Significance of non-linear terms in the relativistic coupled-cluster theory in the determination of molecular properties

The relativistic coupled-cluster (RCC) theory has been applied recently to a number of heavy molecules to determine their properties very accurately. Since it demands large computational resources, the method is often approximated to singles and doubles excitations (RCCSD method). The effective electric fields (${\cal E}_{eff}$) and molecular permanent electric dipole moments (PDMs) of SrF, BaF and mercury monohalides (HgX with X = F, Cl, Br, and I) molecules are of immense interest for probing fundamental physics. In our earlier calculations of ${\cal E}_{eff}$ and PDMs for the above molecules, we had neglected the non-linear terms in the property evaluation expression of the RCCSD method. In this work, we demonstrate the roles of these terms in determining above quantities and their computational time scalability with number of processors of a computer. We also compare our results with previous calculations that employed variants of RCC theory as well as other many-body methods, and available experimental values

Multireference approaches for excited states of molecules

Understanding the properties of electronically excited states is a challenging task that becomes increasingly important for numerous applications in chemistry, molecular physics, molecular biology, and materials science. A substantial impact is exerted by the fascinating progress in time-resolved spectroscopy, which leads to a strongly growing demand for theoretical methods to describe the characteristic features of excited states accurately. Whereas for electronic ground state problems of stable molecules the quantum chemical methodology is now so well developed that informed nonexperts can use it efficiently, the situation is entirely different concerning the investigation of excited states. This review is devoted to a specific class of approaches, usually denoted as multireference (MR) methods, the generality of which is needed for solving many spectroscopic or photodynamical problems. However, the understanding and proper application of these MR methods is often found to be difficult due to their complexity and their computational cost. The purpose of this review is to provide an overview of the most important facts about the different theoretical approaches available and to present by means of a collection of characteristic examples useful information, which can guide the reader in performing their own applications

Application of quantum Monte Carlo methods to molecular potential energy surfaces

Various computational methods have been used to generate potential energy surfaces, which can help us simulate and interpret how atoms or molecules behave during a chemical reaction. For accurate work, ab initio wavefunction methods have traditionally been used, which have some disadvantages. For example, highly accurate methods scale poorly with system size (n7 or higher) and are mostly not well parallelized for calculations with multiple processors. One alternative method that has more favorable scaling with system size and is well parallelized is a computational technique called quantum Monte Carlo (QMC). QMC methods scale with the number of electrons as n3 and have been found to scale almost linearly with the number of processors, even beyond 500,000 cores. However, despite the favorable scaling towards large systems, the cost of QMC methods is relatively expensive for small systems. Small systems nevertheless make important benchmarks necessary for the new methods to gain acceptance. Thus, it was determined to study QMC methods in a few benchmark systems in order to assess its accuracy and routine applicability. It was found that QMC methods can be very accurate comparing well with experimental measurements and other high-level ab initiomethods. Benchmark calculations with QMC produced realistic spectroscopic parameters for CO and N2. However, for small system sizes, they are relatively very expensive to perform with the cost being orders of magnitude higher than traditional methods. Consequently, their use in small systems will likely most often be restricted to only a few geometrical points of interest, unlike traditional methods. Nevertheless, deep insight into the electronic structure of a system can be obtained --Abstract, page iv

Equation-of-motion coupled-cluster theory based on the 4-component Dirac-Coulomb(-Gaunt) Hamiltonian:Energies for single electron detachment, attachment, and electronically excited states

<p>This entry contains the figures included in the paper titled "Equation-of-Motion Coupled-Cluster Theory based on the 4-component Dirac--Coulomb(--Gaunt) Hamiltonian. Energies for single electron detachment, attachment and electronically excited states", by Avijit Shee, Trond Saue, Lucas Visscher and Andre Severo Pereira Gomes.</p> <p>It accompanies the dataset found at the DOI: 10.5281/zenodo.1320320</p> <p>There are three figures that use the (original) png files included in <a href="https://zenodo.org/api/files/7bda2e2b-ac69-41aa-a21e-821e88bfb973/original-figures.tar.bz2">original-figures.tar.bz2 </a>:</p> <p>figure 1: Potential energy curves of the spin-orbit split X²Π and A²Π states of the XO molecules, obtained with EOM-IP and the ²DCG^M Hamiltonian.</p> <p>figure 2: Internuclear distances (in Angstrom), harmonic vibrational frequencies (in cm⁻¹) and the vertical Ω = 3/2 − 1/2 energy difference (in eV) for the X²Π and A²Π states of the XO molecules, obtained with EOM-IP and the ²DCG^M Hamiltonian.</p> <p>figure 3: SO-ZORA/QZ4P/Hartree-Fock (ADF) spinor magnetization plots (isosurfaces at 0.03 a.u.) and energies (in Eh) for the valence spinors of the XO⁻ species (from left to right: X = Cl, Br, I, At, Ts).</p

