Avoided crossings, conical intersections, and low-lying excited states with a single reference method: The restricted active space spin-flip configuration interaction approach

The restricted active space spin-flip CI (RASCI-SF) performance is tested in the electronic structure computation of the ground and the lowest electronically excited states in the presence of near-degeneracies. The feasibility of the method is demonstrated by analyzing the avoided crossing between the ionic and neutral singlet states of LiF along the molecular dissociation. The two potential energy surfaces (PESs) are explored by means of the energies of computed adiabatic and approximated diabatic states, dipole moments, and natural orbital electronic occupancies of both states. The RASCI-SF methodology is also used to study the ground and first excited singlet surface crossing involved in the double bond isomerization of ethylene, as a model case. The two-dimensional PESs of the ground (S(0)) and excited (S(1)) states are calculated for the complete configuration space of torsion and pyramidalization molecular distortions. The parameters that define the state energetics in the vicinity of the S(0)/S(1) conical intersection region are compared to complete active space self-consistent field (CASSCF) results. These examples show that it is possible to describe strongly correlated electronic states using a single reference methodology without the need to expand the wavefunction to high levels of collective excitations. Finally, RASCI is also examined in the electronic structure characterization of the ground and 2(1)A(g) (-), 1(1)B(u) (+), 1(1)B(u) (-), and 1(3)B(u) (-) states of all-trans polyenes with two to seven double bonds and beyond. Transition energies are compared to configuration interaction singles, time-dependent density functional theory (TDDFT), CASSCF, and its second-order perturbation correction calculations, and to experimental data. The capability of RASCI-SF to describe the nature and properties of each electronic state is discussed in detail. This example is also used to expose the properties of different truncations of the RASCI wavefunction and to show the possibility to use an excitation operator with any number of α-to-β electronic promotions.     

On low‐lying excited states of extended nanographenes

Low‐lying excited states of planarly extended nanographenes are investigated using the long‐range corrected (LC) density functional theory (DFT) and the spin‐flip (SF) time‐dependent density functional theory (TDDFT) by exploring the long‐range exchange and double‐excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long‐range exchange interaction significantly improves the C C bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long‐range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long‐range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long‐range exchange effects, the SF‐TDDFT calculations show that the double‐excitation correlation effects are negligible in the low‐lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long‐range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP–EA values. © 2017 Wiley Periodicals, Inc.     

Quasidegenerate scaled opposite spin second order perturbation corrections to single excitation configuration interaction

Scaled opposite spin (SOS) second order perturbative corrections to single excitation configuration interaction (CIS) are extended to correctly treat quasidegeneracies between excited states. Two viable methods, termed as SOS-CIS(D(0)) and SOS-CIS(D(1)), are defined, implemented, and tested. Each involves one empirical parameter (plus a second for the SOS-MP2 ground state), has computational cost that scales with the fourth power of molecule size, and has storage requirements that are cubic, with only quantities of the rank of single excitations produced and stored during iterations. Tests on a set of low-lying adiabatic valence excitation energies and vertical Rydberg excitations of organic and inorganic molecules show that the empirical parameter can be acceptably transferred from the corresponding nondegenerate perturbation theories without any further fitting. Further tests on higher excited states show that the new methods correctly perform for surface crossings for which nondegenerate approaches fail. Numerical results show that SOS-CIS(D(0)) appears to treat Rydberg excitations in a more balanced way than SOS-CIS(D(1)) and is, therefore, likely to be the preferred approach. It should be useful for exploring excited state geometries, transition structures, and conical intersections for states of medium to large organic molecules that are dominated by single excitations.     

