correcting terms. Until now, it was always applied on top of Hartree-Fock ground-state wave functions (LRESC/HF) to calculate and analyze NMR shieldings. In this work, we show the performance of the LRESC formalism on top of some density functional theory (DFT) functionals to compute tin shielding constants in SnX₄ (X = H, F, Cl, Br, I) molecular systems. We analyze the performance of each LRESC/DFT scheme on reproducing the electronic mechanisms of the shieldings, taking as a benchmark the results of relativistic calculations at the RPA level of approach (4c/RPA). As in previous works, we divide the LRESC relativistic correcting terms into two groups: core-dependent and ligand-dependent contributions. It is shown here that core-dependent corrections are well-reproduced for the selected DFT functionals, but some differences arise in the ligand-dependent ones. We focus on the performance of different functionals, including the same electron correlation part but containing different amounts of HF exchange. The best results are obtained for the BHandHLYP functional (50% of HF exchange) and the worst for BLYP (0%). When the percentage of HF exchange increases, ligand-dependent contributions are better described, and the final LRESC/DFT results are closer to those obtained with LRESC/HF and 4c/RPA methods. The spin-orbit correction to the shielding constant is one of the main ligand-dependent contributions (there are two more) with total value depending on the amount of HF exchange included in the functional. When the amount of HF exchange decreases, the spin-orbit contribution becomes larger, overestimating the shielding constant even when nonrelativisitc DFT values are much smaller than the nonrelativistic HF ones, as it happens for the heaviest molecular system studied here (SnI₄).

Calculation of Diamagnetic Susceptibility Tensors of Organic Crystals: From Coronene to Pharmaceutical Polymorphs

Understanding why crystallization in strong magnetic fields can lead to new polymorphs requires methods to calculate the diamagnetic response of organic molecular crystals. We develop the calculation of the macroscopic diamagnetic susceptibility tensor, χ^cryst, for organic molecular crystals using periodic density functional methods. The crystal magnetic susceptibility tensor, χ^cryst, for all experimentally known polymorphs, and its molecular counterpart, χ^mol, are calculated for flexible pharmaceuticals such as carbamazepine, flufenamic acid, and chalcones, and rigid molecules, such as benzene, pyridine, acridine, anthracene, and coronene, whose molecular magnetic properties have been traditionally studied. A tensor addition method is developed to approximate the crystal diamagnetic susceptibility tensor, χ^cryst, from the molecular one, χ^mol, giving good agreement with those calculated directly using the more costly periodic density functional method for χ^cryst. The response of pharmaceutical molecules and crystals to magnetic fields, as embodied by χ^cryst, is largely determined by the packing in the crystal, as well as the molecular conformation. The anisotropy of χ^cryst can vary considerably between polymorphs though the isotropic terms are fairly constant. The implications for developing a computational method for predicting whether crystallization in a magnetic field could produce a novel or different polymorph are discussed.

Force Based Canonical Approximation of Molecular Potentials: Average Force versus Pointwise Force

This work presents a new force-based canonical approach that utilizes the average force rather than the pointwise force, on which previously developed canonical approaches were based. Advantageously, the average force based method only requires the evaluation of the potential function and not its derivative. The average force and the pointwise force based methods are applied to a variety of diatomic molecules, and their accuracy is compared. It is demonstrated that the average force based method gives an improved accuracy compared to the pointwise force based method. This improved accuracy is attributed to the fact that the average force based method eliminates the need to use the numerical approximation of the derivative of the potential function that, in practice, is only known at discrete points. In addition, an algorithm is developed to apply the average force based method as a practical tool for generating potential curves for pairwise interatomic interactions utilizing the classical Lennard-Jones potential as reference. Moreover, application of the average force based method leads to a new canonical approximation paradigm. In this new paradigm, only the coordinates of the equilibrium configuration (the bottom of the potential well) of a molecule are required for accurate generation of the potential function. Moreover, theoretical results are presented, demonstrating the effectiveness of the canonical transformation procedure in producing highly accurate potential approximations. In particular, it is proved that a certain general set of qualitative conditions on potential-like functions are sufficient for a given potential function to be in the same canonical transformation class as a (dimensionless) Lennard-Jones potential. For functions satisfying these assumptions, it is shown that they have canonical approximations with arbitrarily small approximation errors.

