Multiconfiguration Self-consistent Field Theory Research Articles

ICISCF: An Iterative Configuration Interaction-Based Multiconfigurational Self-Consistent Field Theory for Large Active Spaces.

An iterative configuration interaction (iCI)-based multiconfigurational self-consistent field (SCF) theory, iCISCF, is proposed to handle systems that require large active spaces. The success of iCISCF stems from three ingredients: (1) efficient selection of individual configuration state functions spanning the active space while maintaining full spin symmetry; (2) the use of Jacobi rotation for optimization of the active orbitals in conjunction with a quasi-Newton algorithm for the core/active-virtual and core-active orbital rotations; (3) a second-order perturbative treatment of the residual space left over by the selection procedure (i.e., iCISCF(2)). Several examples that go beyond the capability of CASSCF are taken as showcases to reveal the efficacy of iCISCF and iCISCF(2), facilitated by iCAS for imposed automatic selection and localization of active orbitals.

Vibronic transitions and spin-orbit coupling of three-membered metallacycles formed by lanthanide-mediated dehydrogenation of dimethylamine.

Metal-mediated N-H and C-H bond activation of aliphatic amines is an effective strategy for synthesizing biologically important molecules. Ln (Ln = La and Ce) atom reactions with dimethylamine are carried out in a pulsed-laser vaporization supersonic molecular beam source. A series of dehydrogenation species are observed with time-of-flight mass spectrometry, and the dehydrogenated Ln-containing species in the formula Ln(CH2NCH3) are characterized by single-photon mass-analyzed threshold ionization (MATI) spectroscopy and quantum chemical calculations. The theoretical calculations include density functional theory for both Ln species and multiconfiguration self-consistent field and quasi-degenerate perturbation theory for the Ce species. The MATI spectrum of La(CH2NCH3) consists of a single vibronic band system, which is assigned to the ionization of the doublet ground state of N-methyl-lanthanaaziridine. The MATI spectrum of Ce(CH2NCH3) displays two vibronic band systems, which are attributed to the ionization of two-pair lowest-energy spin-orbit coupling states of N-methyl-ceraaziridine. Both metallaaziridines are three-membered metallacycles and formed by the thermodynamically and kinetically favorable concerted dehydrogenation of the amino group and one of the methyl groups.

Multiconfigurational Effects on the Density Coherence.

This paper is a study of density coherences in multiconfiguration self-consistent field theory and Kohn-Sham (KS) density functional theory. We visualize and compare the nondiagonal elements of the first-order reduced density matrix in the electronic coordinate representation. This is the electronic density coherence, and it also appears in Hartree-Fock (HF) theory in the integrand of the exchange integral. The density coherence is calculated as a function of the internuclear distance for three diatomic molecules (H2, F2, and HF) using both restricted and unrestricted KS and HF theory, as well as the complete active space self-consistent field method. We identify a group of closely associated peaks corresponding to the coherence of electrons on opposite sides of the center of the molecule, and we call this the exchange massif. We find that Slater-determinant methods with a higher percentage of HF exchange tend to underestimate the density coherence at the exchange massif. We explain the trends in terms of a multireference diagnostic and the number of unpaired electrons.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces.

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.

A matrix isolation ESR investigation of the MgCH radical.

