Engineering topics

Scuseria, Gustavo E.

Publications and source records attributed to Scuseria, Gustavo E..

15 records

DOE OSTI2024

Determining the N -Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1999

Linear Scaling Density Functional Calculations with Gaussian Orbitals

Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.

Scuseria, Gustavo E.↗

NASA NTRS1999

What is the Best Alternative to Diagonalization of the Hamiltonian in Large Scale Semiempirical Calculations?

Recently, several linear scaling approaches have been introduced which replace the time dominating diagonalization step in semiempirical methods, enabling practical calculations to be performed, on very large molecules. This paper compares the accuracy and performance of pseudodiagonalization (PD), conjugate gradient density matrix search (CG-DMS), the Chebyshev polynomial expansion method (CEM), and purification of the density matrix (PDM) as linear scaling substitutions for diagonalization. The scaling, speed, and reliability of these methods are compared for AMI single point energy calculations on polyglycine chains (up to 20,000 atoms), water clusters (up to 12,300 atoms), and nucleic acids (up to 6300 atoms).

Daniels, Andrew D.↗

NASA NTRS1998

C2 Fragmentation Energy of C60 Revisited: Theory Disagrees with Most Experiments

Following our earlier work on the subject, we have carried out density functional theory (DFT) and second-order Moller-Plesset perturbation theory (MP2) calculations of the dissociation energy of the reaction C60 yields C58 + C2 using polarized basis sets and geometries optimized with DFT methods. The present theoretical results support an electronic fragmentation energy D(sub e) around 10-11 eV in disagreement with most experimental results that place the dissociation energy D(sub o) (including zero point energy) around 7-8 eV. The plausible errors remaining in the theoretical calculations are unlikely to account for this big difference (2-4 eV).

Boese, A. Daniel↗

NASA NTRS1998

Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations

We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.

Bates, Kevin R.↗

NASA NTRS1998

Why are Buckyonions Round?

Multi-layered round carbon particles (onions) containing tens to hundreds of thousands of atoms form during electron irradiation of graphite. However. theoretical models or large icosahedral fullerenes predict highly faceted shapes for molecules with more than a few hundred atoms. This discrepancy in shape may be explained by the presence of defects during the formation of carbon onions. Here, we use the semi-empirical tight-binding method for carbon to simulate the incorporation of pentagon-heptagon defects on to the surface of large icosahedral fullerenes. We show a simple mechanism that results in energetically competitive derivative structures and a global change in molecular shape from faceted to round. Our results provide a plausible explanation of the apparent discrepancy between experimental observations or round buckyonions and theoretical predictions of faceted icosahedral fullerenes.

Bates, Kevin R.↗

NASA NTRS1997

Why Are Buckyonions Round?

Multi-layered round carbon particles (onions) containing tens to hundreds of thousands of atoms form during electron irradiation of graphite carbon. However, theoretical models of large icosahedral fullerenes predict highly faceted shapes for molecules with more than a few hundred atoms. This discrepancy in shape may be explained by the presence of defects during the formation of carbon onions. Here, we use the semi-empirical tight-binding method for carbon to simulate the incorporation of pentagon-heptagon defects on to the surface of large icosahedral fullerenes. We show a simple mechanism that results in energetically competitive derivative structures and a global change in molecular shape from faceted to round. Our results provide a plausible explanation of the apparent discrepancy between experimental observations of round buckyonions and theoretical predictions of faceted icosahedral fullerenes.

Bates, Kevin R.↗

NASA NTRS1997

Computational Nanotechnology Program

The objectives are: (1) development of methodological and computational tool for the quantum chemistry study of carbon nanostructures and (2) development of the fundamental understanding of the bonding, reactivity, and electronic structure of carbon nanostructures. Our calculations have continued to play a central role in understanding the outcome of the carbon nanotube macroscopic production experiment. The calculations on buckyonions offer the resolution of a long controversy between experiment and theory. Our new tight binding method offers increased speed for realistic simulations of large carbon nanostructures.

