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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Towards a spectroscopically accurate set of potentials for heavy hydride laser cooling candidates: Effective core potential calculations of BaH

BaH (and its isotopomers) is an attractive molecular candidate for laser cooling to ultracold temperatures and a potential precursor for the production of ultracold gases of hydrogen and deuterium. The theoretical challenge is to simulate the laser cooling cycle as reliably as possible and this paper addresses the generation of a highly accurate ab initio {sup 2}Σ{sup +} potential for such studies. The performance of various basis sets within the multi-reference configuration-interaction (MRCI) approximation with the Davidson correction is tested and taken to the Complete Basis Set (CBS) limit. It is shown that the calculated molecular constants using a 46 electron effective core-potential and even-tempered augmented polarized core-valence basis sets (aug-pCVnZ-PP, n = 4 and 5) but only including three active electrons in the MRCI calculation are in excellent agreement with the available experimental values. The predicted dissociation energy D{sub e} for the X{sup 2}Σ{sup +} state (extrapolated to the CBS limit) is 16 895.12 cm{sup −1} (2.094 eV), which agrees within 0.1% of a revised experimental value of <16 910.6 cm{sup −1}, while the calculated r{sub e} is within 0.03 pm of the experimental result.

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

Electronic structure theory with molecular point group symmetries on quantum annealers

Quantum computation has the potential to revolutionize quantum chemistry through major speedups in computation times and an exponential reduction in computational resources. Here, we combine the symmetry-adapted Jordan–Wigner encoding based on the full Boolean symmetry group $\mathbb{Z}$$^{k}_{2}$ with our new implementation of the Xia–Bian–Kais (XBK) method for improving the efficiency of electronic structure theory calculations on quantum annealers, particularly by reducing the number of qubits needed to achieve the same accuracy. By providing a more extensive symmetry-adapted encoding (SAE) than previous work, we are able to simulate molecules larger than those previously reported that have been studied using methods developed for quantum annealers and without using an active space. We calculated the potential energy surfaces of H 2 , LiH, He 2 , H 2 O, O 2 , N 2 , Li 2 , F 2 , CO, BH 3 , NH 3 , and CH 4 , with the largest molecule in the STO-6G basis set requiring 16 qubits with our SAE, and compared them with full configuration interaction results. The application of SAE to the XBK method provides an exponential reduction in the size of the Hilbert space and scales well with the size of the problem. It does not introduce significant additional errors for even or large values of a key variational parameter that determines the number of ancilla qubits used in the XBK method’s Hamiltonian embedding, or for certain molecules such as He 2 and H 2 O. Here, we provide an explanation for this behavior and a recommendation on the usage of our method. In addition, we briefly discuss the potential of extracting electronic excited states from our method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Ab initio calculations of the electronic structure of the low-lying states for the ultracold LiYb molecule

Ab initio techniques have been applied to investigate the electronic structure of the LiYb molecule. The potential energy curves have been computed in the Born–Oppenheimer approximation for the ground and 29 low-lying doublet and quartet excited electronic states. Complete active space self-consistent field, multi-reference configuration interaction, and Rayleigh Schrödinger perturbation theory to second order calculations have been utilized to investigate these states. The spectroscopic constants, ω{sub e}, R{sub e}, B{sub e}, …, and the static dipole moment, μ, have been investigated by using the two different techniques of calculation with five different types of basis. The eigenvalues, E{sub v}, the rotational constant, B{sub v}, the centrifugal distortion constant, D{sub v}, and the abscissas of the turning points, R{sub min} and R{sub max}, have been calculated by using the canonical functions approach. The comparison between the values of the present work, calculated by different techniques, and those available in the literature for several electronic states shows a very good agreement. Twenty-one new electronic states have been studied here for the first time.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Seniority number description of potential energy surfaces: Symmetric dissociation of water, N{sub 2}, C{sub 2}, and Be{sub 2}