The MgCH radical and its magnesium-25, carbon-13, and deuterated isotopologs have been isolated in low temperature neon matrices and examined by the matrix isolation electron spin resonance technique for the first time. The radicals were formed through the reactions of laser ablated natural abundance magnesium metal and magnesium-25 enriched magnesium metal with carbon-13 and deuterated isotopologs of acetone. The MgCH radical was shown to have a X4Σ- ground electronic state, and the magnetic parameters determined for this state were g⊥ = 2.001 81(45), g∥ = 2.0018(10), D = 4970(5) MHz, A⊥(13C) = 115(6) MHz, A∥(13C) = 65(15) MHz, A⊥(H) = 34(6) MHz, A∥(H) = 5(10) MHz, A⊥(D) = 5(3) MHz, A⊥(25Mg) = 82(5) MHz, and A∥(25Mg) = 85(10). Comparisons are made between the electronic structure of this radical and the MgCH3 and MgN radicals. Theoretical hyperfine parameters were also evaluated for the MgCH radical, and a potential energy surface for the low-lying electronic states was constructed using complete active space multiconfigurational self-consistent field theory. The leading configuration (96.6%) for the X4Σ- ground electronic state was shown to be 1σ22σ23σ21π44σ25σ26σ27σ12π12π1 with an Mg-C bond length of 2.041 Å for a fixed C-H bond length of 1.090 Å. The Mg-C bond dissociation energy (De) was 48.26 kcal/mol. The optimized geometry from a density functional theory calculation using the B3LYP functional gave a Mg-C bond length of 2.061 Å and a C-H bond length of 1.090 Å.

Symmetry-Broken Many-Body Excited States of the Gaseous Atomic Double-Well Bose-Einstein Condensate.

Macroscopic, many-body self-trapped and quantum superposition states of the gaseous double-well Bose-Einstein condensate (BEC) are investigated within the context of a multiconfigurational bosonic self-consistent field theory based upon underlying spatially symmetry-broken one-body wave functions. To aid in the interpretation of our results, an approximate model is constructed in the extreme Fock state limit, in which self-trapped and superposition states emerge in the many-body spectrum, striking a delicate balance between the degree of symmetry breaking, the effects of the condensate's mean field, and that of atomic correlation. It is found, in both the model and full theory, that the superposition state lies energetically below its related self-trapped counterpart even when many configurations are involved. Noticeably different spatial density profiles are associated with each type of excited state, thus providing a rigorous justification for approximate descriptions of high-lying excited states of the BEC.

Multiconfigurational Self-Consistent Field Theory with Density Matrix Embedding: The Localized Active Space Self-Consistent Field Method.

Density matrix embedding theory (DMET) is a fully quantum-mechanical embedding method which shows great promise as a method of defeating the inherent exponential cost scaling of multiconfigurational wave function-based calculations by breaking large systems into smaller, coupled subsystems. However, we recently [ Pham et al. J. Chem. Theory Comput. 2018 , 14 , 1960 .] encountered evidence that the approximate single-determinantal bath picture inherent to DMET is sometimes problematic when the complete active space self-consistent field (CASSCF) is used as a solver and the method is applied to realistic models of strongly correlated molecules. Here, we show this problem can be defeated by generalizing DMET to use a multiconfigurational wave function as a bath without sacrificing practically attractive features of DMET, such as a second-quantization form of the embedded subsystem Hamiltonian, by dividing the active space into unentangled active subspaces each localized to one fragment. We introduce the term localized active space (LAS) to refer to this kind of wave function. The LAS bath wave function can be obtained by the DMET algorithm itself in a self-consistent manner, and we refer to this approach, introduced here for the first time, as the localized active space self-consistent field (LASSCF) method. LASSCF exploits a modified DMET algorithm, but it is a variational wave function method; it does not require DMET's ambiguous error function minimization, and it reproduces full-molecule CASSCF in cases where comparable DMET calculations fail. Our results for test calculations on the nitrogen double-bond dissociation potential energy curves of several diazene molecules suggest that LASSCF can be an appropriate starting point for a perturbative treatment. Outside of the context of embedding, the LAS wave function is inherently an attractive alternative to a CAS wave function because of its favorable cost scaling, which is exponential only with respect to the size of individual fragment active subspaces, rather than the whole active space of the entire system.

Towards an automated and efficient calculation of resonating vibrational states based on state-averaged multiconfigurational approaches.

