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DOE OSTI2024

Ab initio exploration of low–lying electronic states of linear and bent MNX + (M = Ca, Sr, Ba, Ra; X = O, S, Se, Te, Po) and their origins

High-level multireference and coupled cluster quantum calculations were employed to analyze low-lying electronic states of linear-MNX + and side-bonded-M[NX] + (M = Ca, Sr, Ba, Ra; X = O, S, Se, Te, Po) species. Their full potential energy curves (PECs), dissociation energies (D e s), geometric parameters, excitation energies (T e s), and harmonic vibrational frequencies (ω e s) are reported. The first three chemically bound electronic states of MNX + and M[NX] + are 3 Σ – , 1 Δ, 1 Σ + and 3 A", 1 A', 1 A", respectively. The 3 Σ – , 1 Δ, 1 Σ + of MNX + originate from the M + ( 2 D) + NX( 2 Π) fragments, whereas the 3 A", 1 A', 1A" states of M[NX] + dissociate to M + ( 2 S) + NX( 2 Π) as a result of avoided crossings. The MNX + and M[NX] + are real minima on the potential energy surface and their interconversions are possible. The M 2+ NX – /M 2+ [NX] – ionic structure is an accurate representation for their low-lying electronic states. The D e s of MNX + species were found to depend on the dipole moment (μ) of the corresponding NX ligands and a linear relationship between these two parameters was observed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

A benchmark study of electronic excitation energies, transition moments, and excited-state energy gradients on the nicotine molecule

In this work, we report a comparative study of computed excitation energies, oscillator strengths, and excited-state energy gradients of (S)-nicotine, chosen as a test case, using multireference methods, coupled cluster singles and doubles, and methods based on time-dependent density functional theory. This system was chosen because its apparent simplicity hides a complex electronic structure, as several different types of valence excitations are possible, including n-π{sup *}, π-π{sup *}, and charge-transfer states, and in order to simulate its spectrum it is necessary to describe all of them consistently well by the chosen method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Propargyl + O 2 Reaction in Helium Droplets: Entrance Channel Barrier or Not?

A combination of liquid He droplet experiments and multireference electronic structure calculations is used to probe the potential energy surface for the reaction between the propargyl radical and O 2 . Infrared laser spectroscopy is used to probe the outcome of the low temperature, liquid He-mediated reaction. Bands in the spectrum are assigned to the acetylenic CH stretch (ν 1 ), the symmetric CH 2 stretch (ν 2 ), and the antisymmetric CH 2 stretch (ν 13 ) of the trans-acetylenic propargyl peroxy radical (•OO—CH 2 —C≡CH). The observed band origins are in excellent agreement with previously reported anharmonic frequency computations for this species. The Stark spectrum of the ν 1 band provides further evidence that the reaction leads only to the trans -acetylenic species. There are no other bands in the CH 2 stretching region that can be attributed to any of the other three propargyl peroxy isomers/conformers that are predicted to be minimum energy structures ( gauche -acetylenic, cis -allenic, and trans -allenic). There is also no evidence for the kinetic stabilization of a van der Waals complex between propargyl and O 2 . A combination of multireference and coupled-cluster electronic structure calculations is used to probe the potential energy surface in the neighborhood of the transition state connecting reactants with the acetylenic adduct. The multireference based evaluation of the doublet-quartet splitting added to the coupled-cluster calculated quartet state energies yields what are likely the most accurate predictions for the doublet potential curve. As a result, this calculation suggests that there is no saddle point for the addition process, in agreement with the experimental observations. Other calculations suggest the possible presence of a small submerged barrier.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Threshold Ionization Spectroscopy and Theoretical Calculations of LnO (Ln = La and Ce)

Mass-analyzed threshold ionization (MATI) spectroscopy was used to measure the vibronic spectra of LnO (Ln = La and Ce). Single-reference coupled cluster and relativistic multireference configuration calculations were carried out to compare with the measured vibronic energies. The spectrum of LaO displays a single vibronic band system, while that of CeO shows multiple ones. The ionization energies of LaO and CeO are measured as 5.2446 (6) and 5.3332(6) eV, respectively, which are a hundredfold improvement over the literature values. The vibrational energies of the neutral molecule and corresponding ion reveal the charge effect on the metal-oxygen bond of both species. The single band system in the spectrum of LaO arises from the transition of the ground state of the neutral molecule with the La(6s 1 )O(2p 6 ) valence configuration to the ground state of the singly charged ion with the La(6s o )O(2p 6 ) configuration. Here, the multiple band systems in the spectrum of CeO are attributed to the spin-orbit coupling for the Ce(4f 1 6s 1 )O(2p 6 ) configuration of the neutral molecule and an excited state for the Ce(4f 1 )O(2p 6 ) configuration of the ion.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