Dyson orbitals within the fc-CVS-EOM-CCSD framework: theory and application to X-ray photoelectron spectroscopy of ground and excited states

Ionization energies and Dyson orbitals within frozen-core core–valence separated equation-of-motion coupled cluster singles and doubles (fc-CVS-EOM-CCSD) enable efficient and reliable calculations of standard XPS and of UV-pump/XPS probe spectra.

DFT computational schemes for 1 H and 13 C NMR chemical shifts of natural products, exemplified by strychnine

A number of computational schemes based on different Density Functional Theory (DFT) functionals in combination with a number of basis sets were tested in the calculation of ¹ H and ¹³ C NMR chemical shifts of strychnine, as a typical representative of the vitally important natural products, and used as a challenging benchmark and a rigorous test for such calculations. It was found that the most accurate computational scheme, as compared with experiment, was PBE0/pcSseg-4//pcseg-3 characterized by a mean absolute error of 0.07 ppm for the range of about 7 ppm for ¹ H NMR chemical shifts and that of only 1.13 ppm for ¹³ C NMR chemical shifts spread over the range of about 150 ppm. For more practical purposes, including investigation of larger molecules from this series, a much more economical computational scheme, PBE0/pcSseg-2//pcseg-2, characterized by almost the same accuracy and much less computational demand, was recommended.

Computational 1 H NMR: Part 3. Biochemical studies

This is the third and the last part of three closely interrelated reviews dealing with computation of ¹ H nuclear magnetic resonance chemical shifts and ¹ H-¹ H spin-spin coupling constants. Present review deals with the computation of these parameters in biologically active natural products, carbohydrates, and other molecules of biological origin focusing on stereochemical applications of computational ¹ H nuclear magnetic resonance to these objects.

Spin-flip methods in quantum chemistry

This Perspective discusses salient features of the spin-flip approach to strong correlation and describes different methods that sprung from this idea. The spin-flip treatment exploits the different physics of low-spin and high-spin states and is based on the observation that correlation is small for same-spin electrons. By using a well-behaved high-spin state as a reference, one can access problematic low-spin states by deploying the same formal tools as in the excited-state treatments (i.e., linear response, propagator, or equation-of-motion theories). The Perspective reviews applications of this strategy within wave function and density functional theory frameworks as well as the extensions for molecular properties and spectroscopy. The utility of spin-flip methods is illustrated by examples. Limitations and proposed future directions are also discussed.

How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core–valence separation

We present a novel approach with robust convergence of the response equations for computing resonant inelastic X-ray scattering (RIXS) cross sections within the equation-of-motion coupled-cluster (EOM-CC) framework.

Computational 1 H NMR: Part 2. Chemical applications

This is the second one of three closely interrelated reviews dealing with computation of ¹ H NMR chemical shifts and ¹ H-¹ H spin-spin coupling constants prepared for Magnetic Resonance in Chemistry. Presented in this review are some basic notes and illustrative examples of how modern computational ¹ H NMR could be used for structural elucidation and stereoelectronic studies of the medium-sized organic molecules involving saturated, unsaturated, aromatic, and heteroaromatic compounds together with their functional derivatives and coordination complexes to get deeper insight into their stereochemical structure and stereodynamic behavior.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. I. Formalism

Analytic gradients of electronic eigenvalues require one calculation per nuclear geometry, compared to at least 3n + 1 calculations for finite difference methods, where n is the number of nuclei. Analytic nonadiabatic derivative coupling terms (DCTs), which are calculated in a similar fashion, are used to remove nondiagonal contributions to the kinetic energy operator, leading to more accurate nuclear dynamics calculations than those that employ the Born-Oppenheimer approximation, i.e., that assume off-diagonal contributions are zero. The current methods and underpinnings for calculating both of these quantities, gradients and DCTs, for the State-Averaged MultiReference Configuration Interaction with Singles and Doubles (MRCI-SD) wavefunctions in COLUMBUS are reviewed. Before this work, these methods were not available for wavefunctions of a relativistic MRCI-SD Hamiltonian. Calculation of these terms is critical in successfully modeling the dynamics of systems that depend on transitions between potential energy surfaces split by the spin-orbit operator, such as diode-pumped alkali lasers. A formalism for calculating the transition density matrices and analytic derivative coupling terms for such systems is presented.