The present study further explores the concept of the seniority number (Ω) by examining different configuration interaction (CI) truncation strategies in generating compact wave functions in a systematic way. While the role of Ω in addressing static (strong) correlation problem has been addressed in numerous previous studies, the usefulness of seniority number in describing weak (dynamic) correlation has not been investigated in a systematic way. Thus, the overall objective in the present work is to investigate the role of Ω in addressing also dynamic electron correlation in addition to the static correlation. Two systematic CI truncation strategies are compared beyond minimal basis sets and full valence active spaces. One approach is based on the seniority number (defined as the total number of singly occupied orbitals in a determinant) and another is based on an excitation-level limitation. In addition, molecular orbitals are energy-optimized using multiconfigurational-self-consistent-field procedure for all these wave functions. The test cases include the symmetric dissociation of water (6-31G), N{sub 2} (6-31G), C{sub 2} (6-31G), and Be{sub 2} (cc-pVTZ). We find that the potential energy profile for H{sub 2}O dissociation can be reasonably well described using only the Ω = 0 sector of the CI wave function. For the Be{sub 2} case, we show that the full CI potential energy curve (cc-pVTZ) is almost exactly reproduced using either Ω-based (including configurations having up to Ω = 2 in the virtual-orbital-space) or excitation-based (up to single-plus-double-substitutions) selection methods, both out of a full-valence-reference function. Finally, in dissociation cases of N{sub 2} and C{sub 2}, we shall also consider novel hybrid wave functions obtained by a union of a set of CI configurations representing the full valence space and a set of CI configurations where seniority-number restriction is imposed for a complete set (full-valence-space and virtual) of correlated molecular orbitals, simultaneously. We discuss the usefulness of the seniority number concept in addressing both static and dynamic electron correlation problems along dissociation paths.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Communication: CDFT-CI couplings can be unreliable when there is fractional charge transfer

Constrained density functional theory with configuration interaction (CDFT-CI) is a useful, low-cost tool for the computational prediction of electronic couplings between pseudo-diabatic constrained electronic states. Such couplings are of paramount importance in electron transfer theory and transition state theory, among other areas of chemistry. Unfortunately, CDFT-CI occasionally fails significantly, predicting a coupling that does not decay exponentially with distance and/or overestimating the expected coupling by an order of magnitude or more. In this communication, we show that the eigenvalues of the difference density matrix between the two constrained states can be used as an a priori metric to determine when CDFT-CI are likely to be reliable: when the eigenvalues are near 0 or ±1, transfer of a whole electron is occurring, and CDFT-CI can be trusted. We demonstrate the utility of this metric with several illustrative examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Two-photon absorption cross sections within equation-of-motion coupled-cluster formalism using resolution-of-the-identity and Cholesky decomposition representations: Theory, implementation, and benchmarks

The equation-of-motion coupled-cluster (EOM-CC) methods provide a robust description of electronically excited states and their properties. Here, we present a formalism for two-photon absorption (2PA) cross sections for the equation-of-motion for excitation energies CC with single and double substitutions (EOM-CC for electronically excited states with single and double substitutions) wave functions. Rather than the response theory formulation, we employ the expectation-value approach which is commonly used within EOM-CC, configuration interaction, and algebraic diagrammatic construction frameworks. In addition to canonical implementation, we also exploit resolution-of-the-identity (RI) and Cholesky decomposition (CD) for the electron-repulsion integrals to reduce memory requirements and to increase parallel efficiency. The new methods are benchmarked against the CCSD and CC3 response theories for several small molecules. We found that the expectation-value 2PA cross sections are within 5% from the quadratic response CCSD values. The RI and CD approximations lead to small errors relative to the canonical implementation (less than 4%) while affording computational savings. RI/CD successfully address the well-known issue of large basis set requirements for 2PA cross sections calculations. The capabilities of the new code are illustrated by calculations of the 2PA cross sections for model chromophores of the photoactive yellow and green fluorescent proteins.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