COLUMBUS─An Efficient and General Program Package for Ground and Excited State Computations Including Spin–Orbit Couplings and Dynamics

The COLUMBUS program system provides the tools for performing high-level multireference (MR) computations, including the multireference configuration interaction (MRCI) method and its multireference averaged quadratic coupled cluster (MR-AQCC) extension, allowing computations on a wide range of fascinating atomic and molecular systems, including the treatment of open-shells and complicated excited state phenomena. The inclusion of spin−orbit coupling (SOC) directly within the MRCI step enables the description of systems containing heavy elements, such as lanthanides and actinides, whose properties are strongly influenced by SOC. Analytic energy gradients and nonadiabatic couplings at the correlated MRCI level provide the foundation for a variety of dynamics studies, giving insight into ultrafast photochemistry. New and ongoing method developments in COLUMBUS include the computation of spin densities, improved descriptions of ionic states, enhancements to the AQCC method, and the porting of COLUMBUS to graphical processing units (GPUs). New external interfaces enable an enhanced description of electronic resonances and molecules in strong laser fields. This work highlights these new developments while providing a detailed account of the diverse applications of COLUMBUS in recent years.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Thorium Monosilicide, ThSi: An Experimental and Theoretical Study

The present theoretical and experimental combination study investigates the ThSi molecule in detail. Computationally, we utilized high-level multireference and coupled-cluster levels of theory conjoined with large correlation consistent basis sets to study a series of electronic and spin–orbit states of ThSi. Here, we report potential energy curves (PECs), electron configurations at equilibrium distances, spectroscopic constants, energetics, and spin–orbit coupling effects for 16 electronic states of ThSi. The studied 16 electronic states are arranged tightly within 0.9 eV, highlighting the complexity of the electronic spectrum of ThSi. The ground electronic state of ThSi is a single-reference 1 1 Σ + state that derives from the 1σ 2 2σ 2 1π 4 electronic configuration. The Ω = 0 + spin–orbit ground state of ThSi is composed of 1 1 Σ + (47%) and 13Π (44%) electronic states. Our measured bond energy (D0) of ThSi, obtained using resonant two-photon ionization (R2PI) spectroscopy is 3.146(4) eV, where the assigned error limit is given in parentheses in units of the last quoted digits. The computed D0 of ThSi (Ω = 0 + ) at the CBS-C-CCSD(T)-δT(Q)-δDK-δSO level (3.181 eV) is in good agreement with the experimental value. Our derived enthalpy of formation for ThSi, Δ f H 0K o (ThSi(g)), is 971.8(6.0) kJ/mol. Finally, we have performed density functional theory (DFT) calculations for ThSi(1 1 Σ + ) using 16 exchange correlation functionals that span multiple rungs of “Jacob’s ladder” of density functional approximation (DFA) to assess the DFT errors on D 0 , r e , and ω e of ThSi with respect to experimental and ab initio coupled-cluster values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Ground and excited state properties of ThB − and ThB: a theoretical study

In the present work, we studied a series of electronic and spin–orbit states of ThB − and ThB using high-level multireference and coupled-cluster theories. We report the potential energy curves (PECs), equilibrium electron configurations, spectroscopic constants, energetics, and spin–orbit coupling effects of 17 and 19 electronic states of ThB − and ThB, respectively. The ground state of ThB − is a single-reference 1 3 Π with a 1σ 2 2σ 2 3σ 1 1π 3 electron configuration. Detachment of an electron from the doubly occupied 1π orbital of ThB − (1 3 Π) produces the single-reference ground electronic state of ThB (1 4 Σ − ). The ground spin–orbit states of ThB − and of ThB are 1 3 Π + 0 and 1 4 Σ − 3/2 , respectively. The vertical electron detachment energy (VDE) of ThB − and the adiabatic electron attachment energy (AEA) of ThB at our largest CBS-C-CCSD(T)+δT(Q)+δSO (complete basis set effect, spin–orbit effect, and triple and perturbative quadruple electron correlation effect added coupled-cluster theory with single, double, and perturbative triple excitations) level are 1.473 eV and 1.459, respectively. The reaction of Th( 3 F) + B( 2 P o ) produces the ground state of ThB with a bond energy of 2.843 eV. Finally, we estimated a heat of formation, Δ H 0 f (298 K), of 891.01 kJ mol −1 for the ThB molecule. The high-level findings of this work are expected to aid and motivate future experimental spectroscopic investigations of ThB and ThB − species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