Computational Ag/AgCl Reference Electrode from Density Functional Theory-Based Molecular Dynamics

We have developed a scheme to compute the standard potential of the Ag/AgCl reference electrode using density functional theory-based molecular dynamics, similar to the computational standard hydrogen electrode (SHE) developed by Cheng, Sulpizi, and Sprik [J. Chem. Phys. 2009, 131, 154504], with which our new computational reference electrode was compared. We have obtained a similar value of the potential of the Ag/AgCl electrode versus SHE to the experiment. The newly developed computational reference electrode will be extended to nonaqueous solvents in the future, where it will be used to predict standard equilibrium potentials to be compared with experimental data.

Electronic transitions for a fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles: Linear and corrected linear response regimes

The fully polarizable Quantum Mechanics/Molecular Mechanics (QM/MM) approach based on fluctuating charges and fluctuating dipoles, named QM/FQFμ [T. Giovannini et al., J. Chem. Theory Comput. 15, 2233 (2019)], is extended to the calculation of vertical excitation energies of solvated molecular systems. Excitation energies are defined within two different solvation regimes, i.e., linear response (LR), where the response of the MM portion is adjusted to the QM transition density, and corrected-Linear Response (cLR) in which the MM response is adjusted to the relaxed QM density, thus being able to account for charge equilibration in the excited state. The model, which is specified in terms of three physical parameters (electronegativity, chemical hardness, and polarizability) is applied to vacuo-to-water solvatochromic shifts of aqueous solutions of para-nitroaniline, pyridine, and pyrimidine. The results show a good agreement with their experimental counterparts, thus highlighting the potentialities of this approach.

Probing basis set requirements for calculating hyperfine coupling constants

A series of basis sets optimized for the calculation of the hyperfine coupling constant is proposed. The pcH-n basis sets are defined in qualities from double-ζ to pentuple-ζ for the elements H to Ar. They are derived from the polarization consistent basis sets by addition of two tight s-functions and one tight p-, d-, and f-function and are shown to provide an exponential convergence toward the complete basis set limit, and they have significantly lower basis set errors than other commonly used basis sets for a given ζ quality. The pcH basis sets display very similar basis set convergence with a range of density functional theory methods and may also be suitable for wave function based methods.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

Computational 1 H NMR: Part 1. Theoretical background

This is the first one of the three closely interrelated reviews to be published in Magnetic Resonance in Chemistry dealing with accordingly theoretical background, chemical applications, and biochemical studies of and by means of computational ¹ H NMR. Presented in the first part of the review is a general outline of the modern theoretical methods and accuracy factors of computational ¹ H NMR involving locally dense basis set schemes, solvent effects, vibrational corrections, and relativistic effects performed at the density functional theory and/or nonempirical levels. This review is dedicated to Prof. Stephan Sauer in view of his invaluable contribution to the field of computational nuclear magnetic resonance.

Analytic first-order derivatives of partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2)

A balanced treatment of dynamic and static electron correlation is important in computational chemistry, and multireference perturbation theory (MRPT) is able to do this at a reasonable computational cost. In this paper, analytic first-order derivatives, specifically gradients and dipole moments, are developed for a particular MRPT method, state-specific partially contracted n-electron valence state second-order perturbation theory (PC-NEVPT2). Only one linear equation needs to be solved for the derivative calculation if the Z-vector method is employed, which facilitates the practical application of this approach. A comparison of the calculated results with experimental geometrical parameters of O₃ indicates excellent agreement although the calculated results for O₃ ^- are slightly outside the experimental error bars. The 0-0 transition energies of various methylpyrimidines and trans-polyacetylene are calculated by performing geometry optimizations and seminumerical second-order geometrical derivative calculations. In particular, the deviations of 0-0 transition energies of trans-polyacetylene from experimental values are consistently less than 0.1 eV with PC-NEVPT2, indicating the reliability of the method. These results demonstrate the importance of adding dynamic electron correlation on top of methods dominated by static electron correlation and of developing analytic derivatives for highly accurate methods.

