Multi-reference Level Research Articles

Knowles Partitioning at the Multireference Level.

A multireference generalization of the partitioning introduced recently by Knowles (J. Chem. Phys. 2022 156, 011101) is presented with the aim to study electronic systems at a medium level of correlation. The multireference formalism applied is the general framework of multiconfiguration perturbation theory (MCPT).

Reconciling TD-DFT and CASPT2 electronic structure methods for describing the photophysics of DNA.

Time-dependent density functional theory (TD-DFT) and multiconfigurational second-order perturbation theory (CASPT2) are two of the most widely used methods to investigate photoinduced dynamics in DNA-based systems. These methods sometimes give diverse dynamics in physiological environments usually modeled by quantum mechanics/molecular mechanics (QM/MM) protocol. In this work, we demonstrate for the uridine test case that the underlying topology of the potential energy surfaces of electronic states involved in photoinduced relaxation is similar in both electronic structure methods. This is verified by analyzing surface-hopping dynamics performed at the QM/MM level on aqueous solvated uridine at TD-DFT and CASPT2 levels. By constraining the dynamics to remain on state we observe similar fluctuations in energy and relaxation lifetimes in surface-hopping dynamics in both TD-DFT and experimentally validated CASPT2 methods. This finding calls for a systematic comparison of the ES potential energy surfaces of DNA and RNA nucleosides at the single- and multi-reference levels of theory. The anomalous long excited state lifetime at the TD-DFT level is explained by trapping due to the tendency of TD-DFT in QM/MM schemes with electrostatic embedding to underestimate the energy of the state leading to a wrong energetic order. A study of the FC energetics suggests that improving the description of the surrounding environment through polarizable embedding or by the expansion of QM layer with hydrogen-bonded waters helps restore the correct state order at TD-DFT level. Thus by combining TDDFT with an accurate modeling of the environment, TD-DFT is positioned as the standout protocol to model photoinduced dynamics in DNA-based aggregates and multimers.

Gas-Phase Peroxyl Radical Recombination Reactions: AComputational Study of Formation and Decomposition of Tetroxides.

The recombination (“dimerization”) of peroxyl radicals (RO2•) is one of the pathways suggested in the literature for the formation of peroxides (ROOR′, often referred to as dimers or accretion products in the literature) in the atmosphere. It is generally accepted that these dimers play a major role in the first steps of the formation of submicron aerosol particles. However, the precise reaction pathways and energetics of RO2• + R′O2• reactions are still unknown. In this work, we have studied the formation of tetroxide intermediates (RO4R′): their formation from two peroxyl radicals and their decomposition to triplet molecular oxygen (3O2) and a triplet pair of alkoxyl radicals (RO•). We demonstrate this mechanism for several atmospherically relevant primary and secondary peroxyl radicals. The potential energy surface corresponds to an overall singlet state. The subsequent reaction channels of the alkoxyl radicals include, but are not limited to, their dimerization into ROOR′. Our work considers the multiconfigurational character of the tetroxides and the intermediate phases of the reaction, leading to reliable mechanistic insights for the formation and decomposition of the tetroxides. Despite substantial uncertainties in the computed energetics, our results demonstrate that the barrier heights along the reaction path are invariably small for these systems. This suggests that the reaction mechanism, previously validated at a multireference level only for methyl peroxyl radicals, is a plausible pathway for the formation of aerosol-relevant larger peroxides in the atmosphere.

Stereoinversion of tetrahedral p-block element hydrides.

The potential energy surfaces of 15 tetrahedral p-block element hydrides were screened on the multireference level. It was addressed whether stereoinversion competes against other reactions, such as reductive H2-elimination or hydride loss, and if so, along which pathway the stereomutation occurs. Importantly, stereoinversion transition structures for the ammonium cation (C4v) and the tetrahydridoborate anion (Cs) were identified for the first time. Revisiting methane's Cs symmetric inversion transition structure with the mHEAT+ protocol revealed an activation enthalpy for stereoinversion, in contrast to all earlier studies, which is 5 kJ mol-1 below the C-H bond dissociation enthalpy. Square planar structures were identified lowest in energy only for the inversion of AlH4 -, but a novel stepwise Cs-inversion was discovered for SiH4 or PH4 +. Overall, the present contribution delineates essentials of the potential energy surfaces of p-block element hydrides, while structure-energy relations offer design principles for the synthetically emerging field of structurally constrained compounds.