A comparison of neutral and charged species of one- and two-dimensional models of graphene nanoribbons using multireference theory

This study examines the dependence of the polyradical character of charged quasi-linear n-acenes and two-dimensional periacenes used as models for graphene nanoribbons in comparison to the corresponding neutral compounds. For this purpose, high-level ab initio calculations have been performed using the multireference averaged quadratic coupled cluster theory. Vertical ionization energies and electron affinities have been computed. Systematic tests show that the dependence on chain length of these quantities can be obtained from a consideration of the π system only and that remaining contributions coming from the σ orbitals or extended basis sets remain fairly constant. Using best estimate values, the experimental values for the ionization energy of the acene series can be reproduced within 0.1 eV and the experimental electron affinities within 0.4 V. The analysis of the natural orbital occupations and related unpaired electron densities shows that the ionic species exhibit a significant decrease in polyradical character and thus an increased chemical stability as compared to the neutral state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Solutions of the two-dimensional Hubbard model: Benchmarks and results from a wide range of numerical algorithms

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Furthermore, cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Electronic structure of Li 1,2,3 +,0,– and nature of the bonding in Li 2,3 +,0,–

Abstract The current study of the small lithium molecules Li 2 +,0,− and Li 3 +,0,− focuses on the nature of the bonding in these molecules as well as their structures and energetics (bond energies, ionization energies, and electron affinities). Valence CASSCF (2s,2p) calculations incorporate nondynamical electron correlation in the calculations, while the corresponding multireference configuration interaction and coupled cluster calculations incorporate dynamical electron correlation. Treatment of nondynamical correlation is critical for properly describing the Li 2,3 +,0,− molecules as well as the Li − anion with dynamical correlation, in general, only fine‐tuning the predictions. All lithium molecules and ions are bound, with the Li 3 + and Li 2 + ions being the most strongly bound, followed by Li 3 − , Li 2 , Li 2 − and Li 3 . The minimum energy structures of Li 3 +,0,− are, respectively, an equilateral triangle, an isosceles triangle, and a linear structure. The results of SCGVB calculations are analyzed to obtain insights into the nature of the bonding in these molecules. An important finding of this work is that interstitial orbitals, a concept first put forward by McAdon and Goddard in 1985, play an essential role in the bonding of all lithium molecules considered here except for Li 2 . The interstitial orbitals found in the Li 3 +,0 molecules likely give rise to the non‐nuclear attractors/maxima observed in these molecules.

Chemistry↗

DOE OSTI2014

Analysis of and remedies for unphysical ground states of the multireference averaged coupled-pair functional

A Multireference Configuration Interaction (MRCI) wavefunction includes both static and dynamic electron correlation. MRCI's well-known flaw, a lack of size extensivity, can be ameliorated with the Multireference Averaged Coupled-Pair Functional (MRACPF). However, the original MRACPF is frequently unstable, sometimes producing unphysical results. The more Multireference Averaged Quadratic Coupled-Cluster and MRACPF2 functionals also occasionally exhibit unphysical behavior. We find that these instabilities are avoided crossings with unphysical solutions to the MRACPF equations. We present two approaches to avoid the undesirable unphysical solutions.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2014

Static electric dipole polarizabilities of An{sup 5+/6+} and AnO{sub 2}{sup +/2+} (An = U, Np, and Pu) ions