Resonating vibrational states cannot consistently be described by single-reference vibrational self-consistent field methods but request the use of multiconfigurational approaches. Strategies are presented to accelerate vibrational multiconfiguration self-consistent field theory and subsequent multireference configuration interaction calculations in order to allow for routine calculations at this enhanced level of theory. State-averaged vibrational complete active space self-consistent field calculations using mode-specific and state-tailored active spaces were found to be very fast and superior to state-specific calculations or calculations with a uniform active space. Benchmark calculations are presented for trans-diazene and bromoform, which show strong resonances in their vibrational spectra.

Stochastic Multiconfigurational Self-Consistent Field Theory.

The multiconfigurational self-consistent field theory is considered the standard starting point for almost all multireference approaches required for strongly correlated molecular problems. The limitation of the approach is generally given by the number of strongly correlated orbitals in the molecule, since its cost will grow exponentially with this number. We present a new multiconfigurational self-consistent field approach, wherein linear determinant coefficients of a multiconfigurational wave function are optimized via the stochastic full configuration interaction quantum Monte Carlo technique at greatly reduced computational cost, with nonlinear orbital rotation parameters updated variationally based on this sampled wave function. This extends this approach to strongly correlated systems with far larger active spaces than it is possible to treat via conventional means. By comparison with this traditional approach, we demonstrate that the introduction of stochastic noise in both the determinant amplitudes and the gradient and Hessian of the orbital rotations does not preclude robust and reliable convergence of the orbital optimization. It can even improve the ability to avoid convergence to local minima in the orbital space, and therefore aid in finding variationally lower-energy solutions. We consider the effect on the convergence of the orbitals as the number of walkers and the sampling time within the active space increases, as well as the effect on the final energy and error. The scope of the new protocol is demonstrated with a study of the increasingly strongly correlated electronic structure in a series of polycyclic aromatic hydrocarbons, up to the large coronene molecule in a complete active space of 24 π electrons in 24 orbitals, requiring only modest computational resources

Can Multiconfigurational Self-Consistent Field Theory and Density Functional Theory Correctly Predict the Ground State of Metal-Metal-Bonded Complexes?

The electronic structure of a diiron (FeFe) complex with strong metal-metal interaction and those of analogous complexes (CoCo, CoMn, CoFe, and FeMn) with much weaker metal-metal bonding are investigated with wave function-based methods and density functional theory. The delocalization and bonding between the metal centers in the diiron complex is only fully captured after inclusion of the complete set of 3d and 4d orbitals in the active space, a situation best suited for restricted active space (RAS) approaches. Truncation of the included set of 4d orbitals results in inappropriate localization of some 3d orbitals, incorrect description of the ground spin state as well as wrong spin state energetics, as compared to experiment. Using density functional theory, some local functionals are able to predict the correct ground spin states, and describe the chemical bonding and structural properties of all the metal-metal complexes considered in this work. In contrast, the introduction of some exact exchange results in increased localization of 3d orbitals and wrong spin state energetics, a situation that is particularly troublesome for the diiron complex.

Polarizable embedding based on multiconfigurational methods: Current developments and the road ahead

This perspective gives a brief overview of recent developments within the polarizable embedding (PE) method — a multiscale approach developed over the last years. In particular, we are concerned with a recent coupling of the PE method to a multiconfiguration self‐consistent field (MCSCF) code. Current applications and target systems are outlined, and methods to incorporate dynamical correlation are discussed. With respect to dynamical correlation, the focus is on perturbative treatments as well as a range‐separated multiconfigurational hybrid between MCSCF and density functional theory (MC‐srDFT). A short discussion of CAS active spaces is also given. A few sample results using a retinal chromophore surrounded by a protein environment illustrate both the importance of the choice of active space and the importance of dynamical correlation. © 2014 Wiley Periodicals, Inc.