RPA(D) and HRPA(D): Two new models for calculations of NMR indirect nuclear spin-spin coupling constants

In this article, the RPA(D) and HRPA(D) models for the calculation of linear response functions are presented. The performance of the new RPA(D) and HRPA(D) models is compared to the performance of the established RPA, HRPA, and SOPPA models in calculations of indirect nuclear spin-spin coupling constants using the CCSD model as a reference. The doubles correction offers a significant improvement on both the RPA and HRPA models; however, the improvement is more dramatic in the case of the RPA model. For all coupling types investigated in this study, the results obtained using the HRPA(D) model are comparable in accuracy to those given by the SOPPA model, while requiring between 30% and 90% of the calculation time needed for SOPPA. The RPA(D) model, while of slightly lower accuracy compared to the CCSD model than HRPA(D), offered calculation times of only approximately 25% of those required for SOPPA for all the investigated molecules. © 2018 Wiley Periodicals, Inc.

DFT and spatial confinement: a benchmark study on the structural and electrical properties of hydrogen bonded complexes

An extended set of 37 exchange correlation functionals, representing different DFT approximations, has been evaluated on a difficult playground represented by the dipole moment (μ_z), polarizability (α_zz), first hyperpolarizability (β_zzz), and the corresponding interaction-induced electrical properties (Δμ_z, Δα_zz, Δβ_zzz) of spatially confined hydrogen bonded (HB) dimers. A two-dimensional harmonic oscillator potential was used to exert the effect of spatial restriction. The performance of DFT methods in predicting hydrogen bond lengths in the studied molecular complexes upon confinement has also been examined. The data determined using a high-level CCSD(T) method serve as a reference. The conducted analyses allow us to conclude that methods rooted in DFT constitute a precise tool for the calculation of μ_z and α_zz as well as Δμ_z and Δα_zz, as most of the tested functionals provide results affected by rather small relative errors. On the other hand, an accurate description of the nonlinear optical response of the studied HB systems remains a great challenge for most of the analyzed DFT functionals, both in vacuum and in the presence of an analytical confining potential. Some of the tested DFT methods are found to be prone to catastrophic failure in the prediction of β_zzz as well as Δβ_zzz. The obtained results indicate that there is no great chasm in performance between functionals belonging to different DFT approximations or functionals including different amount of Hartree-Fock exchange when the values of dipole moment and first hyperpolarizability as well as the corresponding interaction-induced electrical properties are considered. However, a higher fraction of Hartree-Fock exchange improves the quality of predictions of α_zz and Δα_zz. Additionally, it has been shown that only three functionals from the examined set, namely B2PLYP, B3LYP and ωB97X-D, provide highly accurate structural parameters for the investigated systems. Of significant importance is the conclusion that the ωB97X-D functional, representing a modern and highly parametrized range-separated hybrid, demonstrates the most coherent behavior, showing rather small deviations from the reference data in the case of μ_z, α_zz, Δμ_z and Δα_zz as well as the structural parameters of the studied HB dimers. Moreover, our results indicate that the presence of spatial confinement has a rather small effect on the performance of DFT methods.

Theoretical Assessment of the Second-Order Nonlinear Optical Responses of Lindqvist-Type Organoimido Polyoxometalates