The parallel components of static electric dipole polarizabilities have been calculated for the lowest lying spin-orbit states of the penta- and hexavalent oxidation states of the actinides (An) U, Np, and Pu, in both their atomic and molecular diyl ion forms (An{sup 5+/6+} and AnO{sub 2}{sup +/2+}) using the numerical finite-field technique within a four-component relativistic framework. The four-component Dirac-Hartree-Fock method formed the reference for MP2 and CCSD(T) calculations, while multireference Fock space coupled-cluster (FSCC), intermediate Hamiltonian Fock space coupled-cluster (IH-FSCC) and Kramers restricted configuration interaction (KRCI) methods were used to incorporate additional electron correlation. It is observed that electron correlation has significant (∼5 a.u.{sup 3}) impact upon the parallel component of the polarizabilities of the diyls. To the best of our knowledge, these quantities have not been previously reported and they can serve as reference values in the determination of various electronic and response properties (for example intermolecular forces, optical properties, etc.) relevant to the nuclear fuel cycle and material science applications. The highest quality numbers for the parallel components (α{sub zz}) of the polarizability for the lowest Ω levels corresponding to the ground electronic states are (in a.u.{sup 3}) 44.15 and 41.17 for UO{sub 2}{sup +} and UO{sub 2}{sup 2+}, respectively, 45.64 and 41.42 for NpO{sub 2}{sup +} and NpO{sub 2}{sup 2+}, respectively, and 47.15 for the PuO{sub 2}{sup +} ion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1991

The energy separation between the classical and nonclassical isomers of protonated acetylene - An extensive study in one- and n-particle space saturation

The energy separation between the classical and nonclassical forms of protonated acetylene has been reinvestigated in light of the recent experimentally deduced lower bound to this value of 6.0 kcal/mol. The objective of the present study is to use state-of-the-art ab initio quantum mechanical methods to establish this energy difference to within chemical accuracy (i.e., about 1 kcal/mol). The one-particle basis sets include up to g-type functions and the electron correlation methods include single and double excitation coupled-cluster (CCSD), the CCSD(T) extension, multireference configuration interaction, and the averaged coupled-pair functional methods. A correction for zero-point vibrational energies has also been included, yielding a best estimate for the energy difference between the classical and nonclassical forms of 3.7 + or - 1.3 kcal/mol.

Lindh, Roland↗

DOE OSTI2015

Ab Initio Unimolecular Reaction Kinetics of CH 2 C(＝)OCH 3 and CH 3 C(＝O)OCH 2 Radicals

The unimolecular dissociation and isomerization kinetics of the methyl ester combustion intermediates methoxycarbonylmethyl (CH 2 C(＝O)OCH 3 ) and acetyloxylmethyl (CH 3 C(＝O)OCH 2 ) are theoretically investigated using high-level ab initio methods and the Rice–Ramsperger–Kassel–Marcus (RRKM)/master equation (ME) theory. Potential energy surfaces (PESs) are obtained using coupled cluster singles and doubles with perturbative triples correction (CCSD(T)), multireference singles and doubles configuration interaction (MRSDCI) with the Davidson–Silver (DS) correction, and multireference averaged coupled pair functional (MRACPF2) theory. The transition states exhibit high T1 diagnostics in coupled cluster calculations, suggesting the need for a multireference correlated wave function treatment. MRSDCI+DS and MRACPF2 capture their multiconfigurational character well, yielding lower barrier heights than CCSD(T) for these reactions. Additionally, the rate coefficients are computed using the RRKM/ME theory over a 500–2500 K temperature range and at a pressure range of 0.01 atm to the high-pressure limit. The temperature- and pressure-dependent rate coefficients are given in modified Arrhenius expressions. The β-scission of CH 2 C(＝O)OCH 3 is predicted to have a much higher barrier than the corresponding isomerization reaction and the β-scission of CH 3 C(＝O)OCH 2 . Consequently, the rate coefficients for β-scission of CH 2 C(＝O)OCH 3 are the smallest among the three reactions and the isomerization followed by decomposition to CH 3 C(＝O) and HCHO is the dominant reaction pathway for CH 2 C(＝O)OCH 3 . Furthermore, both radicals CH 2 C(＝O)OCH 3 and CH 3 C(＝O)OCH 2 are predicted to mainly decompose to CH 3 C(＝O) + HCHO rather than to the bimolecular product CH 2 C(＝O) + CH 3 O. A newly developed MA combustion mechanism, using our theoretical rate coefficients for the MA-related reactions, predicts combustion properties in good agreement with available experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Synergy between pair coupled cluster doubles and pair density functional theory