CAS without SCF—Why to use CASCI and where to get the orbitals

The complete active space self-consistent field (CASSCF) method has seen broad adoption due to its ability to describe the electronic structure of both the ground and excited states of molecules over a broader swath of the potential energy surface than is possible with the simpler Hartree–Fock approximation. However, it also has a reputation for being unwieldy, computationally costly, and un-black-box. Here, we discuss a class of alternatives, complete active space configuration interaction (CASCI) methods, paying particular attention to their application to electronic excited states. The goal of this Perspective is fourfold. First, we argue that CASCI is not merely an approximation to CASSCF, in that it can be designed to have important qualitative advantages over CASSCF. Second, we present several insights drawn from our experience experimenting with different schemes for computing orbitals to be employed in CASCI. Third, we argue that CASCI is well suited for application to nanomaterials. Lastly, we reason that, with the rise in new low-scaling approaches for describing multireference systems, there is a greater need than ever to develop new methods for defining orbitals that provide an efficient and accurate description of both static correlation and electronic excitations in a limited active space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Multireference linearized coupled cluster theory for strongly correlated systems using matrix product states

We propose a multireference linearized coupled cluster theory using matrix product states (MPSs-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles, for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries to highly multireference systems such as the chromium dimer and lattice models such as periodic two-dimensional 1-band and 3-band Hubbard models. The MPS-LCC theory shows a speed up of several orders of magnitude over the usual Density Matrix Renormalization Group (DMRG) algorithm while delivering energies in excellent agreement with converged DMRG calculations. Also, in all the benchmark calculations presented here, MPS-LCC outperformed the commonly used multi-reference quantum chemistry methods in some cases giving energies in excess of an order of magnitude more accurate. As a size-extensive method that can treat large active spaces, MPS-LCC opens up the use of multireference quantum chemical techniques in strongly correlated ab initio Hamiltonians, including two- and three-dimensional solids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Laser cooling of MgCl and MgBr in theoretical approach

Ab initio calculations for three low-lying electronic states (X{sup 2}Σ{sup +}, A{sup 2}Π, and 2{sup 2}Π) of MgCl and MgBr molecules, including spin-orbit coupling, are performed using multi-reference configuration interaction plus Davidson correction method. The calculations involve all-electronic basis sets and Douglas–Kroll scalar relativistic correction. Spectroscopic parameters well agree with available theoretical and experimental data. Highly diagonally distributed Franck-Condon factors f{sub 00} for A{sup 2}Π{sub 3/2,1/2} (υ′ = 0) → X{sup 2}Σ{sup +}{sub 1/2} (υ″ = 0) are determined for both MgCl and MgBr molecules. Suitable radiative lifetimes τ of A{sup 2}Π{sub 3/2,1/2} (υ′ = 0) states for rapid laser cooling are also obtained. The proposed laser drives A{sup 2}Π{sub 3/2} (υ′ = 0) → X{sup 2}Σ{sup +}{sub 1/2} (υ″ = 0) transition by using three wavelengths (main pump laser λ{sub 00}; two repumping lasers λ{sub 10} and λ{sub 21}). These results indicate the probability of laser cooling MgCl and MgBr molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

First-principles analysis of X-ray magnetic circular dichroism for transition metal complex oxides

X-ray magnetic circular dichroism (XMCD) is widely used for the characterization of magnetism of materials. However, information from XMCD related to the atomic, electronic, and magnetic structures is not fully utilized due to the lack of reliable theoretical tools for spectral analysis. In this work, the first-principles configuration interaction (CI) calculations for X-ray absorption spectra developed by the author were extended for the calculation of XMCD, where the Zeeman energy was taken into the Hamiltonian of the CI to mimic magnetic polarization in the solid state. This technique was applied to interpret the L{sub 2,3} XMCD from 3d transition metal complex oxides, such as NiFe{sub 2}O{sub 4} and FeTiO{sub 3}. The experimental XMCD spectra were quantitatively reproduced using this method. The oxidation states as well as the magnetic ordering between transition metal ions on crystallographically different sites in NiFe{sub 2}O{sub 4} can be unambiguously determined. A first-principles analysis of XMCD in FeTiO{sub 3} revealed the presence of Fe{sup 3+} and Ti{sup 3+} ions, which indicates that the charge transfer from Fe to Ti ions occurs. The origin of magnetic polarization of Ti ions in FeTiO{sub 3} was also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Interpretation of the vacuum ultraviolet photoabsorption spectrum of iodobenzene by ab initio computations