Calibration of energy density functionals with deformed nuclei

Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or multireference level), the predictive power of the theory depends strongly on how the parameters of the energy functionals have been calibrated with experimental data. Expanded algorithms and computing power have enabled recent optimization protocols to include data in deformed nuclei in order to optimize the coupling constants of the energy functional. The primary motivation of this work is to test the robustness of such protocols with respect to some of the technical and numerical details of the underlying calculations, especially when the calibration explores a large parameter space. To this end, we quantify the effect of these uncertainties on both the optimization and statistical emulation of composite objective functions. We also emphasize that Bayesian calibration can provide better estimates of the theoretical errors used to define objective functions.

Ring coupled cluster doubles at the multireference level.

A ring approximation within an internally contracted multireference (MR) Coupled Cluster (CC) framework is worked out and tested. Derivation of equations utilizes MR based, generalized normal ordering and the corresponding generalized Wick-theorem (MR-GWT). Contractions among cluster operators are avoided by adopting a normal ordered exponential ansatz. The original version of the MR ring CC doubles (MR-rCCD) equations [Á. Szabados and Á. Margócsy, Mol. Phys. 115, 2731 (2017)] is rectified in two aspects. On the one hand, over-completeness of double excitations is treated by relying on the concept of frames. On the other hand, restriction on the maximal cumulant rank is lifted from two to four. This is found essential for obtaining reliable correlation corrections to the energy. The MR function underlying the approach is provided by the Generalized Valence Bond (GVB) model. The pair structure of the reference ensures a fragment structure of GVB cumulants. This represents a benefit when evaluating cumulant contractions appearing as a consequence of MR-GWT. In particular, cumulant involving terms remain less expensive than their traditional, pair-contracted counterpart, facilitating an O(N6) eventual scaling of the proposed MR-rCCD method. Pilot applications are presented for covalent bond breaking, deprotonation energies, and torsional potentials.

A single‐ and multireference study on CH (X2Π) reaction with O2 ()

AbstractThis study focuses on the dynamics of the reaction of CH (X2Π) radicals with O2 () in the presence of N2, as the bath gas molecule. A general description of the reaction mechanism was investigated by employing molecular dynamics simulations with an implanted reactive force field under a realistic system that could account for both reactive and nonreactive collisions. This tool helped to provide an initial guess for the reaction mechanism to unravel some information about the potential reaction paths and secondary products. The initial guess was used to explore the detailed reaction mechanism quantum mechanically over the lowest doublet and quadruplet surfaces at the single‐reference level of CCSD(T)/aug‐cc‐pVTZ and the multireference level of CASPT2/aug‐cc‐pVTZ. The theoretical bimolecular reaction rate constants were computed by solving a master equation over the lowest doublet single‐ and multireference potential energy surfaces. The calculated rate constant for loss of the reactants and formation of the HCO and CO products declared noticeable agreement with the available experimental rate constants. HCO, CO, and CO2 are identified as the main products along with the following single‐reference (multireference)‐based product branching ratios at 450 K: [triangular 1CO2 + 2H and linear 1CO2 + 2H]: 69.1% (79.3%); 1CO + 2OH: 18.2% (15.0%); 2HCO + 3O: 12.7% (5.7%). Both single‐ and multireference calculations demonstrated reliable chemical kinetics results, in the context of the available experimental rate constants and resulted in fair agreement with the experimentally reported branching ratios.

