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Item A comparison of linear scaling replacements for diagonalization in electronic structure calculations(2001) Daniels, Andrew D.; Scuseria, Gustavo E.Show more Even when using parametrized semiempirical methods, quantum chemical calculations on molecules containing more than a few hundred atoms become prohibitively expensive due to O (N3) time and memory costs where N is the number of atoms. I implemented methods to allow the CPU time cost of semiempirical methods to scale linearly with system size enabling semiempirical calculations on large biological systems such as proteins and nucleic acids. The cost of forming the initial guess density matrix was reduced by replacing the O (N3) diagonalization of the Huckel Hamiltonian with an approach which uses localized molecular orbitals based on the Lewis dot structure to build the density matrix. The Fock matrix build was reduced from O (N2) to linear scaling in CPU time using atom-atom distance cutoffs. The diagonalization step was replaced by several linear scaling methods described in the literature: conjugate gradient density matrix search (CGDMS), purification of the density matrix (PDM), pseudodiagonalization (PD), and the Chebyshev expansion method (CEM). While in my semiempirical implementation all of these methods demonstrated linear scaling, CGDMS, PDM and PD required about the same amount of CPU time for calculations on water clusters and polyglycine chains but CEM was found to be about three times as expensive as the other methods. However, CGDMS stands out among the other methods by having the added property of enhancing self-consistent field (SCF) convergence in cases where diagonalization has convergence difficulties. Finally, to demonstrate the effectiveness of the linear scaling semiempirical method on a realistic system we performed the first-ever semiempirical geometry optimization using PM3 implemented with CGDMS on a 1226 atom kringle 1 of plasminogen.Show more Item A comprehensive ab initio study of gallium and arsenic containing molecules(1992) Graves, Richard Marshall; Scuseria, Gustavo E.Show more Theoretical calculations for the ground states of arsine (AsH$\sb3$), trimethylgallium (TMG) (Ga(CH$\sb3$)$\sb3$), the arsine$\cdot$TMG adduct, gallane (GaH$\sb3$), the gallane$\cdot$arsine adduct, small Ga$\sb{x}$As$\sb{y}$ clusters (x = y; x = 2-4), and small gallium hydrides are carried out at the self consistent field (SCF) Hartree-Fock level of theory, using analytic energy gradients for rapid geometry optimization. In addition, the SCF results are compared with theoretical predictions obtained at the coupled cluster level of theory including all single and double excitations, (CCSD). The precursors to the formation of GaAs, arsine and TMG, were determined to be of C$\sb{3v}$ and C$\sb3$ symmetries, respectively, while gallane was found to be D$\sb{3h}$ The equilibrium structures for Ga$\sb2$As$\sb2$, Ga$\sb3$As$\sb3$, and Ga$\sb4$As$\sb4$ are found to be of D$\sb{2h}$, C$\sb1$, and C$\sb{i}$ symmetry, respectively. The adduct binding energies and vibrational frequencies (SCF) are also obtained resulting in two stable bonded adduct species, arsine$\cdot$TMG of symmetry point group C$\sb3$ and arsine$\cdot$gallane of C$\sb{3v}$ symmetry. Finally, our theoretical predictions support a slightly exothermic gas-phase reaction yielding GaAs through a TMG$\cdot$AsH$\sb3$ adduct which is formed without an activation barrier.Show more Item A cycloaddition-based fullerene assembly mechanism(1996) Strout, Douglas; Scuseria, Gustavo E.Show more Since their discovery, the fullerenes have challenged scientists with a wide array of problems concerning their properties, behavior and potential applications. One such fundamental question is that of the assembly of these carbon cages. Much effort has been directed at obtaining an understanding of the process whereby graphite is transformed into fullerenes. In this work, a theoretical study is carried out to explore the nature of carbon clusters, including the fullerenes themselves as well as other structures which may be intermediates along the path to fullerenes. The experiments which generate fullerenes are interpreted by the use of theoretical calculations, and this interpretation is used to develop a model for a fullerene assembly pathway. The principal tenets of the model are as follows: (1) The process of forming fullerenes is begun by the cycloaddition of monocyclic carbon rings, (2) The cycloadducts, once formed, undergo unimolecular reactions to form cylindrical carbon "hoops", (3) Closed cages can form from "hoops" through a sequence of 1,2-carbon shifts and cyclization reactions, and (4) The cages can "anneal" to find the most stable isomer by rearranging their bonds. Energetics of the reactions involved in each step of the model will be explored computationally by the Hartree-Fock method and several electron