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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Fast methods for multisite charge transfer processes. I. Constrained, state averaged CASSCF(1,n) and CASSCF(2n − 1,n) simulations

We design a dynamically weighted state-averaged constrained complete active space self-consistent field (DW-SA-cCASSCF) algorithm to treat electrons or holes moving between n molecular fragments (where n can be larger than 2). Within such a so-called eDSCn/hDSCn approach, we consider configurations that are mutually single excitations of each other, and we apply a generalized set of constraints to tailor the method for studying charge transfer problems. The constrained optimization problem is efficiently solved using a DIIS-SQP algorithm, thus maintaining computational efficiency. We demonstrate the method for a finite Su–Schrieffer–Heeger chain, successfully reproducing the expected exponential decay of diabatic couplings with distance. When combined with a gradient, the current extension immediately enables efficient nonadiabatic dynamics simulations of complex multi-state charge transfer processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Accurate energies for ππ* excited states via exchange scaling: the XS-CASSCF method

The state-averaged complete-active space self-consistent field method (SA-CASSCF) is a widely employed electronic structure method used for studying photochemistry and dynamics owing to its ability to provide a reliable description even of complicated cases while still retaining computational efficiency. However, SA-CASSCF suffers from one Achilles heel, related to the description of ionic ππ* excited states, whose energy is often overestimated by 1–2 eV. In light of this challenge, we present the XS-CASSCF method, a new approach based on the idea of exchange scaling (XS) that screens the involved energy terms to improve the excitation energies of singlet ionic ππ* states. First, we illustrate the power of the XS-CASSCF method using hexatriene and para-quinodimethane as examples, showing that it corrects the targeted ionic states while leaving the other states largely unaffected, giving root-mean-square errors (RMSE) below 0.2 eV for the four lowest states in both cases. Subsequently, XS-CASSCF vertical excitation energies are tested against theoretical best estimates for a set of 11 molecules and 56 excited states. XS-CASSCF performs exceptionally well for the ππ* states of hydrocarbons, reducing the RMSE over 21 excitation energies from 0.96 to 0.27 eV. In the challenging subset of molecules with heteroatoms and a larger number of ππ* and nπ* states, we find that improvements can also be obtained, albeit not as pronounced. We conclude with an outlook into more realistic molecular materials focusing on their singlet–triplet (S 1 /T 1 ) gaps, finding that significant improvements can be obtained along the whole range of S 1 /T 1 gaps studied, going from 0.1 eV to more than 1.5 eV. Owing to notable improvements across significant classes of molecules combined with its conceptual simplicity, we believe that XS-CASSCF is a promising addition to the electronic structure toolbox, serving both as a standalone electronic structure method and as a starting point for further correlated treatment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

CASSCF with Extremely Large Active Spaces Using the Adaptive Sampling Configuration Interaction Method

The complete active space self-consistent field (CASSCF) method is the principal approach employed for studying strongly correlated systems. However, exact CASSCF can only be performed on small active spaces of ~20 electrons in ~20 orbitals due to exponential growth in the computational cost. Here, we show that employing the Adaptive Sampling Configuration Interaction (ASCI) method as an approximate Full CI solver in the active space allows CASSCF-like calculations within chemical accuracy (<1 kcal/mol for relative energies) in active spaces with more than ~50 active electrons in ~50 active orbitals, significantly increasing the sizes of systems amenable to accurate multiconfigurational treatment. The main challenge with using any selected CI-based approximate CASSCF is the orbital optimization problem; they tend to exhibit large numbers of local minima in orbital space due to their lack of invariance to active–active rotations (in addition to the local minima that exist in exact CASSCF). We highlight methods that can avoid spurious local extrema as a practical solution to the orbital optimization problem. We employ ASCI-SCF to demonstrate a lack of polyradical character in moderately sized periacenes with up to 52 correlated electrons and compare against heat-bath CI on an iron porphyrin system with more than 40 correlated electrons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Fully variational incremental CASSCF