The second-order nonlinear optical properties of Lindqvist-type organoimido polyoxometalates bearing donor and acceptor substituents are evaluated by employing density functional theory and time-dependent density functional theory using the ωB97X-D range-separated hybrid exchange-correlation functional to describe accurately the field-induced effects. The hyper-Rayleigh scattering responses, β_HRS (-2ω; ω, ω), and the depolarization ratio are the targeted quantities. They are analyzed by resorting to the two-state model, which reduces the full summation-over-state expression to a single diagonal term and relates the response to a few spectroscopic quantities. The validity of this model is demonstrated by its ability to reproduce the β_HRS variations as a function of the nature of the ligand, owing to the dominant 1D character of these organic-inorganic hybrids. The calculated values are in good agreement with the recent experimental work of Al-Yasari et al. (Inorg. Chem. 2017, 56, 10181-10194), which demonstrates that the hexamolybdate moiety plays the role of an electron acceptor group. On the contrary, they contradict previous studies, which attributed an electron donor character to the polyoxometalate moiety. Calculations highlight that (i) combining the hexamolybdate unit with an organic ligand bearing a strong donor substituent leads to an enhanced first hyperpolarizability, associated with a dominant low-energy excited state, characterized by a large excitation-induced electron transfer from the donating ligand to the hexamolybdate, therefore coupling the polyoxometalate (POM) and its substituted ligand; (ii) in the case of weaker donor substituents, the hexamolybdate still behaves as an electron acceptor, but the first hyperpolarizability is smaller and the coupling has a reduced spatial extension; and, on the contrary, (iii) in the presence of an acceptor substituent, there is a competition between the hexamolybdate and this group so that the first hyperpolarizability becomes very small. The whole set of results demonstrates that polyoxometalate moieties are good candidates to achieve large second-order nonlinear optical (NLO) responses while keeping a rather large transparency window and also that there remains space to improve their integration into NLO efficient organic-inorganic hybrids.

General framework for calculating spin-orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions

Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., M_s = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner-Eckart's theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin-orbit matrix elements by applying Wigner-Eckart's theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born-Oppenheimer's separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin-orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin-orbit treatment. Intrinsic issues of constructing spin-orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

Data-Driven Acceleration of the Coupled-Cluster Singles and Doubles Iterative Solver

Solving the coupled-cluster (CC) equations is a cost-prohibitive process that exhibits poor scaling with system size. These equations are solved by determining the set of amplitudes (t) that minimize the system energy with respect to the coupled-cluster equations at the selected level of truncation. Here, a novel approach to predict the converged coupled-cluster singles and doubles (CCSD) amplitudes, thus the coupled-cluster wave function, is explored by using machine learning and electronic structure properties inherent to the MP2 level. Features are collected from quantum chemical data, such as orbital energies, one-electron Hamiltonian, Coulomb, and exchange terms. The data-driven CCSD (DDCCSD) is not an alchemical method because the actual iterative coupled-cluster equations are solved. However, accurate energetics can also be obtained by bypassing solving the CC equations entirely. Our preliminary data show that it is possible to achieve remarkable speedups in solving the CCSD equations, especially when the correct physics are encoded and used for training of machine learning models.

DFT computational schemes for 15 N NMR chemical shifts of the condensed nitrogen-containing heterocycles

A systematic density functional theory (DFT) study of the accuracy factors (functionals, basis sets, and solvent effects) for the computation of ¹⁵ N NMR chemical shifts has been performed in the series of condensed nitrogen-containing heterocycles. The behavior of the most representative functionals was examined based on the benchmark calculations of ¹⁵ N NMR chemical shifts in the reference set of compounds. It was found that the best agreement with experiment was achieved with OLYP functional in combination with aug-pcS-3(N)//pc-2 locally dense basis set scheme providing mean absolute error of 5.2 ppm in the range of about 300 ppm. Taking into account solvent effects was performed within a general Tomasi's polarizable continuum model scheme. It was also found that computationally demanding supermolecular solvation model computations essentially improved some "difficult" cases, as was illustrated with phenanthroline dissolved in methanol. Based on the performed calculations, some 200 unknown ¹⁵ N NMR chemical shifts were predicted with a high level of confidence for about 50 real-life condensed nitrogen-containing heterocycles, which could serve as a practical guide in structural elucidation of this class of compounds.