Nuclear Segmentation of Glioblastoma Multiforme Cells by Multireference Level Set

Histological tissue section consists of rich information about cell type, cellular morphology, cell state and health etc. which is very important for clinical diagnosis and therapy. Automated analysis provides insights of tumor subtypes. Since tumor sections are collected from different laboratory, some issues arises called technical and biological variations. In this paper we developed an approach for nuclear segmentation on tumours histological section, which addresses problems of processing tissues at different laboratory under microscope. Eventually, the resolution is formulated in multi reference level set frame. Experimental results show performance of proposed method.

No-core configuration-interaction model for the isospin- and angular-momentum-projected states

[Background] Single-reference density functional theory is very successful in reproducing bulk nuclear properties like binding energies, radii, or quadrupole moments throughout the entire periodic table. Its extension to the multi-reference level allows for restoring symmetries and, in turn, for calculating transition rates. [Purpose] We propose a new no-core-configuration-interaction (NCCI) model treating properly isospin and rotational symmetries. The model is applicable to any nucleus irrespective of its mass and neutron- and proton-number parity. It properly includes polarization effects caused by an interplay between the long- and short-range forces acting in the atomic nucleus. [Methods] The method is based on solving the Hill-Wheeler-Griffin equation within a model space built of linearly-dependent states having good angular momentum and properly treated isobaric spin. The states are generated by means of the isospin and angular-momentum projection applied to a set of low-lying (multi)particle-(multi)hole deformed Slater determinants calculated using the self-consistent Skyrme-Hartree-Fock approach. [Results] The theory is applied to calculate energy spectra in N~Z nuclei that are relevant from the point of view of a study of superallowed Fermi beta-decays. In particular, a new set of the isospin-symmetry-breaking corrections to these decays is given. [Conclusions] It is demonstrated that the NCCI model is capable to capture main features of low-lying energy spectra in light and medium-mass nuclei using relatively small model space and without any local readjustment of its low-energy coupling constants. Its flexibility and a range of applicability makes it an interesting alternative to the conventional nuclear shell model.

O + C2H4 potential energy surface: lowest-lying singlet at the multireference level

In previous studies (West et al. in J Phys Chem A 113(45):12663, 2009; West et al. in Theor Chem Acc 131:1123, 2012), the lowest-lying O(3P) + C2H4 and singlet PES near the ·CH2CH2O· biradical were extensively explored at several levels of theory. In this work, the lowest-lying O(1D) + C2H4 PES is further examined at the multiconfigurational self-consistent field (MCSCF), MRMP2, CR-CC(2,3), GVB-PP, and MR-AQCC levels. This study aims to provide a detailed comparison of these different levels of theory for this particular system. In particular, many reactions for this system involve multiple bond rearrangements and require various degrees of both non-dynamic and dynamic correlation for reasonable energetics. As a result of this variety, coupled cluster results parallel but do not always match up with multireference results as previously anticipated. In the case of the CH2CHOH → oxirane pathway, MCSCF results show the possibility of a two-step mechanism rather than an elementary step, but the case is very difficult to elucidate. In the case of the CH3C:–OH → H2CCO + H2 pathway, a non-traditional NEB MEP at the GVB-PP level and MR-AQCC stationary point determination illustrate the need for a complex treatment of this surface.

Multireference level set for the characterization of nuclear morphology in glioblastoma multiforme.

Histological tissue sections provide rich information and continue to be the gold standard for the assessment of tissue neoplasm. However, there are a significant amount of technical and biological variations that impede analysis of large histological datasets. In this paper, we have proposed a novel approach for nuclear segmentation in tumor histology sections, which addresses the problem of technical and biological variations by incorporating information from both manually annotated reference patches and the original image. Subsequently, the solution is formulated within a multireference level set framework. This approach has been validated on manually annotated samples and then applied to the TCGA glioblastoma multiforme (GBM) dataset consisting of 440 whole mount tissue sections scanned with either a 20 × or 40 × objective, in which, each tissue section varies in size from 40k × 40k pixels to 100k × 100k pixels. Experimental results show a superior performance of the proposed method in comparison with present state of art techniques.