We report the complete-active-space self-consistent field (CASSCF) method is a canonical electronic structure theory that holds a central place in conceptualizing and practicing first principles simulations. For application to realistic molecules, however, the CASSCF must be approximated to circumvent its exponentially scaling computational costs. Applying the many-body expansion - also known as the method of increments - to CASSCF (iCASSCF) has been shown to produce a polynomially scaling method that retains much of the accuracy of the parent theory and is capable of treating full valence active spaces. Due to an approximation made in the orbital gradient, the orbital parameters of the original iCASSCF formulation could not be variationally optimized, which limited the accuracy of its nuclear gradient. Herein, a variational iCASSCF is introduced and implemented, where all parameters are fully optimized during energy minimization. This method is able to recover electronic correlations from the full valence space in large systems, produce accurate gradients, and optimize stable geometries as well as transition states. Demonstrations on challenging test cases, such as the oxoMn(salen)Cl complex with 84 electrons in 84 orbitals and the automerization of cyclobutadiene, show that the fully variational iCASSCF is a powerful tool for describing challenging molecular chemistries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

A Cautionary Tale: Failure of the Valence CASSCF to Describe the Hallmark of Hydrogen Bonding

Valence CASSCF (vCAS) calculations for the hydrogen-bonded (H2O)2, (HF)2, and HF–H2O dimers fail to predict the lengthening of the hydrogen donor bond and the corresponding red shift in the donor bond vibrational stretching frequency. Analysis of the active orbitals in the vCAS calculation reveals that one of the weakly occupied orbitals in each dimer is used to correlate the electrons in the acceptor lone pairs rather than those in the donor bonding orbitals. This has significant implications for subsequent treatments of the dynamical correlation that are based on the vCAS wavefunction.

Nguyen, Long H.↗
NASA NTRS1994

On The Choice of a Zeroth-Order Hamiltonian for Second-Order Perturbation Theory with A CASSCF Reference Function

A new approach to perturbation theory based on a CASSCF reference function has been developed. The key to the approach is the definition of the zeroth order Hamiltonian, H(sub 0), which includes the full CI Hamiltonian for the active space. In the the inactive and secondary spaces, operators may be chosen which reduce to the usual Moller-Plesset or Epstein-Nesbet forms in the limit of a null active space. These operators are diagonal in the orbital indices and permit the block-diagonalization of H(sub 0). The reference is an eigenfunction of Ho without N-particle projection. H(sub 0) automatically incorporates denominator shifts in the style of those appearing in recent open-shell perturbation theories. Comparative results are presented for a few test cases.

Dyall, Kenneth G.↗
DOE OSTI2020

A cautionary tale: Problems in the valence-CASSCF description of the ground state (X1Σ+) of BF

In the full optimized reaction space and valence-complete active space self-consistent field (vCAS) methods, a set of active orbitals is defined as the union of the valence orbitals on the atoms, all possible configurations involving the active orbitals are generated, and the orbitals and configuration coefficients are self-consistently optimized. Such wave functions have tremendous flexibility, which makes these methods incredibly powerful but can also lead to inconsistencies in the description of the electronic structure of molecules. In this paper, the problems that can arise in vCAS calculations are illustrated by calculations on the BH and BF molecules. BH is well described by the full vCAS wave function, which accounts for molecular dissociation and 2s–2p near-degeneracy in the boron atom. The same is not true for the full vCAS wave function for BF. There is mixing of core and active orbitals at short internuclear distances and swapping of core and active orbitals at large internuclear distances. In addition, the virtual 2π orbitals, which were included in the active space to account for the 2s–2p near degeneracy effect, are used instead to describe radial correlation of the electrons in the F2pπ-like pairs. Although the above changes lead to lower vCAS energies, they lead to higher vCAS+1+2 energies as well as irregularities and/or discontinuities in the potential energy curves. All of the above problems can be addressed by using the spin-coupled generalized valence bond-inspired vCAS wave function for BF, which includes only a subset of the atomic valence orbitals in the active space.

Xu, Lu T. (ORCID:0000000182064902)↗
NASA NTRS2001

Theoretical Studies of Possible Synthetic Routes for the High Energy Density Material Td N4: Excited Electronic States