Accurate Band Gap Predictions of Semiconductors in the Framework of the Similarity Transformed Equation of Motion Coupled Cluster Theory

In this work, we present a detailed comparison between wave-function-based and particle/hole techniques for the prediction of band gap energies of semiconductors. We focus on the comparison of the back-transformed Pair Natural Orbital Similarity Transformed Equation of Motion Coupled-Cluster (bt-PNO-STEOM-CCSD) method with Time Dependent Density Functional Theory (TD-DFT) and Delta Self Consistent Field/DFT (Δ-SCF/DFT) that are employed to calculate the band gap energies in a test set of organic and inorganic semiconductors. Throughout, we have used cluster models for the calculations that were calibrated by comparing the results of the cluster calculations to periodic DFT calculations with the same functional. These calibrations were run with cluster models of increasing size until the results agreed closely with the periodic calculation. It is demonstrated that bt-PNO-STEOM-CC yields accurate results that are in better than 0.2 eV agreement with the experiment. This holds for both organic and inorganic semiconductors. The efficiency of the employed computational protocols is thoroughly discussed. Overall, we believe that this study is an important contribution that can aid future developments and applications of excited state coupled cluster methods in the field of solid-state chemistry and heterogeneous catalysis.

In this work, it is shown that a combination of the embedded cluster approach with wave-function-based ab initio methods in the framework of the Similarity Transformed Equation of Motion Coupled Cluster (bt-PNO STEOM-CC) provides an accurate protocol for band gap energy predictions in classes of organic and inorganic semiconductors.

Computational protocols for calculating 13C NMR chemical shifts

The most recent results dealing with the computation of ¹³C NMR chemical shifts in chemistry (small molecules, saturated, unsaturated and aromatic compounds, heterocycles, functional derivatives, coordination complexes, carbocations, and natural products) are reviewed, paying special attention to theoretical background and accuracy, the latter involving solvent effects, vibrational corrections, and relativistic effects.

CASSCF linear response calculations for large open-shell molecules

The complete active space self-consistent-field (CASSCF) linear response method for the simulation of ultraviolet-visible (UV/Vis) absorption and electronic circular dichroism (ECD) spectra of large open-shell molecules is presented. By using a one-index transformed Hamiltonian, the computation of the most time-consuming intermediates can be pursued in an integral-direct fashion, which allows us to employ the efficient resolution-of-the-identity and overlap-fitted chain-of-spheres approximation. For the iterative diagonalization, pairs of Hermitian and anti-Hermitian trial vectors are used which facilitate, on the one hand, an efficient solution of the pair-structured generalized eigenvalue problem in the reduced space, and on the other hand, make the full multiconfigurational random phase approximation as efficient as the corresponding Tamm-Dancoff approximation. Electronic transitions are analyzed and characterized in the particle-hole picture by natural transition orbitals that are introduced for CASSCF linear response theory. For a small organic radical, we can show that the accuracy of simulated UV/Vis absorption spectra with the CASSCF linear response approach is significantly improved compared to the popular state-averaged CASSCF method. To demonstrate the efficiency of the implementation, the 50 lowest roots of a large Ni triazole complex with 231 atoms are computed for the simulated UV/Vis and ECD spectra.

New and Efficient Equation-of-Motion Coupled-Cluster Framework for Core-Excited and Core-Ionized States

We present a fully analytical implementation of the core-valence separation (CVS) scheme for the equation-of-motion (EOM) coupled-cluster singles and doubles (CCSD) method for calculations of core-level states. Inspired by the CVS idea as originally formulated by Cederbaum, Domcke, and Schirmer, pure valence excitations are excluded from the EOM target space and the frozen-core approximation is imposed on the reference-state amplitudes and multipliers. This yields an efficient, robust, practical, and numerically balanced EOM-CCSD framework for calculations of excitation and ionization energies as well as state and transition properties (e.g., spectral intensities, natural transition, and Dyson orbitals) from both the ground and excited states. The errors in absolute excitation/ionization energies relative to the experimental reference data are on the order of 0.2-3.0 eV, depending on the K-edge considered and on the basis set used, and the shifts are systematic for each edge. Compared to a previously proposed CVS scheme where CVS was applied as a posteriori projection only during the solution of the EOM eigenvalue equations, the new scheme is computationally cheaper. It also achieves better cancellation of errors, yielding similar spectral profiles but with absolute core excitation and ionization energies that are systematically closer to the corresponding experimental data. Among the presented results are calculations of transient-state X-ray absorption spectra, relevant for interpretation of UV-pump/X-ray probe experiments.