A Neoteric Neodymium Model: Ground and Excited Electronic State Analysis of NdF2+

Neodymium monofluoride dication was studied as a model of the Nd-F bond in NdFx. Multiconfigurational self-consistent field (MCSCF) and second order multireference quasi-degenerate perturbation theory (MCQDPT2) methods were used with a variety of active spaces to elucidate the roles of the Nd 4f, 5d, and 6s orbitals. Spin-orbit coupling calculations were performed at the SO-MCQDPT2 level, and potential energy curves were obtained for the four lowest energy quartet states as well as for the four lowest doublet states and the lowest sextet state. Inclusion of spin-orbit coupling splits these states into 30 levels. Equilibrium bond lengths, dissociation energies, transition energies, and crossing points were determined.

Structure and Bonding of Palladium Oxos as Possible Intermediates in Metal–Carbon Oxy Insertion Reactions

Analysis of the electronic structure of PdO complexes is reported utilizing multiconfigurational self-consistent field (MCSCF) theory. Models include hard (N) and soft (Cl) donors to mimic proposed Pd oxo intermediates. Calculations argue against formulation of a PdIV oxo intermediate as posited in earlier experimental studies of PdII-mediated oxy insertion: i.e., a square-pyramidal complex with a basal oxo ligand. However, low-energy structures with other coordination geometries (trigonal bipyramidal) and isomerism (basal O) were identified. The supporting ligand plays a role in stabilization of the PdO bond as indicated by calculations on the PdOCl2 fragment and LPdOCl2 (L = model diimine ligand).

Computational study of bond dissociation enthalpies for lignin model compounds: β-5 Arylcoumaran

The biopolymer lignin is a potential source of valuable chemicals. The β-5 linkage comprises ∼10% of the linkages in lignin. Density Functional Theory (DFT) was used to calculate the Cα–O and Cα–Cβ bond dissociation enthalpies (BDEs) for β-5 models with varied substituents, which are important for understanding initial lignin decomposition. The Cα–O (Cα–Cβ) BDEs were in the range of 40–44 (57–62)kcal/mol. The products resulting from either homolysis are bi-radicals with multi-determinant character in the singlet electronic state. Multiconfiguration self-consistent field (MCSCF) theory results were used to verify that unrestricted DFT and broken-symmetry DFT were sufficient to study these reactions.

Anharmonic Frequencies of CX2Y2 (X, Y = O, N, F, H, D) Isomers and Related Systems Obtained from Vibrational Multiconfiguration Self-Consistent Field Theory

Accurate anharmonic frequencies are provided for molecules of current research, i.e., diazirines, diazomethane, the corresponding fluorinated and deuterated compounds, their dioxygen analogs, and others. Vibrational-state energies were obtained from state-specific vibrational multiconfiguration self-consistent field theory (VMCSCF) based on multilevel potential energy surfaces (PES) generated from explicitly correlated coupled cluster, CCSD(T)-F12a, and double-hybrid density functional calculations, B2PLYP. To accelerate the vibrational structure calculations, a configuration selection scheme as well as a polynomial representation of the PES have been exploited. Because experimental data are scarce for these systems, many calculated frequencies of this study are predictions and may guide experiments to come.

Photoexcited conversion of gauche-1,3-butadiene to bicyclobutane via a conical intersection: Energies and reduced density matrices from the anti-Hermitian contracted Schrödinger equation

The photoexcited reaction pathway from gauche-1,3-butadiene to bicyclobutane via a conical intersection is analyzed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions to the anti-Hermitian contracted Schrödinger equation (ACSE). The study utilizes the recent generalization of the ACSE method for the treatment of excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)]. We computed absolute energies of the critical points as well as various intermediate points along the ground-and excited-state potential energy surface of gauche-1,3-butadiene and bicyclobutane. To treat multi-reference correlation, we seeded the ACSE with an initial 2-RDM from a multi-configuration self-consistent field (MCSCF) calculation. The ACSE, MCSCF, and second-order multi-reference many-body perturbation theory (MRPT2) all demonstrate that there exists a family of pathways from gauche-1,3-butadiene to bicyclobutane via a conical intersection that are monotonically decreasing in energy, confirming a conjecture by Sicilia et al. [J. Phys. Chem. A 111, 2182 (2007)]. The ACSE recovers more single-reference correlation energy than MRPT2 and more multi-reference correlation energy than comparable single-reference wave function methods. The 2-RDMs from the ACSE nearly satisfy all necessary N-representability conditions.