O + C2H4 potential energy surface: excited states and biradicals at the multireference level

The focus of this study is to understand the multiconfigurational nature of the biradical species involved in the early reaction paths of the oxygen plus ethylene PES. In previous work (J Phys Chem A 113, 12663, 2009), the lowest-lying O(3P) + C2H4 PES was extensively explored at the MCSCF, MRMP2, and MR-AQCC levels of theory. In the current work, ground and excited, triplet- and singlet-state reaction paths for the initial addition of oxygen to ethylene were found at the MCSCF and MRMP2 levels along with five singlet pathways near the ·CH2CH2O· biradical at the MCSCF, MRMP2, and CR-CC(2,3) levels. One of these five paths can lead to the CH2CO + H2 products from CH3CHO rather than from the ·CH2CH2O· biradical, and this pathway was investigated with a variety of CAS sizes. To provide further comparison between the MRMP2 and CR-CC(2,3) levels, MR-AQCC single-point energies and optimizations were performed for select geometries. After the initial exploration of this region of the surface, the lowest singlet–triplet surface crossings were explicitly determined at the MCSCF level. Additional MRMP2 calculations were performed to demonstrate the limitations of single-state perturbation theory in this biradical region of the PES, and SO-MCQDPT2 single-point energies using SA MCSCF were calculated on a grid of geometries around the primary surface crossing. In particular, these calculations were examined to determine a proper active space and a physically reasonable number of electronic states. The results of this examination show that at least four states must be considered to represent this very complex region of the PES.

First principles study of the ground and excited states of FeO, FeO+, and FeO−

Through a variety of highly correlated methods combined with large basis sets we have studied the electronic structure of FeO, FeO(+), and FeO(-). In particular, we have constructed complete potential energy curves for 48, 24, and 4 states for the FeO, FeO(+), and FeO(-) species, respectively, at the multireference level of theory. For all states examined we report energetics, common spectroscopic parameters, and dipole moments. Overall our results are in good agreement with experiment, but we have encountered as well interesting differences between experiment and theory deserving further investigation.

Columbus—a program system for advanced multireference theory calculations

AbstractThe COLUMBUS Program System allows high‐level quantum chemical calculations based on the multiconfiguration self‐consistent field, multireference configuration interaction with singles and doubles, and the multireference averaged quadratic coupled cluster methods. The latter method includes size‐consistency corrections at the multireference level. Nonrelativistic (NR) and spin–orbit calculations are available within multireference configuration interaction (MRCI). A prominent feature of COLUMBUS is the availability of analytic energy gradients and nonadiabatic coupling vectors for NR MRCI. This feature allows efficient optimization of stationary points and surface crossings (minima on the crossing seam). Typical applications are systematic surveys of energy surfaces in ground and excited states including bond breaking. Wave functions of practically any sophistication can be constructed limited primarily by the size of the CI expansion rather than by its complexity. A massively parallel CI step allows state‐of‐the art calculations with up to several billion configurations. Electrostatic embedding of point charges into the molecular Hamiltonian gives access to quantum mechanical/molecular mechanics calculations for all wave functions available in COLUMBUS. The analytic gradient modules allow on‐the‐fly nonadiabatic photodynamical simulations of interesting chemical and biological problems. Thus, COLUMBUS provides a wide range of highly sophisticated tools with which a large variety of interesting quantum chemical problems can be studied. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 191‐199 DOI: 10.1002/wcms.25This article is categorized under: Software > Quantum Chemistry

O(3P) + C2H4 Potential Energy Surface: Study at the Multireference Level

The O((3)P) + C(2)H(4) reaction provides a crucial, initial understanding of hydrocarbon combustion. In this work, the lowest-lying triplet potential energy surface is extensively explored at the multiconfiguration self-consistent field (MCSCF) and MRMP2 levels with a preliminary surface crossing investigation; and in cases that additional dynamical correlation is necessary, MR-AQCC stationary points are also determined. In particular, a careful determination of the active space along the intrinsic reaction pathway is necessary; and in some cases, more than one active space must be explored for computational feasibility. The resulting triplet potential energy surface geometries mostly agree with geometries from methods using single determinant references. However, although the selected multireference methods lead to energetics that agree well, only qualitative agreement was found with the energetics from the single determinant reference methods. Challenges and areas of further exploration are discussed.