Identification of many Rydberg states in iodobenzene, especially from the first and fourth ionization energies (IE{sub 1} and IE{sub 4}, X{sup 2}B{sub 1} and C{sup 2}B{sub 1}), has become possible using a new ultraviolet (UV) and vacuum-ultraviolet (VUV) absorption spectrum, in the region 29 000-87 000 cm{sup −1} (3.60-10.79 eV), measured at room temperature with synchrotron radiation. A few Rydberg states based on IE{sub 2} (A{sup 2}A{sub 2}) were found, but those based on IE{sub 3} (B{sup 2}B{sub 2}) are undetectable. The almost complete absence of observable Rydberg states relating to IE{sub 2} and IE{sub 3} (A{sup 2}A{sub 2} and B{sup 2}B{sub 2}, respectively) is attributed to them being coupled to the near-continuum, high-energy region of Rydberg series converging on IE{sub 1}. Theoretical studies of the UV and VUV spectra used both time-dependent density functional (TDDFT) and multi-reference multi-root doubles and singles-configuration interaction methods. The theoretical adiabatic excitation energies, and their corresponding vibrational profiles, gave a satisfactory interpretation of the experimental results. The calculations indicate that the UV onset contains both 1{sup 1}B{sub 1} and 1{sup 1}B{sub 2} states with very low oscillator strength, while the 2{sup 1}B{sub 1} state was found to lie under the lowest ππ{sup ∗} 1{sup 1}A{sub 1} state. All three of these {sup 1}B{sub 1} and {sup 1}B{sub 2} states are excitations into low-lying σ{sup ∗} orbitals. The strongest VUV band near 7 eV contains two very strong ππ{sup ∗} valence states, together with other weak contributors. The lowest Rydberg 4b{sub 1}6s state (3{sup 1}B{sub 1}) is very evident as a sharp multiplet near 6 eV; its position and vibrational structure are well reproduced by the TDDFT results.

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

High-level coupled-cluster energetics by Monte Carlo sampling and moment expansions: Further details and comparisons

We recently proposed a novel approach to converging electronic energies equivalent to high-level coupled-cluster (CC) computations by combining the deterministic CC(P;Q) formalism with the stochastic configuration interaction (CI) and CC Quantum Monte Carlo (QMC) propagations. This article extends our initial study [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)], which focused on recovering the energies obtained with the CC method with singles, doubles, and triples (CCSDT) using the information extracted from full CI QMC and CCSDT-MC, to the CIQMC approaches truncated at triples and quadruples. It also reports our first semi-stochastic CC(P;Q) calculations aimed at converging the energies that correspond to the CC method with singles, doubles, triples, and quadruples (CCSDTQ). The ability of the semi-stochastic CC(P;Q) formalism to recover the CCSDT and CCSDTQ energies, even when electronic quasi-degeneracies and triply and quadruply excited clusters become substantial, is illustrated by a few numerical examples, including the F–F bond breaking in F 2 , the automerization of cyclobutadiene, and the double dissociation of the water molecule.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

The total position-spread tensor: Spin partition

The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H{sub n} (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Accurate high level ab initio-based global potential energy surface and dynamics calculations for ground state of CH{sub 2}{sup +}

A global many-body expansion potential energy surface is reported for the electronic ground state of CH{sub 2}{sup +} by fitting high level ab initio energies calculated at the multireference configuration interaction level with the aug-cc-pV6Z basis set. The topographical features of the new global potential energy surface are examined in detail and found to be in good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations available in the literature. In turn, in order to validate the potential energy surface, a test theoretical study of the reaction CH{sup +}(X{sup 1}Σ{sup +})+H({sup 2}S)→C{sup +}({sup 2}P)+H{sub 2}(X{sup 1}Σ{sub g}{sup +}) has been carried out with the method of time dependent wavepacket on the title potential energy surface. The total integral cross sections and the rate coefficients have been calculated; the results determined that the new potential energy surface can both be recommended for dynamics studies of any type and as building blocks for constructing the potential energy surfaces of larger C{sup +}/H containing systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Neutral gas pressure dependence of ion–ion mutual neutralization rate constants using Landau–Zener theory coupled with trajectory simulations