Modern quantum chemistry with [Open]Molcas

Artículo escrito por un elevado número de autores, sólo se referencian el que aparece en primer lugar, los autores pertenecientes a la UAM y el nombre del grupo de colaboración, si lo hubiereThe following article appeared in The Journal of Chemical Physics 152.21 (2020): 214117 and may be found at https://doi.org/10.1063/5.0004835MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree–Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functionsF.A. acknowledges financial support from the EU-H2020 research and innovation programme under Grant Agreement No. 654360 within the framework of the NFFA-Europe Transnational Access Activity. Part of this work was performed, thanks to computer resources provided by CINECA, under Project No. HPC-EUROPA3 (Grant No. INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action of the H2020 Programme. D.-C.S. and J.A. acknowledge support from the U.S. Department of Energy, Office of Basic Energy Sciences, Heavy Element Chemistry program, under Grant No. DE-SC0001136. S.B. acknowledges support from the Swiss National Science Foundation (Grant No. P2SKP2_184034). A.B. is grateful for support from ETH Zurich (ETH Fellowship No. FEL-49 18-1). M.R. acknowledges support from the Swiss National Science Foundation (Project No. 200021_182400). L.D.V., L.P.-G., and M.Ol. acknowledge a MIUR (Ministero dell’Istruzione, dell’Università e della Ricerca) grant “Dipartimento di Eccellenza 2018-2022.” M.Ol. acknowledges NSF Grant No. CHE-CLP-1710191. M.D. and M.L. acknowledges support from the Olle Engkvist Foundation. E.D.L. and V.V. acknowledge computational resources provided by SNIC through LUNARC and NSC. T.B.P. acknowledges support from the Research Council of Norway through its Centres of Excellence scheme, Project No. 262695, and through Research Grant No. 240698. K.P. acknowledges financial support from KU Leuven through Grant No. C14/15/052. L.S. acknowledges financial support from Ministerio de Economía y Competitividad, Spain (Dirección General de Investigación y Gestión del Plan Nacional de I+D+i, Grant No. MAT2017-83553- P). J.S.-M. acknowledges support from the EU-H2020 Marie Curie Actions (AttoDNA, FP8-MSCA-IF, Grant No. 747662). I.S. gratefully acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant No. 678169 PhotoMutant). L.U. and X.G. gratefully acknowledge scientific Grant Nos. R-143-000-A80- 114 and R-143-000-A65-133 from the National University of Singapore. Computational resources of the NSCC (ASPIRE-1, Grant No. 11001278) were used for this study

Beyond Density Functional Theory: the Multiconfigurational Approach to Model Heterogeneous Catalysis

Catalytic processes are crucially important for many practical chemical applications. Heterogeneous catalysts are especially appealing because of their high stability and the relative ease with which they may be recovered and reused. Computational modeling can play an important role in the design of more catalytically active materials through the identification of reaction mechanisms and the opportunity to assess hypothetical catalysts in silico prior to experimental verification. Kohn-Sham density functional theory (KS-DFT) is the most used method in computational catalysis because it is affordable and it gives results of reasonable accuracy in many instances. Furthermore, it can be employed in a “black-box” mode that does not require significant a priori knowledge of the system. However, KS-DFT has some limitations: it suffers from self-interaction error (sometime referred to as delocalization error), but a greater concern is that it provides an intrinsically single-reference description of the electronic structure, and this can be especially problematic for modeling catalysis when transition metals are involved. In this perspective, we highlight some noteworthy applications of KS-DFT to heterogeneous computational catalysis, as well as cases where KS-DFT fails accurately to describe electronic structures and intermediate spin states in open-shell transition metal systems. We next provide an introduction to state-of-the-art multiconfigurational (MC; also referred to as multireference (MR)) methods and their advantages and limitations for modeling heterogeneous catalysis. We focus on specific examples to which MC methods have 2 been applied and discuss the challenges associated with these calculations. We conclude by offering our vision for how the community can make further progress in the development of MC methods for application to heterogeneous catalysis