Pair coupled cluster doubles (pCCD) has been recently studied as a method capable of accounting for static correlation with low polynomial cost. We present three combinations of pCCD with Kohn–Sham functionals of the density and on-top pair density (the probability of finding two electrons on top of each other) to add dynamic correlation to pCCD without double counting. With a negligible increase in computational cost, these pCCD+DFT blends greatly improve upon pCCD in the description of typical problems where static and dynamic correlations are both important. We argue that—as a black-box method with low scaling, size-extensivity, size-consistency, and a simple quasidiagonal two-particle density matrix—pCCD is an excellent match for pair density functionals in this type of fusion of multireference wavefunctions with DFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Electronic properties of ThC − and ThC

The present study investigates the properties of low-lying states of ThC − and ThC using correlated wave function theories. To this end, we employed multireference calculations and various coupled-cluster approaches in combination with large correlation-consistent basis sets. These methods were applied to examine potential energy curves (PECs), electron configurations, energetics, spectroscopic constants, and spin–orbit coupling effects for 9 states of ThC − and 18 states of ThC. The ground states of ThC − and ThC were identified as single-reference 2 Σ + 1/2 (I) and $^3Σ^+_{0^-} (\textrm{I})$, respectively. Electron detachment from the 7s orbital of the Th center in ThC − [ 2 Σ + (I); 1σ 2 2σ1 3 σ2 1 π 4 ] yields ThC [ 3 Σ + (I); 1σ 2 2σ 1 3σ 1 1π 4 ]. The calculated adiabatic detachment energy (ADE) and vertical detachment energy (VDE) for this process are 1.591 and 1.604 eV, respectively. Furthermore, the dissociation energy (D 0 ) of ThC [$^3Σ^+_{0^-} (\textrm{I})$] is predicted to be 5.099 eV. The standard enthalpy of formation, $ΔH^{°}_{\textrm{f}}$ (298 K), of ThC is estimated to be 822.52 ± 6 kJ mol −1 .

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1996

An ab initio benchmark study of the H + CO --> HCO reaction

The H + CO --> HCO reaction has been characterized with correlation consistent basis sets at five levels of theory in order to benchmark the sensitivities of the barrier height and reaction ergicity to the one-electron and n-electron expansions of the electronic wave function. Single and multireference methods are compared and contrasted. The coupled cluster method RCCSD(T) was found to be in very good agreement with Davidson-corrected internally-contracted multireference configuration interaction (MRCI+Q). Second-order Moller-Plesset perturbation theory (MP2) was also employed. The estimated complete basis set (CBS) limits for the barrier height (in kcal/mol) for the five methods, including harmonic zero-point energy corrections, are MP2, 4.66; RCCSD, 4.78; RCCSD(T), 4.15; MRCI, 5.10; and MRCI+Q, 4.07. Similarly, the estimated CBS limits for the ergicity of the reaction are: MP2, -17.99; RCCSD, -13.34; RCCSD(T), -13.79; MRCI, -11.46; and MRCI+Q, -13.70. Additional basis set explorations for the RCCSD(T) method demonstrate that aug-cc-pVTZ sets, even with some functions removed, are sufficient to reproduce the CBS limits to within 0.1-0.3 kcal/mol.

NASA Discipline Exobiology↗

NASA NTRS1992

Ab initio multireference study of the BN molecule

The lowest 1Sigma(+) and 3Pi states of the BN molecule are studied using multireference configuration interaction (MRCI) and averaged coupled-pair functional (ACPF) methods and large atomic natural orbital (ANO) basis sets, as well as several coupled cluster methods. Our calculations strongly support a 3Pi ground state, but the a1Sigma(+) state lies only 381 +/- 100/cm higher. The a1Sigma(+) state wave function exhibits strong multireference character and, consequently, the predictions of the perturbationally-based single-reference CCSD(T) coupled cluster method are not as reliable in this case as the multireference results. The theoretical predictions for the spectroscopic constants of BN are in good agreement with experiment for the Chi3Pi state, but strongly suggest a misassignment of the fundamental vibrational frequency for the a1Sigma(+) state.

Martin, J. M. L.↗