CERES: An ab initio code dedicated to the calculation of the electronic structure and magnetic properties of lanthanide complexes

We have developed and implemented a new ab initio code, Ceres (Computational Emulator of Rare Earth Systems), completely written in C++11, which is dedicated to the efficient calculation of the electronic structure and magnetic properties of the crystal field states arising from the splitting of the ground state spin‐orbit multiplet in lanthanide complexes. The new code gains efficiency via an optimized implementation of a direct configurational averaged Hartree–Fock (CAHF) algorithm for the determination of 4f quasi‐atomic active orbitals common to all multi‐electron spin manifolds contributing to the ground spin‐orbit multiplet of the lanthanide ion. The new CAHF implementation is based on quasi‐Newton convergence acceleration techniques coupled to an efficient library for the direct evaluation of molecular integrals, and problem‐specific density matrix guess strategies. After describing the main features of the new code, we compare its efficiency with the current state–of–the–art ab initio strategy to determine crystal field levels and properties, and show that our methodology, as implemented in Ceres , represents a more time‐efficient computational strategy for the evaluation of the magnetic properties of lanthanide complexes, also allowing a full representation of non‐perturbative spin‐orbit coupling effects. © 2017 Wiley Periodicals, Inc.     

A new route towards redox bistability through the inspection of manganese-porphyrin complexes

The redox and spin versatilities of manganese–porphyrin complexes [Mn^IIP] are examined to construct a redox‐switchable device. The electronic structure of [Mn^IIIP]⁺ was analyzed by using wavefunction‐based calculations (complete active spaces plus single excitations on top of the active spaces, that is, CAS+singles). A non‐negligible σ‐type electron‐transfer configuration is present in the [Mn^IIIP]⁺ S=2 ground state. By contrast, the [Mn^IIP^.]⁺ valence tautomer is a purely π‐type intramolecular charge transfer, thus reflecting an S=3 spin state as a result of the strong ferromagnetic interaction (J=30 meV) between the S=5/2 Mn^II ion and the S=1/2 porphyrin radical cation P^.+. The change of the redox‐sensitive site in the valence tautomer leads to a ‘triangular scheme’ that involves a critical step in which a simultaneous electron transfer and spin change are expected to induce bistability. From the wavefunction inspection, a meso‐substituted porphyrin candidate was designed to support this scenario. The complete active‐space second‐order perturbation theory (CASPT2) adiabatic energy difference between the S=2 and the S=3 spin states was reduced down to 0.15 eV, thereby giving rise to a metastable S=3 state characterized by a 0.10 Å extension of the porphyrin cavity radius. These results not only confirm the rather versatile nature of these inorganic systems but also demonstrate that redox and spin changes are intermingled in this class of compounds and can be used for applied devices.     

Ab initio calculations of the ground and excited states of the ZrN molecule including spin‐orbit effects

The electronic structures with spin‐orbit effects of the zirconium nitride ZrN molecule are investigated by the methods of multireference single and double configuration interaction. The potential energy curves are calculated along with the spectroscopic constants for the lowest‐lying 34 spin‐orbit states Ω in ZrN. A good agreement is displayed by comparing the calculated spectroscopic constants with those available experimentally. The permanent dipole moments are calculated along with the vibrational energies. New results are obtained in this work for 29 spin‐orbit states and their spectroscopic constants calculated. © 2015 Wiley Periodicals, Inc.     

The momentum distribution in some electronic states of the neutral and singly ionized nitrogen molecule

Momentum densities for the N₂ molecule are investigated. Differences between the ground state and low-lying excited states as well as the effects of ionization are discussed. The densities are calculated by taking Fournier transforms of natural spin orbitals of wavefunctions calculated in a minimal basis with configuration interaction.     