Development of an Automatic Code Generator and Implementation of Multireference Equation of Motion Coupled-Cluster Theory in the ORCA Program Package

Over the past 50 years, single-reference coupled-cluster theory has emerged as a cornerstone of quantum chemistry. While it is an accurate methodology for the calculation of the properties of the electronic states of many systems, there are still many strongly-correlated (multireference) systems which cannot be adequately treated with single-reference coupled-cluster theory. Hence, in the past four decades, there have been significant efforts to develop multireference generalizations of coupled-cluster theory to treat such systems. In this work, we review some of the major developments in single-reference and multireference molecular electronic structure theory. We discuss the details of the Multireference Equation of Motion (MR-EOM) coupled-cluster approach, developed in the Nooijen group, and introduce a new variant which makes use of a Hermitizing transformation. The MR-EOM methodology constitutes a transform and diagonalize approach to electronic structure theory, that is applicable to both ground and excited states. A major topic of this thesis concerns the development of an automatic code generation tool, that has been used to implement the MR-EOM approach in the ORCA quantum chemistry software package. The implementation in ORCA is employed for the characterization and calculation of the excitation energies of transition metal complexes. We also introduce an orbital selection scheme which can be used to extend the applicability of the MR-EOM approach to larger systems for the calculation of excitation spectra. A variety of MR-EOM approaches are then considered in benchmark applications to organic molecules and the various approximations, introduced in the ORCA implementation of MR-EOM, are studied for several transition metal complexes. Finally, we discuss how the implementation in ORCA might be improved in the future, in order to push applications to larger systems and larger active spaces.4 month

Extension and applications of the GVVPT2 method to the study of transition metals

The ground and low-lying excited electronic states of molecules of the first ( 2 Sc , 2 Cr , 2 Mn , and 2 Ni ) and second ( 2 Y , 2 Mo , and 2 Tc ) row of transition elements have been investigated for the first time with the generalized Van Vleck second order multireference perturbation theory (GVVPT2) method, a variant of MRPT. All potential energy curves (PECs) obtained in these studies were smooth and continuous; that is, they are free from wiggles or inflexion points. In order to account for relativistic effects, which become important in heavy elements, the GVVPT2 method was extended to include scalar relativistic effects through the spin-free exact two component (sf-X2C) method and used in the studies of all molecules of second row transition elements and some of those of the first row considered in this present work. GVVPT2 studies of triatomic lithium and beryllium were also done as a first step to studies of small clusters of transition metals. The spectroscopic constants (bond lengths, harmonic frequencies, bond energies, and adiabatic transition energies) obtained for all PECs at the GVVPT2 level were in good agreement with experimental data, where available, and with results from previous studies using other high level ab initio methods. Optimized geometries of the triatomics were also in good agreement with previous findings. The studies included electronic states (e.g., the g 1 g 1 2 Σ and 3 Σ states of 2 Y as well as the g 5 1 Σ and g 9 1 Σ states of 2 Tc ) not previously discussed in the literature. As a first step to applying GVVPT2 to the study of relatively larger systems, the present work includes the results of efforts on improving DFT-in-DFT embedding theory. New equations were determined which involved an additional constraint of orthogonality of the orbitals of one subsystem to those of the complementary subsystem as warranted by formal arguments based on the formulation of DFT-in-DFT embedding. A computer program was realized using the new embedding equations and test calculations performed. Analyses of electron density deformations in embedding theory, in comparison with conventional Kohn-Sham (KS)-DFT densities, were performed using the new embedding program and a computer code that was also written to compute electron densities of molecules in real space, given reduced one particle density matrices. The results revealed that whereas the current formulation of DFT-in-DFT embedding theory generally underestimates electron density, at the interface between subsystems in comparison with conventional KS-DFT calculations of the supermolecule, the new DFT-in-DFT embedding scheme with the external orthogonality constraint was found to remedy the situation. Worthy of special note in this new embedding protocol is the fact that the nonadditive kinetic potential ( T v ), thought to be a major cause of weaknesses in DFT-in-DFT embedding and to which many previous research efforts have been devoted, can be set exactly to zero. The present work therefore realized, for the first time, a new DFT-in-DFT embedding theory that neither relies on kinetic functionals nor requires a supermolecular DFT calculation. Test calculations using the new embedding theory and supermolecular basis set expansion of KS orbitals reproduced conventional KS-DFT energies to at least the 7th decimal place (and even exactly at many geometries). A new way of expanding KS orbitals was also employed in the new embedding protocol, which is intermediate between the usual supermolecular and monomer basis expansions, referred to as the “extended monomer expansion”. The monomer basis expansion scheme was inadequate for the new DFT-in-DFT embedding protocol. Test calculations found this novel, computationally cheaper, extended monomer approach to give results quite close to those from supermolecular basis expansions