Configuration selection within vibrational multiconfiguration self-consistent field theory: Application to bridged lithium compounds

A configuration selection scheme has been used to speed up vibrational multiconfiguration self-consistent field calculations. Deviations with respect to reference calculations were found to be negligible while yielding an acceleration of about two orders of magnitude. Its application to bridged lithium compounds (Li(2)H(2), Li(2)F(2), Li(2)O(2), and Li(3)F(3)) based on high-level coupled-cluster potential energy surfaces provides accurate vibrational transitions for all fundamental modes. The explicit inclusion of 4-mode couplings was found to be important for Li(2)H(2).

ChemInform Abstract: Ring-Opening Reactions of Dioxetene, Oxetene, Dithiete, and Thiete

A series of electrocyclic isomerizations related to the cyclobutene to butadiene reaction have been studied by ab initio theory. In addition to the cyclobutene isomerization, the ring-opening reactions of dioxetene, oxetene, dithiete, and thiete to cis-glyoxal, cis-acrolein, dithioglyoxal, and cis-thioacrolein have been examined. Structures and vibrational frequencies have been determined for reactants, transition states, and products with split-valence and split-valence plus polarization self-consistent field (SCF) methods. For the cyclobutene to butadiene, dioxetene to glyoxal, and oxetene to acrolein reactions, multiconfiguration SCF (MCSCF) geometries were optimized. The use of unrestricted Hartree-Fock natural orbitals (UHF-NO) to define the active space for complete active-space SCF (CASSCF) computations on the transition states was examined. MCSCF, configuration interaction (CISD), and Moller-Plesset perturbation theory (MP4SDTQ) methods were used to determine the activation barriers and reaction energies

Ground state potential energy surface between cyclobutadiene and tetrahedrane looked down from S 1/S 0 conical intersections

We have explored the singlet ground state potential energy surface (S 0 PES) between cyclobutadiene (CBD) and tetrahedrane (THD) looked down from S 1/S 0 conical intersections through multi-configuration self-consistent field theory. On the basis of the obtained S 0 PES, we propose the revised process of the THD to CBD symmetry-forbidden reaction. According to the present result, the THD to CBD rearrangement occurs via plural steps similarly to previous suggestions, but via a tetra-radical species (instead of an endo-species), which is considered for the first time in this paper. Since the endo-species is significantly destabilized when hydrogen atoms are replaced by bulky substituents (such as tert-butyl group), the present one, where endo-species are not involved, would be realized in actual systems having bulky substituents.

Conical intersections in triplet excited states of methylene from the anti-Hermitian contracted Schrödinger equation

A conical intersection in triplet excited states of methylene is computed through the direct calculation of two-electron reduced density matrices (2-RDMs) from solutions of the anti-Hermitian contracted Schrodinger equation (ACSE). The study synthesizes recent extensions of the ACSE method for the treatment of excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)] and arbitrary-spin states [A. E. Rothman, J. J. Foley, and D. A. Mazziotti, Phys. Rev. A 80, 052508 (2009)]. We compute absolute energies of the 1 (3)B(1), 1 (3)A(2), and 2 (3)B(1) states of methylene (CH(2)) and the location of the conical intersection along the 1 (3)A(2)-2 (3)B(1) potential-energy surfaces. To treat multireference correlation, we seed the ACSE with an initial 2-RDM from a multiconfiguration self-consistent field (MCSCF) calculation. The ACSE produces energies that significantly improve upon those from MCSCF and second-order multireference many-body perturbation theory, and the 2-RDMs from the ACSE nearly satisfy necessary N-representability conditions. Comparison of the results from augmented double-zeta and triple-zeta basis sets demonstrates the importance of augmented (or diffuse) functions for determining the location of the conical intersection.