Multireference space without first solving the configuration interaction problem

We further develop an idea to generate a compact multireference space without first solving the configuration interaction problem previously proposed for the ground state (GS) (Glushkov, Chem. Phys. Lett. 1995, 244, 1). In the present contribution, our attention is focused on low‐lying excited states (ESs) with the same symmetry as the GS which can be adequately described in terms of an high‐spin open‐shell formalism. Two references Møller–Plesset (MP) like perturbation theory for ESs is developed. It is based on: (1) a main reference configuration constructed from the parent molecular orbitals adjusted to a given ES and (2) secondary double excitation configuration built on the GS like orbitals determined by the Hartree–Fock equations subject to some orthogonality constraints. It is shown how to modify the MP zeroth‐order Hamiltonian so that the reference configurations and corresponding excitations are eigenfunctions of it and are compatible with orthogonality conditions for the GS and ES. Intruder states appearance is also discussed. The proposed scheme is applied to the GS, ES, and excitation energies of small molecules to illustrate and calibrate our calculations. © 2013 Wiley Periodicals, Inc.     

Efficient calculations of a large number of highly excited states for multiconfigurational wavefunctions

Electronically excited states play important roles in many chemical reactions and spectroscopic techniques. In quantum chemistry, a common technique to solve excited states is the multiroot Davidson algorithm, but it is not designed for processes like X-ray spectroscopy that involves hundreds of highly excited states. We show how the use of a restricted active space wavefunction together with a projection operator to remove low-lying electronic states offers an efficient way to reach single and double-core-hole states. Additionally, several improvements to the stability and efficiency of the configuration interaction (CI) algorithm for a large number of states are suggested. When applied to a series of transition metal complexes the new CI algorithm does not only resolve divergence issues but also leads to typical reduction in computational time by 70%, with the largest savings for small molecules and large active spaces. Together, the projection operator and the improved CI algorithm now make it possible to simulate a wide range of single- and two-photon spectroscopies. © 2019 Wiley Periodicals, Inc.     

Quantum chemical topology at the spin–orbit configuration interaction level: Application to astatine compounds

We report a methodology that allows the investigation of the consequences of the spin–orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the “state-specific” natural orbitals (NOs; expressed in a Cartesian Gaussian-type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin–orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = At F) and trihalide anions (IAtI⁻ , BrAtBr⁻ , and IAtBr⁻ ) are studied, at exact two-component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spin–orbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin–orbit couplings.     

Modification of optimal complete active space choices for the multiconfigurational spin‐tensor electron propagator method for ionization potentials

The multiconfigurational spin tensor electron propagator (MCSTEP) method was developed as an implementation of electron propagator/single particle Green's function methods. MCSTEP was specifically designed for open‐shell and highly correlated (nondynamically correlated) initial states. Ionization or electron attachment is always from a state of pure spin symmetry to a state of pure spin symmetry even if the initial state is open shell. MCSTEP can be used as well for molecules with initial states that can be accurately described by a single determinant‐based theory. The initial state that is used in MCSTEP is typically a small complete active space (CAS) multiconfigurational self‐consistent field (MCSCF) state. We previously examined different small CAS choices for MCSTEP initial states and have developed a generally workable scheme. This article further examines some different ways to choose the CAS for MCSTEP. With several logical CAS choices, we have calculated the low‐lying vertical MCSTEP ionization potentials (IPs) of C₂, N₂, linear H₂O, O₂, CH₂, and NH₂, comparing them with large multireference configuration interaction (MRCI) calculations. We conclude that generally a small modification and extension of our previous schemes for choosing the MCSTEP CAS gives IPs that most effectively mimics the results of large scale MRCI IPs in general. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

State‐specific multireference perturbation theory with improved virtual orbitals: Taming the ground state of F2, Be2, and N2