Vertical electronic excitation energies for single states have been computed for the high energy density material (HEDM) Td N4 in order to assess possible synthetic routes that originate from excited electronic states of N2 molecules. Several ab initio theoretical approaches have been used, including complete active space self-consistent field (CASSCF), state averaged CASSCF (SA-CASSCF), singles configuration interaction (CIS), CIS with second-order and third-order correlation corrections [CIS(D)) and CIS(3)], and linear response singles and doubles coupled-cluster (LRCCSD), which is the highest level of theory employed. Standard double zeta polarized (DZP) and triple zeta double polarized (TZ2P) one-particle basis sets were used. The CASSCF calculations are found to overestimate the excitation energies, while the SA-CASSCF approach rectifies this error to some extent, but not completely. The accuracy of the CIS calculations varied depending on the particular state, while the CIS(D), CIS(3), and LRCCSD results are in generally good agreement. Based on the LRCCSD calculations, the lowest six excited singlet states are 9.35(l(sup)T1), 10.01(l(sup)T2), 10.04(1(sup)A2), 10.07(1(sup)E), 10.12(2(sup)T1), and 10.42(2(sup)T2) eV above the ground state, respectively. Comparison of these excited state energies with the energies of possible excited states of N2+N2 fragments, leads us to propose that the most likely synthetic route for Td N4 involving this mechanism arises from combination of two bound quintet states of N2.

Lee, Timothy J.↗
DOE OSTI2020

Benchmarking an Embedded Adaptive Sampling Configuration Interaction Method for Surface Reactions: H 2 Desorption from and CH 4 Dissociation on Cu(111)

Embedded (emb-) correlated wavefunction (CW) theory enables accurate assessments of both ground- and excited-state reaction mechanisms involved in heterogeneous catalysis. Embedded multireference second-order perturbation theory (emb-MRPT2) based on reference wavefunctions generated via embedded complete active space self-consistent field (emb-CASSCF) theory is currently state-of-the-art. However, the factorial scaling of CASSCF limits the size of active space and the complexity of systems that can be studied. In this work, we assess the efficacy of an alternative CW method, adaptive sampling configuration interaction (ASCI)–which enables large active spaces to be used–for studying surface reactions. We couple ASCI with density functional embedding theory (DFET) and benchmark its performance for two reactions: H 2 desorption from and CH 4 dissociation on the Cu(111) surface. Unlike embedded complete active space second-order perturbation theory (emb-CASPT2) that accurately reproduces a measured H 2 desorption barrier, embedded ASCI, using a very large active space (though one that still comprises a small portion of the full set of orbitals) fails to do so. Adding an extra correlation term from embedded Møller–Plesset second-order perturbation theory (emb-MP2) improves the desorption barrier and endothermicity predictions. Thus, the inaccuracy of embedded ASCI comes from the missing dynamic correlation from the many other electrons and orbitals not included in the active space. For CH 4 dissociation, again embedded ASCI overestimates the dissociation barrier compared to emb-CASPT2 predictions. Adding dynamic correlation from emb-MP2 helps correct the barrier. However, this composite approach suffers from double counting of correlation within embedded ASCI followed by emb-MP2 calculations. We therefore conclude that the state-of-the-art emb-MRPT2 based on reference wavefunctions generated via emb-CASSCF remains the method of choice for studying surface reactions. emb-ASCI is useful when large active spaces beyond the limit of emb-CASSCF are essential, such as to study complex surface reactions with significant multiconfigurational character (static correlation) but weak dynamic correlation.

08 HYDROGEN↗
DOE OSTI2024

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe–2S] Systems: A Benchmark Study of the [Fe 2 S 2 (SCH 3 ) 4 ] 2–,3–,4– , [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S- p -tol) 4 ] 2– , and [Fe 2 S 2 (S- o -xyl) 4 ] 2– Complexes

Iron–sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Here, using a [2Fe–2S] model complex with Fe II and Fe III oxidation states, which leads to different charges, i.e., [Fe 2 S 2 (SMe) 4 ] 2–,3–,4– , we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree–Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe 2 S 2 (SCys) 4 ] 2– , [Fe 2 S 2 (S-o-tol) 4 ] 2– , and [Fe 2 S 2 (S-o-xyl) 4 ] 2– , via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the Fe III /Fe III → Fe II /Fe III (4.27 eV) and Fe II /F III → Fe II /F II (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The nature of the chemical bond and the role of non-dynamical and dynamical correlation in Be2