correlation methods. Energetic details will include both overall reaction energetics and transition barriers for the reactions. The computational results will be shown to be consistent with experimental results, so that a reasonable synthesis of theory and experiment can be presented.Show more Item A theoretical study of the higher fullerenes carbon(76) and carbon(78)(1993) Colt, John R.; Scuseria, Gustavo E.Show more Ab initio self-consistent field Hartree-Fock calculations employing minimal and double-zeta basis sets have been carried out on the possible isolated-pentagon fullerene isomers of C$\sb{76}$ and C$\sb{78}$. Two possible isolated-pentagon fullerene isomers exist for C$\sb{76}$: a chiral $D\sb2$ structure with a closed-shell electronic configuration and a $T\sb{d}$ structure with an open-shell electronic configuration that symmetry lowers to a closed-shell $\sp1A\sb1$ state in $D\sb{2d}$ symmetry. The D$\sb2$ isomer is found to be 43 kcal/mol more stable than the $T\sb{d}$ $\to$ $D\sb{2d}$ isomer. Five isolated-pentagon isomers exist for C$\sb{78}$ ($C\sb{2v}$(I), $C\sb{2v}$(II), $D\sb3$, $D\sb{3h}$(I) and $D\sb{3h}$(II)). The predicted order of stability for the five structures is found to be $C\sb{2v}$,(I) $>$ $C\sb{2v}$(II) $>$ D$\sb3$ $>$ $D\sb{3h}$(I) $>$ $D\sb{3h}$(II). Thermodynamic predictions of C$\sb{76}$ and C$\sb{78}$ seem to straightforwardly correlate with experimental results.Show more Item Ab initio theoretical study of the small fullerenes carbon(20)-carbon(36)(1997) Delabroy, Laurent Pierre; Scuseria, Gustavo E.Show more Ab initio SCF Hartree-Fock calculations have been carried out on all the fullerene isomers of C$\sb{20}$ to C$\sb{36}.\ C\sb{20},\ C\sb{24},$ and C$\sb{26}$ have only one fullerene isomer each, of $C\sb{2h},\ D\sb6$ and $D\sb{3h}$ symmetry respectively. C$\sb{28}$ has two distinct fullerene isomers, C$\sb{30}$ has three, C$\sb{32}$ and C$\sb{34}$ have six, and C$\sb{36}$ has fifteen. Their lowest energy structures were found to be of $T\sb{d}\ C\sb{2v},\ D\sb3,\ C\sb2,$ and $D\sb{2d}$ symmetry respectively. All ground-state isomers have closed-shell electronic configurations except C$\sb{26}$-$D\sb{3h}$ (open-shell $\rm\sp5A\sp\prime\sb1)$ and C$\sb{28}$-$T\sb {d}$ (open-shell $\sp5{\rm A}\sb2).$ A new mechanism, called "peeling", is proposed in order to explain the end of the C$\sb2$ loss fragmentation pattern at C$\sb{32}$ observed in photodissociation studies. It consists of opening the fullerene surface and excising long carbon chains. MNDO calculations show the "peeling" channel to be more competitive than the C$\sb2$ loss fragmentation process for C$\sb{32}.$Show more Item Actinide chemistry using singlet-paired coupled cluster and its combinations with density functionals(AIP Publishing LLC, 2016) Garza, Alejandro J.; Alencar, Ana G. Sousa; Scuseria, Gustavo E.Show more Singlet-paired coupled cluster doubles (CCD0) is a simplification of CCD that relinquishes a fraction of dynamic correlation in order to be able to describe static correlation. Combinations of CCD0 with density functionals that recover specifically the dynamic correlation missing in the former have also been developed recently. Here, we assess the accuracy of CCD0 and CCD0+DFT (and variants of these using Brueckner orbitals) as compared to well-established quantum chemical methods for describing ground-state properties of singlet actinide molecules. The f0 actinyl series (UO2+2, NpO3+2, PuO4+2), the isoelectronic NUN, and thorium (ThO, ThO2+) and nobelium (NoO, NoO2) oxides are studied.Show more Item AGP-based unitary coupled cluster theory for quantum computers(IOP Publishing, 2022) Khamoshi, Armin; Chen, Guo P.; Evangelista, Francesco A.; Scuseria, Gustavo E.Show more Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. The same goes for ansätze on a quantum computer. We develop a unitary coupled cluster method based on the antisymmetrized geminal power (AGP)—a state formally equivalent to the number-projected Bardeen–Cooper–Schrieffer wavefunction. We demonstrate our method for the single-band Fermi–Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than O(√M) in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry.Show more Item Analytic energy gradient for the projected Hartree–Fock method(AIP Publishing, 2014) Schutski, Roman; Jiménez-Hoyos, Carlos A.; Scuseria, Gustavo E.Show more We derive and implement the analytic energy gradient for the symmetry Projected Hartree–Fock (PHF) method avoiding the solution of coupled-perturbed HF-like equations, as in the regular unprojected method. Our formalism therefore has mean-field computational scaling and cost, despite the elaborate multi-reference character of the PHF wave function. As benchmark examples, we here apply our gradient implementation to the ortho-, meta-, and para-benzyne biradicals, and discuss their equilibrium geometries and vibrational frequencies.Show more Item Assessment of the Tao-Mo