Adaptation of improved virtual orbitals (IVOs) in state‐specific multireference perturbation theory using Møller–Plesset multipartitioning of the Hamiltonian (IVO‐SSMRPT) is examined in which the IVO‐complete active space configuration interaction (CASCI) is used as an inexpensive alternative to the more involved CAS‐self‐consistent field (CASSCF) orbitals. Unlike the CASSCF approach, IVO‐CASCI does not bear tedious and costly iterations beyond those in the initial SCF calculation. The IVO‐SSMRPT is intruder‐free, and explicitly size‐extensive. In the present preliminary study, the IVO‐SSMRPT method which relies on a small reference space is applied to study potential energy surfaces (PES) of the ground state of challenging, multiconfigurational F₂, Be₂, and N₂ molecules. These systems provide a serious challenge to any ab initio methodology due to the presence of an intricate interplay of nondynamical and dynamical correlations to the entire PES. The quality of the computed PES has been judged by extracting spectroscopic parameters and vibrational levels. The reported results illustrate that the IVO‐SSMRPT method has a potential to yield accuracies as good as the CASSCF‐SSMRPT one with reduced computational labor. Even with small reference spaces, our estimates demonstrate a good agreement with the available experimental values, and some benchmark computations. The blend of accuracy and low computational cost of IVO‐SSMRPT should deserve future attention for the accurate treatment of electronic states of small to large molecular systems for which the wavefunction is characterized by various configurations. © 2015 Wiley Periodicals, Inc.     

Excited‐State Dynamics of the Metal String Complex Co3(dpa)4(NCS)2 from Femtosecond Transient Absorption Spectra

Transient absorption spectroscopy is used to study the excited‐state dynamics of Co₃(dpa)₄(NCS)₂, where dpa is the ligand di(2‐pyridyl)amido. The ππ*, charge‐transfer, and d–d transition states are excited upon irradiation at wavelengths of 330, 400 and 600 nm, respectively. Similar transient spectra are observed under the experimental temporal resolution and the transient species show weak absorption. We thus propose that a low‐lying metal‐centered d–d state is accessed immediately after excitation. Analyses of the experimental kinetic traces reveal rapid conversion from the ligand‐centered ππ* and the charge‐transfer states to this metal‐centered d‐d state within 100 fs. The excited molecule then crosses to a second d–d state within the ligand‐field manifold, with a time coefficient of 0.6–1.4 ps. Because the ground‐state bleaching band recovers with a time coefficient of 10–23 ps, we propose that an excited molecule crosses from the low‐lying d–d state either directly within the same spin system or with spin crossing via the state ²B to the ground state ²A₂ (symmetry group C₄). In this trimetal string complex, relaxation to the ground electronic surface after excitation is thus rapid.     

Finite-field many-body perturbation theory. VI. Multipole polarizabilities of beryllium. A comparative study

A high-resolution ESCA N1s spectrum from free p-aminobenzonitrile molecules is presented. The spectrum is very different from the corresponding spectrum from a solid sample. It shows one uncommonly intense shape-up line from the N1s ionization in the nitrile group, while ionization in the NH₂ group does not give rise to any such anomalous shake-up features. The spectrum is theoretically analyzed by means of a large-scale ab initio calculation by the CAS SCF method, in which a full π-orbital active space was employed for the ground and N1s ionic states. The calculations strongly underline the role of multiple excitations in the charge transfer following N1s(CN) ionization, as well as the importance of separate self-consistent treatment of all states involved. In particular, it is shown that an unsuitable choice of orbitals can lead to an apparent “shake-down”.     

Investigation of challenging spin systems using Monte Carlo configuration interaction and the density matrix renormalization group

We investigate if a range of challenging spin systems can be described sufficiently well using Monte Carlo configuration interaction (MCCI) and the density matrix renormalization group (DMRG) in a way that heads toward a more “black box” approach. Experimental results and other computational methods are used for comparison. The gap between the lowest doublet and quartet state of methylidyne (CH) is first considered. We then look at a range of first‐row transition metal monocarbonyls: MCO when M is titanium, vanadium, chromium, or manganese. For these MCO systems we also employ partially spin restricted open‐shell coupled‐cluster (RCCSD). We finally investigate the high‐spin low‐lying states of the iron dimer, its cation and its anion. The multireference character of these molecules is also considered. We find that these systems can be computationally challenging with close low‐lying states and often multireference character. For this more straightforward application and for the basis sets considered, we generally find qualitative agreement between DMRG and MCCI. © 2017 Wiley Periodicals, Inc.     