Extension and applications of the GVVPT2 method to the study of transition metals

The ground and low-lying excited electronic states of molecules of the first ( 2 Sc , 2 Cr , 2 Mn , and 2 Ni ) and second ( 2 Y , 2 Mo , and 2 Tc ) row of transition elements have been investigated for the first time with the generalized Van Vleck second order multireference perturbation theory (GVVPT2) method, a variant of MRPT. All potential energy curves (PECs) obtained in these studies were smooth and continuous; that is, they are free from wiggles or inflexion points. In order to account for relativistic effects, which become important in heavy elements, the GVVPT2 method was extended to include scalar relativistic effects through the spin-free exact two component (sf-X2C) method and used in the studies of all molecules of second row transition elements and some of those of the first row considered in this present work. GVVPT2 studies of triatomic lithium and beryllium were also done as a first step to studies of small clusters of transition metals. The spectroscopic constants (bond lengths, harmonic frequencies, bond energies, and adiabatic transition energies) obtained for all PECs at the GVVPT2 level were in good agreement with experimental data, where available, and with results from previous studies using other high level ab initio methods. Optimized geometries of the triatomics were also in good agreement with previous findings. The studies included electronic states (e.g., the g 1 g 1 2 Σ and 3 Σ states of 2 Y as well as the g 5 1 Σ and g 9 1 Σ states of 2 Tc ) not previously discussed in the literature. As a first step to applying GVVPT2 to the study of relatively larger systems, the present work includes the results of efforts on improving DFT-in-DFT embedding theory. New equations were determined which involved an additional constraint of orthogonality of the orbitals of one subsystem to those of the complementary subsystem as warranted by formal arguments based on the formulation of DFT-in-DFT embedding. A computer program was realized using the new embedding equations and test calculations performed. Analyses of electron density deformations in embedding theory, in comparison with conventional Kohn-Sham (KS)-DFT densities, were performed using the new embedding program and a computer code that was also written to compute electron densities of molecules in real space, given reduced one particle density matrices. The results revealed that whereas the current formulation of DFT-in-DFT embedding theory generally underestimates electron density, at the interface between subsystems in comparison with conventional KS-DFT calculations of the supermolecule, the new DFT-in-DFT embedding scheme with the external orthogonality constraint was found to remedy the situation. Worthy of special note in this new embedding protocol is the fact that the nonadditive kinetic potential ( T v ), thought to be a major cause of weaknesses in DFT-in-DFT embedding and to which many previous research efforts have been devoted, can be set exactly to zero. The present work therefore realized, for the first time, a new DFT-in-DFT embedding theory that neither relies on kinetic functionals nor requires a supermolecular DFT calculation. Test calculations using the new embedding theory and supermolecular basis set expansion of KS orbitals reproduced conventional KS-DFT energies to at least the 7th decimal place (and even exactly at many geometries). A new way of expanding KS orbitals was also employed in the new embedding protocol, which is intermediate between the usual supermolecular and monomer basis expansions, referred to as the “extended monomer expansion”. The monomer basis expansion scheme was inadequate for the new DFT-in-DFT embedding protocol. Test calculations found this novel, computationally cheaper, extended monomer approach to give results quite close to those from supermolecular basis expansions