In this computational study, we describe a self-consistent trajectory simulation approach to capture the effect of neutral gas pressure on ion–ion mutual neutralization (MN) reactions. The electron transfer probability estimated using Landau–Zener (LZ) transition state theory is incorporated into classical trajectory simulations to elicit predictions of MN cross sections in vacuum and rate constants at finite neutral gas pressures. Electronic structure calculations with multireference configuration interaction and large correlation consistent basis sets are used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of background gas on ion transport. For H + – H – and Li + – H(D) – , our approach quantitatively agrees with measured speed-dependent cross sections for up to ~10 5 m/s. For the ion pair Ne + – Cl – , our predictions of the MN rate constant at ~1 Torr are a factor of ~2 to 3 higher than the experimentally measured value. Similarly, for Xe + – F – in the pressure range of ~20 000–80 000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. Here, the paradigm of using trajectory simulations to self-consistently capture the effect of gas pressure on MN reactions advanced here provides avenues for the inclusion of additional nonclassical effects in future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Photodissociation of HCN and HNC isomers in the 7-10 eV energy range

The ultraviolet photoabsorption spectra of the HCN and HNC isomers have been simulated in the 7-10 eV photon energy range. For this purpose, the three-dimensional adiabatic potential energy surfaces of the 7 lowest electronic states, and the corresponding transition dipole moments, have been calculated, at multireference configuration interaction level. The spectra are calculated with a quantum wave packet method on these adiabatic potential energy surfaces. The spectra for the 3 lower excited states, the dissociative electronic states, correspond essentially to predissociation peaks, most of them through tunneling on the same adiabatic state. The 3 higher electronic states are bound, hereafter electronic bound states, and their spectra consist of delta lines, in the adiabatic approximation. The radiative lifetime towards the ground electronic states of these bound states has been calculated, being longer than 10 ns in all cases, much longer that the characteristic predissociation lifetimes. The spectra of HCN is compared with the available experimental and previous theoretical simulations, while in the case of HNC there are no previous studies to our knowledge. The spectrum for HNC is considerably more intense than that of HCN in the 7-10 eV photon energy range, which points to a higher photodissociation rate for HNC, compared to HCN, in astrophysical environments illuminated by ultraviolet radiation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Effects of spin-orbit coupling on laser cooling of BeI and MgI

We present the ab initio study of spin-orbit coupling effects on laser cooling of BeI and MgI molecules. Potential energy curves for the X{sup 2}Σ{sup +}{sub 1/2}, A{sup 2}Π{sub 1/2,3/2}, and 2{sup 2}Π{sub 3/2,1/2} states are calculated using multi-reference configuration interaction method plus Davidson corrections. Spectroscopic parameters of BeI and MgI are in excellent agreement with available experimental and theoretical values. The A{sup 2}Π{sub 3/2} state of MgI is a repulsive state. It is an unsuitable scheme for the A{sup 2}Π{sub 3/2}(υ′)← X{sup 2}Σ{sup +}{sub 1/2} (υ″) transition for laser cooling of MgI. Highly diagonally distributed Franck-Condon factors f{sub 00} for the A{sup 2}Π{sub 1/2,3/2} (υ′ = 0) ← X{sup 2}Σ{sup +}{sub 1/2} (υ″ = 0) transitions and suitable radiative lifetimes τ for the A{sup 2}Π{sub 1/2,3/2} (υ′ = 0) of BeI and MgI are obtained. Three laser wavelength drives are required for the A{sup 2}Π{sub 1/2,3/2}(υ′)←X{sup 2}Σ{sup +}{sub 1/2} (υ″) transitions of BeI and MgI. The proposed cooling wavelengths of BeI and MgI are both in the violet region. The results imply the feasibility of laser cooling of BeI and MgI, and that laser cooling of BeI is more possible.

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

Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