Real space Hartree-Fock configuration interaction method for complex lateral quantum dot molecules

We present unrestricted Hartree-Fock method coupled with configuration interaction (CI) method (URHF-CI) suitable for the calculation of ground and excited states of large number of electrons localized by complex gate potentials in quasi-two-dimensional quantum dot molecules. The method employs real space finite difference method, incorporating strong magnetic field, for calculating single particle states. The Hartree-Fock method is employed for the calculation of direct and exchange interaction contributions to the ground state energy. The effects of correlations are included in energies and directly in the many-particle wave functions via CI method using a limited set of excitations above the Fermi level. The URHF-CI method and its performance are illustrated on the example of ten electrons confined in a two-dimensional quantum dot molecule.     

Maximum Spin Polarization in Chromium Dimer Cations as Demonstrated by X‐ray Magnetic Circular Dichroism Spectroscopy

X‐ray magnetic circular dichroism spectroscopy has been used to characterize the electronic structure and magnetic moment of Cr₂⁺. Our results indicate that the removal of a single electron from the 4sσ_g bonding orbital of Cr₂ drastically changes the preferred coupling of the 3d electronic spins. While the neutral molecule has a zero‐spin ground state with a very short bond length, the molecular cation exhibits a ferromagnetically coupled ground state with the highest possible spin of S=11/2, and almost twice the bond length of the neutral molecule. This spin configuration can be interpreted as a result of indirect exchange coupling between the 3d electrons of the two atoms that is mediated by the single 4s electron through a strong intraatomic 3d‐4s exchange interaction. Our finding allows an estimate of the relative energies of two states that are often discussed as ground‐state candidates, the ferromagnetically coupled ¹²Σ and the low‐spin ²Σ state.     

A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

In this work, the automated generator environment for ORCA (ORCA‐AGE) is described. It is a powerful toolchain for the automatic implementation of wavefunction‐based quantum chemical methods. ORCA‐AGE consists of three main modules: (1) generation of “raw” equations from a second quantized Ansatz for the wavefunction, (2) factorization and optimization of equations, and (3) generation of actual computer code. We generate code for the ORCA package, making use of the powerful functionality for wavefunction‐based correlation calculations that is already present in the code. The equation generation makes use of the most elementary commutation relations and hence is extremely general. Consequently, code can be generated for single reference as well as multireference approaches and spin‐independent as well as spin‐dependent operators. The performance of the generated code is demonstrated through comparison with efficient hand‐optimized code for some well‐understood standard configuration interaction and coupled cluster methods. In general, the speed of the generated code is no more than 30% slower than the hand‐optimized code, thus allowing for routine application of canonical ab initio methods to molecules with about 500–1000 basis functions. Using the toolchain, complicated methods, especially those surpassing human ability for handling complexity, can be efficiently and reliably implemented in very short times. This enables the developer to shift the attention from debugging code to the physical content of the chosen wavefunction Ansatz. Automatic code generation also has the desirable property that any improvement in the toolchain immediately applies to all generated code. © 2017 Wiley Periodicals, Inc.     

Quantum Monte Carlo with very large multideterminant wavefunctions

An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman–Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin‐specific determinants: for typical configuration interaction‐type wavefunctions the number of unique spin‐specific determinants ( ) with a non‐negligible weight in the expansion is of order . We show that a careful implementation of the calculation of the N_det ‐dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin‐specific determinants, , over a wide range of total number of determinants (here, N_det up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all‐electron fixed‐node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ～400 compared to a single‐determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc.     

Properties and long range interactions of the calcium atom

The properties of a number of states of calcium are determined from a large basis configuration interaction calculation. The main focus is on the polarizabilities of the low lying states (the 4s2 1Se, 4s3d 1,3De, 4s4p 1,3Po, and 4s5s 1,3Se states) and the dispersion interactions of those states with the calcium ground state, the hydrogen atom, and the rare gases.