In the spin-coupled generalized valence bond (SCGVB) description of Be2, there is a pair of electrons in highly overlapping “inner” orbitals corresponding to a traditional σ bond, but this bond is compromised by Pauli repulsion arising from its overlap with a second “outer” pair. The presence of this outer pair of electrons leads to a repulsive potential energy curve at long range and a bound, but metastable molecule at short range. To obtain further insights into the nature of the bond in Be2, we determined the non-dynamical and dynamical correlation contributions to the potential energy curve of Be2 using four different choices for the zero-order wave function: Restricted Hartree–Fock (RHF), SCGVB, valence-CASSCF(4,4), and valence-CASSCF(4,8). The SCGVB and valence-CASSCF(4,4) wave functions yield similar breakdowns of the total correlation energy, with non-dynamical correlation being the more important contribution. For the RHF and valence-CASSCF(4,8) wave functions, dynamical correlation is critical, without which the potential energy curve is purely repulsive. High accuracy calculations on the HBen−1Be–BeBen−1H molecule as a function of n (n = 1–6) suggest that the intrinsic strength of a Be–Be σ bond uncompromised by Pauli repulsion is on the order of 62–63 kcal/mol, and its length is 2.13–2.14 Å, ∼60 kcal/mol stronger and ∼0.35 Å shorter than in Be2.

Xu, Lu. T. (ORCID:0000000182064902)↗
NASA NTRS1994

The Fraternal Twins of Quartet O4(+)

Eleven stationary geometries of quartet O4(+) have been studied by ab initio methods. The geometries were optimized at the Complete Active Space Self-Consistent Field (CASSCF) level of theory and the energies were calculated by the multiconfigurational second order pertubation method (CASPT2), using Double-Zeta Plus polarization (DZP), Triple-Zeta Plus Double Polarization (TZ2P), average Atomic Natural Orbital (ANO) (5s4p2d) and average ANO (6s5p3d2f) basis sets. The rectangular and trans-planar structures are found to be the most stable, with an energy barrier to conversion between the two at the threshold of dissociation. Both have a delocalized hole and are stable relative to separated 02 and 02(+)by 11.0 and 11.5 kcal/mol for the rectangular and the 2 trans-planar structure, respectively, compared with the experimentally deduced energy in the range of 9.2 to 10.8 kcal/mol. The adiabatic ionization potentials of 04 and 02 are computed to be 11.67 and 12.21 eV, while experimental values are 11.66 and 12.07 eV, respectively. The vibrational frequencies have been computed for all degrees of freedom at the CASSCF level of theory. Symmetry breaking is found to be a particular problem in the computation of the antisymmetric stretch frequency for the delocalized structures at the CASSCF level of theory. Attempts to rectify these problems using the restricted active space self-consistent field (RASSCF) method leads to additional difficulties, but further analysis yields insight into the symmetry breaking and problems with earlier calculations. Finally, a nonorthogonal configuration interaction (CI) calculation based on the interaction of localized CASSCF wave functions using the Complete Active Space State Interation (CASSI) method leads to a balanced treatment of the antisymmetric stretch which is free from symmetry breaking. The study explains the four most prominent absorption frequencies observed in the partially unassigned IR spectrum of O4(+) isolated in solid neon as the antisymmetric OO stretch, and the combination band of the symmetric and antisymmetric 00 stretch of both the rectangular and trans-planar structures.

Lindh, Roland↗
NASA NTRS2007

Theoretical Studies of Routes to Synthesis of Tetrahedral N4

A paper [Chem. Phys. Lett. 345, 295 (2001)] describes theoretical studies of excited electronic states of nitrogen molecules, with a view toward utilizing those states in synthesizing tetrahedral N4, or Td N4 a metastable substance under consideration as a high-energy-density rocket fuel. Several ab initio theoretical approaches were followed in these studies, including complete active space self-consistent field (CASSCF), state-averaged CASSCF (SA-CASSCF), singles configuration interaction (CIS), CIS with second-order and third-order correlation corrections [CIS(D) and CIS(3)], and linear response singles and doubles coupled-cluster (LRCCSD). Standard double zeta polarized and triple zeta double polarized one-particle basis sets were used. The CASSCF calculations overestimated the excitation energies, while SACASSCF calculations partly corrected these overestimates. The accuracy of the CIS calculations varied, depending on the particular state, while the CIS(D), CIS(3), and LRCCSD results were in generally good agreement. The energies of the lowest six excited singlet states of Td N4 as calculated by the LRCCSD were compared with the energies of possible excited states of N2 + N2 fragments, leading to the conclusion that the most likely route for synthesis of Td N4 would involve a combination of two bound quintet states of N2.