nonempirical semilocal density functional in applications to solids and surfaces(American Physical Society, 2017) Mo, Yuxiang; Car, Roberto; Staroverov, Viktor N.; Scuseria, Gustavo E.; Tao, JianminShow more Recently, Tao and Mo developed a semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density-matrix expansion corrected to reproduce the fourth-order gradient expansion of the exchange energy in the slowly-varying-density limit, while the correlation part is based on the Tao-Perdew-Staroverov-Scuseria (TPSS) correlation functional, with a modification for the low-density limit. In the present paper, the Tao-Mo (TM) functional is assessed by computing various properties of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 30 band gaps, seven cohesive energies, and jellium surface exchange and correlation energies for the density parameter rs in the range from 2 to 3 bohr. Our calculations show that the TM approximation can yield consistently high accuracy for most properties considered here, with mean absolute errors (MAEs) of 0.025 Å for lattice constants, 7.0 GPa for bulk moduli, 0.08 eV/atom for cohesive energies, and 35erg/cm2 for surface exchange-correlation energies. The MAE in band gaps is larger than that of TPSS, but slightly smaller than the errors of the local spin-density approximation, Perdew-Burke-Ernzerhof generalized gradient approximation, and revised TPSS. However, band gaps are still underestimated, particularly for large-gap semiconductors, compared to the Heyd-Scuseria-Ernzerhof nonlocal screened hybrid functional.Show more Item Blind test of density-functional-based methods on intermolecular interaction energies(AIP Publishing LLC., 2016) Taylor, DeCarlos E.; Ángyán, János G.; Galli, Giulia; Zhang, Cui; Gygi, Francois; Hirao, Kimihiko; Song, Jong Won; Rahul, Kar; von Lilienfeld, O. Anatole; Podeszwa, Rafał; Bulik, Ireneusz W.; Henderson, Thomas M.; Scuseria, Gustavo E.; Toulouse, Julien; PShow more In the past decade, a number of approaches have been developed to fix the failure of (semi)local density-functional theory (DFT) in describing intermolecular interactions. The performance of several such approaches with respect to highly accurate benchmarks is compared here on a set of separation-dependent interaction energies for ten dimers. Since the benchmarks were unknown before the DFT-based results were collected, this comparison constitutes a blind test of these methods.Show more Item Can Gap Tuning Schemes of Long-Range Corrected Hybrid Functionals Improve the Description of Hyperpolarizabilities?(American Chemical Society, 2014) Garza, Alejandro J.; Osman, Osman I.; Asiri, Abdullah M.; Scuseria, Gustavo E.Show more Long-range corrected hybrid density functionals (LC-DFT), with range separation parameters optimally tuned to obey Koopmans' theorem, are used to calculate the first-order hyperpolarizabilities of prototypical charge-transfer compounds p-nitroaniline (PNA) and dimethylamino nitrostilbene (DANS) in the gas phase and various solvents. It is shown that LC-DFT methods with default range separation parameters tend to underestimate hyperpolarizabilities (most notably in solution) and that the tuning scheme can sharply improve results, especially in the cases when the standard LC-DFT errors are largest. Nonetheless, we also identify pathological cases (two pyrrole derivatives) for which LC-DFT underestimates the hyperpolarizabilities, regardless of tuning. It is noted that such pathological cases do not follow the usual inverse relation between the hyperpolarizability and amount of exact exchange, and thus this behavior may serve as a diagnostic tool for the adequacy of LC-DFT.Show more Item Can Short- and Middle-Range Hybrids Describe the Hyperpolarizabilities of Long-Range Charge-Transfer Compounds?(American Chemical Society, 2014) Garza, Alejandro J.; Wazzan, Nuha A.; Asiri, Abdullah M.; Scuseria, Gustavo E.Show more The hyperpolarizabilities of five prototypical and four recently synthesized long-range charge-transfer (CT) organic compounds are calculated using short- and middle-range (SR and MR) hybrid functionals. These results are compared with data from MP2 and other DFT methods including GGAs, global hybrids, long-range corrected functionals (LC-DFT), and optimally tuned LC-DFT. Although it is commonly believed that the overestimation of hyperpolarizabilities associated with CT excitations by GGA and global hybrid functionals is the result of their wrong asymptotic exchange potential, and that LC-DFT heals this issue, we show here that SR and MR functionals yield results similar to those from LC-DFT. Hence, the long-range correction per se does not appear to be the key element in the well-known improved description of hyperpolarizabilities by LC-DFT. Rather, we argue that the inclusion of substantial amounts of Hartree-Fock exchange, which reduces the many-electron self-interaction error, is responsible for the relatively good