Large systems at ab initio multireference level: A cheap treatment thanks to a division into fragments

Thanks to the use of localized orbitals and the subsequent possibility of neglecting long-range interactions, the linear-scaling methods have allowed to treat large systems at ab initio level. However, the limitation of the number of active orbitals in a complete active space self consistent-field (CASSCF) calculation remains unchanged. The method presented in this paper suggests to divide the system into fragments containing only a small number of active orbitals. Starting from a guess wave function, each orbital is optimized in its corresponding fragment, in the presence of the other fragments. Once all the fragments have been treated, a new set of orbitals is obtained. The process is iterated until convergence. At the end of the calculation, a set of active orbitals is obtained, which is close to the exact CASSCF solution, and an accurate CASSCF energy can be estimated.

Registering the Amica electronic structure code in the Extensible Computational Chemistry Environment

We describe the integration and use of the Amica software package ("Atoms & Molecules In Chemical Accuracy") within the Extensible Computational Chemistry Environment (Ecce). Amica is capable of accurately solving the electronic Schrodinger equation of small atoms and molecules using terms that are linear in the interelectronic distances, r(12), on multireference level of theory, but it requires expert knowledge to configure and execute its algorithms. Ecce is a comprehensive suite of tools that support the computational chemistry research processes of computation setup, execution, and analysis through a convenient graphical user interface. Additionally, Ecce was architected with mechanisms to integrate alternative electronic structure codes. The successful integration of Amica within Ecce validates the architecture of the latter and brings the high-accuracy capabilities of Amica to a wider audience.

2,3-Didehydro-1,4-benzoquinone. A quantum thermochemical study

Correlated electronic structure calculations at single and multireference levels of theory have been carried out for several neutral and radical anion electronic states of 2,3-didehydro-1,4-benzoquinone, a quinone analog of o-benzyne. The molecule is predicted to be a ground-state singlet (1A1) with a 298 K heat of formation of 200.6 kJ mol–1, a heat of hydrogenation (1 equiv.) of –323.5 kJ mol–1, and an electron affinity of 1.95 eV; the latter quantity is in good agreement with an experimental value of 1.86 eV. The lowest energy triplet (13B2), derived from an in-plane π→π* excitation, is predicted to be 2.23 eV higher in energy than the singlet. The singlet and triplet states have biradical stabilization energies of 2.01 and –0.22 eV, respectively. Other triplet states derived from excitations involving the out-of-plane π system are also examined. A recent photoelectron spectrum of the radical anion is interpreted, and a poorly resolved feature is proposed to correspond to the singlet (1A1) ground state of 2,6-didehydro-1,4-benzoquinone. Technical aspects governing the suitability of various levels of theory are also discussed.

The averaged coupled-pair functional (ACPF): A size-extensive modification of MR CI(SD)

To account for unlinked-cluster effects at the multireference level, we propose a generalization (MR ACPF) of the “coupled-pair functional” (CPF). Comparison with full CI results for BeH 2, H 2O, CH 2, O 2 and the five lowest-lying 2A 1 states of CH 2 +, shows the superiority of MR ACPF over MR CI(SD) and MR LCCM. Large-scale calculations for F 2 (up to a [7s5p3d2flg] CGTO basis set and 6 references) show better convergence to the experimental D e values on basis set and reference space extension than does MR CI(SD).

SCF-CI calculations of the potential energy curve and one-electron property curves of theX1II ground state of NO

The energy and many important one-electron properties of the nitric oxide molecule in the ground state (X 2II) have been evaluated at various internuclear separations near the equilibrium geometry, using the direct CI method and the Graphical Unitary Group (GUG) method at both single- and multi-reference level. The one-electron properties thus obtained (and vibrationally averaged using Dunham analysis) include the electric field gradients (at both the O and N nuclei) and the multipole moments from dipole to hexadecapole moment (all with respect to the centre of mass).