Lee, Timothy J.↗
DOE OSTI2023

Origin of Ferromagnetic Exchange Coupling in Donor–Acceptor Biradical Analogues of Charge-Separated Excited States

A new donor–acceptor biradical complex, Tp Cum,Me Zn(SQ-VD) (Tp Cum,Me Zn + = zinc(II) hydro-tris(3-cumenyl-5-methylpyrazolyl)borate complex cation; SQ = orthosemiquinone; VD = oxoverdazyl), which is a ground-state analogue of a charge-separated excited state, has been synthesized and structurally characterized. Here, the magnetic exchange interaction between the S = 1/2 SQ and the S = 1/2 VD within the SQ-VD biradical ligand is observed to be ferromagnetic, with $J_{SQ-VD}$ = +77 cm –1 (H = -2$J_{SQ-VD}\bar{S}_{SQ}·\bar{S}_{VD}$) determined from an analysis of the variable-temperature magnetic susceptibility data. The pairwise biradical exchange interaction in Tp Cum,Me Zn(SQ-VD) can be compared with that of the related donor–acceptor biradical complex Tp Cum,Me Zn(SQ-NN) (NN = nitronyl nitroxide, S = 1/2), where $J_{SQ-NN}$ ≅ +550 cm –1 . This represents a dramatic reduction in the biradical exchange by a factor of ~7, despite the isolobal nature of the VD and NN acceptor radical SOMOs. Computations assessing the magnitude of the exchange were performed using a broken-symmetry density functional theory (DFT) approach. These computations are in good agreement with those computed at the CASSCF NEVPT2 level, which also reveals an S = 1 triplet ground state as observed in the magnetic susceptibility measurements. A combination of electronic absorption spectroscopy and CASSCF computations has been used to elucidate the electronic origin of the large difference in the magnitude of the biradical exchange coupling between Tp Cum,Me Zn(SQ-VD) and Tp Cum,Me Zn(SQ-NN). A Valence Bond Configuration Interaction (VBCI) model was previously employed to highlight the importance of mixing an SQ SOMO → NNLUMO charge transfer configuration into the electronic ground state to facilitate the stabilization of the high-spin triplet (S = 1) ground state in Tp Cum,Me Zn(SQ-NN). Here, CASSCF computations confirm the importance of mixing the pendant radical (e.g., VD, NN) LUMO (VD LUMO and NN LUMO ) with the SOMO of the SQ radical (SQ SOMO ) for stabilizing the triplet, in addition to spin polarization and charge transfer contributions to the exchange. An important electronic structure difference between Tp Cum,Me Zn(SQ-VD) and Tp Cum,Me Zn(SQ-NN), which leads to their different exchange couplings, is the reduced admixture of excited states that promote ferromagnetic exchange into the Tp Cum,Me Zn(SQ-VD) ground state, and the intrinsically weaker mixing between the VD LUMO and the SQ SOMO compared to that observed for Tp Cum,Me Zn(SQ-NN), where this orbital mixing is significant. The results of this comparative study contribute to a greater understanding of biradical exchange interactions, which are important to our understanding of excited-state singlet–triplet energy gaps, electron delocalization, and the generation of electron spin polarization in both the ground and excited states of (bpy)Pt(CAT-radical) complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Role of Electron Correlation beyond the Active Space in Achieving Quantitative Predictions of Spin-Phonon Relaxation

Single-molecule magnets (SMMs) are promising candidates for molecular-scale data storage and processing due to their strong magnetic anisotropy and long spin relaxation times. However, as temperature rises, interactions between electronic states and lattice vibrations accelerate spin relaxation, significantly limiting their practical applications. Recently, ab initio simulations have made it possible to advance our understanding of phonon-induced magnetic relaxation, but significant deviations from experiments have often been observed. The description of molecules’ electronic structure has been mostly based on complete active space self-consistent field (CASSCF) calculations, and the impact of electron correlation beyond the active space remains largely unexplored. In this study, we provide the first systematic investigation of spin-phonon relaxation in SMMs with post-CASSCF multiconfigurational methods, specifically CAS followed by second-order perturbation theory and multiconfiguration pair-density functional theory. Taking Co(II)- and Dy(III)-based SMMs as case studies, we analyze how electron correlation influences spin-phonon relaxation rates across a range of temperatures, comparing theoretical predictions with experimental observations. Our findings demonstrate that post-CASSCF treatments make it possible to achieve quantitative predictions for Co(II)-based SMMs. For Dy(III)-based systems, however, accurate predictions require consideration of additional effects, underscoring the urgent necessity of further advancing the study of the effects of electronic correlation in these complex systems.

Energy↗