results afforded by range separated hybrids. Additionally, we evaluate the effects of solvent and frequency on hyperpolarizabilities computed by SR and MR hybrids and compare these predictions with other DFT methods and available experimental data.Show more Item Capturing static and dynamic correlations by a combination of projected Hartree-Fock and density functional theories(American Institute of Physics, 2013) Garza, Alejandro J.; Jiménez-Hoyos, Carlos A.; Scuseria, Gustavo E.Show more This paper explores the possibility of combining projected Hartree-Fock and density functional theories for treating static and dynamic correlations in molecular systems with mean-field computational cost. The combination of spin-projected unrestricted Hartree-Fock (SUHF) with the TPSS correlation functional (SUHF+TPSS) yields excellent results for non-metallic molecular dissociations and singlet-triplet splittings. However, SUHF+TPSS fails to provide the qualitatively correct dissociation curve for the notoriously difficult case of the chromium dimer. By tuning the TPSS correlation parameters and adding complex conjugation symmetry breaking and restoration to SUHF, the right curve shape for Cr2 can be obtained; unfortunately, such a combination is found to lead to overcorrelation in the general case.Show more Item Cluster-based mean-field and perturbative description of strongly correlated fermion systems: Application to the one- and two-dimensional Hubbard model(American Physical Society, 2015) Jiménez-Hoyos, Carlos A.; Scuseria, Gustavo E.Show more We introduce a mean-field and a perturbative approach, based on clusters, to describe the ground state of fermionic strongly correlated systems. In the cluster mean-field approach, the ground-state wave function is written as a simple tensor product over optimized cluster states. The optimization of the single-particle basis where the cluster mean field is expressed is crucial in order to obtain high-quality results. The mean-field nature of the Ansatz allows us to formulate a perturbative approach to account for intercluster correlations; other traditional many-body strategies can be easily devised in terms of the cluster states. We present benchmark calculations on the half-filled 1D and (square) 2D Hubbard model, as well as the lightly doped regime in 2D, using cluster mean-field and second-order perturbation theory. Our results indicate that, with sufficiently large clusters or to second-order in perturbation theory, a cluster-based approach can provide an accurate description of the Hubbard model in the considered regimes. Several avenues to improve upon the results presented in this work are discussed.Show more Item Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations(AIP Publishing LLC., 2016) Qiu, Yiheng; Henderson, Thomas M.; Scuseria, Gustavo E.Show more Spin-projected Hartree-Fock is written as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-Hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them.Show more Item Comparison of self-consistent field convergence acceleration techniques(American Institute of Physics, 2012) Garza, Alejandro J.; Scuseria, Gustavo E.Show more The recently proposed ADIIS and LIST methods for accelerating self-consistent field (SCF) convergence are compared to the previously proposed energy-DIIS (EDIIS) + DIIS technique. We here show mathematically that the ADIIS functional is identical to EDIIS for Hartree-Fock wavefunctions. Convergence failures of EDIIS + DIIS reported in the literature are not reproduced with our codes. We also show that when correctly implemented, the EDIIS + DIIS method is generally better than the LIST methods, at least for the cases previously examined in the literature. We conclude that, among the family of DIIS methods, EDIIS + DIIS remains the method of choice for SCF convergence acceleration.Show more Item Conjugate gradient density matrix search: A linear scaling alternative to diagonalization(1997) Millam, John Mark; Scuseria, Gustavo E.Show more Advances in the computation of the Coulomb, exchange, and correlation contributions to Gaussian-based Hartree-Fock and density functional theory Hamiltonians have demonstrated near-linear scaling with molecular size for these steps. These advances leave the ${\cal O}(N\sp3)$ diagonalization bottleneck as the rate determining step for very large systems. In this work, a conjugate gradient density matrix search (CG-DMS) method has been successfully extended and computationally implemented for use with first principles calculations. A Cholesky decomposition of the overlap matrix and its inverse, which can be formed in near linear time for sparse systems, is used to transform to and back from an orthonormal basis. Linear scaling of CPU time for the density matrix search and crossover of CPU time with diagonalization is demonstrated for polyglycine chains containing up to 493 atoms and water clusters up to 900 atoms.Show more Item