Scuseria, Gustavo E.↗

NASA NTRS1994

Achieving Chemical Accuracy with Coupled-Cluster Theory

Due to formal and computational advances in coupled-cluster theory over the past few years, it is now possible to obtain very accurate molecular geometries, vibrational frequencies, heats of formation, binding energies, and vertical electronic excitation energies. The present monograph reviews the advances that have lead to the current state-of-the art, and also summarizes selected examples from the published literature.

Lee, Timothy J.↗

NASA NTRS1992

A comparison of the coupled cluster and internally contracted averaged coupled-pair functional levels of theory for the calculation of the MCH2(+) binding energies for M = Sc to Cu

The correlation contribution to the M-C binding energy for the MCH2(+) systems can exceed 100 kcal/mol. At the self-consistent field (SCF) level, these systems can be more than 50 kcal/mol above the fragment energies. In spite of the poor zeroth-order reference, the coupled cluster single and double excitation method with a perturbational estimate of triple excitations, CCSD(T), method is shown to provide an accurate description of these systems. The maximum difference between the CCSD(T) and internally contracted averaged coupled-pair functional binding energies is 1.5 kcal/mol for CrCH2(+), with the remaining systems agreeing to within 1.0 kcal/mol.

Bauschlicher, Charles W., Jr.↗

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.↗

NASA NTRS1992

Connected triple excitations in coupled-cluster calculations of hyperpolarizabilities: Neon

We have calculated the second hyperpolarizability gamma of neon using the CCSD(T) method. The accuracy of the CCSD(T) approach has been established by explicit comparison with the single, double and triple excitation coupled-cluster (CCSDT) method using extended basis sets that are known to be adequate for the description of gamma. Our best estimate for gamma(sub 0) of 110 +/- 3 a.u. is in good agreement with other recent theoretical values and with Shelton's recent experimental estimate of 108 +/- 2 a.u. Comparison of the MP2 and CCSD(T) hyperpolarizability values indicates that MP2 gives a very good description of the electron correlation contribution to gamma(sub 0). We have combined MP2 frequency-dependent corrections with the CCSD(T) gamma(sub 0) to yield values of gamma(-2 omega;omega,omega,0) and gamma(exp K)(-omega;omega,0,0).

Rice, Julia E.↗

NASA NTRS1990

Comparison of coupled-cluster methods which include the effects of connected triple excitations

The 'coupled cluster single, double, and triple' (CCSDT) excitation model has been used to ascertain electron correlation energies for 14 different molecules representing a variety of chemical bonds, in conjunction with several methods of this type 'CCSDT-x', which include only an approximate treatment of connected triple excitations; these methods encompass CCSDT-1a, -1b, -2, -3, and -4, as well as the novel CCSD(T). While all methods treat the effects of connected triple excitations iteratively, CCSD(T) approaches then perturbationally. For the 14 molecules considered, the CCSD(T) method's average error relative to CCSDT is substantially lower than any of the CCSDT-x methods.

Scuseria, Gustavo E.↗

NASA NTRS1990

The vibrational frequencies of ozone

The singles and doubles coupled-cluster (CCSD) method is used, together with the recently proposed CCSD(T) and CCSDT-1 methods, to determine the equilibrium structure and harmonic frequencies of ozone at various levels, on the basis of large one-particle basis sets. It is demonstrated that f-type functions are required in order to obtain quantitative accuracy for the equilibrium structure and harmonic frequencies. The CCSD(T) level of theory, in conjunction with a (4s 3p 2d 1f) atomic natural orbital set, yields an equilibrium geometry and harmonic frequencies that are in excellent agreement with experimental results; an effort has accordingly been made to determine the cubic and quartic force constants, and evaluate the anharmonic corrections to the fundamental vibrational frequencies.

Lee, Timothy J.↗

NASA NTRS1989

Ordering of the O-O stretching vibrational frequencies in ozone

The ordering of nu1 and nu3 for O3 is incorrectly predicted by most theoretical methods, including some very high level methods. The first systematic electron correlation method based on one-reference configuration to solve this problem is the coupled cluster single and double excitation method. However, a relatively large basis set, triple zeta plus double polarization is required. Comparison with other theoretical methods is made.

Scuseria, Gustavo E.↗