Correcting the Self-Interaction Error of Approximate Density Functionals(2007) Vydrov, Oleg A.; Scuseria, Gustavo E.Show more Common density functional approximations (DFAs) for the exchange-correlation energy suffer from self-interaction error (SIE), which is believed to be the cause of many of the failures of these approximations, such as poor description of charge transfer and transition states of chemical reactions. The standard self-interaction correction (SIC) of Perdew and Zunger (PZ) removes spurious self-interaction terms orbital-by-orbital. We implemented the Perdew–Zunger SIC self-consistently and carried out systematic tests of its performance. We found that PZ-SIC impairs the accuracy of semi-local functionals for equilibrium properties. PZ-SIC seems to overcorrect many-electron systems. We devised a modified version of the SIC, which is scaled down in many-electron regions. The scaled-down SIC has greatly improved performance for many molecular properties. Studies of fractionally-charged systems led to the new definition of "many-electron self-interaction error", which is a generalization of the one-electron concept. An " M -electron self-interaction-free" functional is one that produces a realistic linear variation of total energy with electron number N between the integers M -1 and M . Semi-local DFAs exhibit large many-electron SIE and therefore fail for systems with fractional average electron number. PZ-SIC and its scaled-down variants are one-electron SIE-free. PZ-SIC is often nearly many-electron SIE-free, but this property is lost in the scaled-down SIC. Another consequence of the SIE is incorrect asymptotic behavior of the exchange-correlation potential in semi-local DFAs. PZ-SIC recovers the exact asymptote, but its scaled-down version does not. An efficient method to impose the exact asymptote in a hybrid functional is to introduce range separation into the exchange component and replace the long-range portion of the approximate exchange by the Hartree-Fock counterpart. We show that this long-range correction works particularly well in combination with the short-range variant of the Perdew, Burke, and Ernzerhof (PBE) exchange functional. This long-range-corrected hybrid, denoted LC-ωPBE, is remarkably accurate for a broad range of molecular properties, such as thermo-chemistry, barrier heights of chemical reactions, bond lengths, and most notably, description of processes involving long-range charge transfer. Although LC-ωPBE is not exactly one-electron SIE-free, it can be nearly many-electron SIE-free in many cases.Show more Item Correlating the antisymmetrized geminal power wave function(AIP, 2020) Henderson, Thomas M.; Scuseria, Gustavo E.Show more Strong pairing correlations are responsible for superconductivity and off-diagonal long-range order in the two-particle density matrix. The antisymmetrized geminal power wave function was championed many years ago as the simplest model that can provide a reasonable qualitative description for these correlations without breaking number symmetry. The fact remains, however, that the antisymmetrized geminal power is not generally quantitatively accurate in all correlation regimes. In this work, we discuss how we might use this wave function as a reference state for a more sophisticated correlation technique such as configuration interaction, coupled cluster theory, or the random phase approximation.Show more Item Coupled cluster channels in the homogeneous electron gas(AIP Publishing, 2014) Shepherd, James J.; Henderson, Thomas M.; Scuseria, Gustavo E.Show more We discuss diagrammatic modifications to the coupled cluster doubles (CCD) equations, wherein different groups of terms out of rings, ladders, crossed-rings, and mosaics can be removed to form approximations to the coupled cluster method, of interest due to their similarity with various types of random phase approximations. The finite uniform electron gas (UEG) is benchmarked for 14- and 54-electron systems at the complete basis set limit over a wide density range and performance of different flavours of CCD is determined. These results confirm that rings generally overcorrelate and ladders generally undercorrelate; mosaics-only CCD yields a result surprisingly close to CCD. We use a recently developed numerical analysis [J. J. Shepherd and A. Grüneis, Phys. Rev. Lett. 110, 226401 (2013)] to study the behaviours of these methods in the thermodynamic limit. We determine that the mosaics, on forming the Brueckner one-body Hamiltonian, open a gap in the effective one-particle eigenvalues at the Fermi energy. Numerical evidence is presented which shows that methods based on this renormalisation have convergent energies in the thermodynamic limit including mosaic-only CCD, which is just a renormalised MP2. All other methods including only a single channel, namely, ladder-only CCD, ring-only CCD, and crossed-ring-only CCD, appear to yield divergent energies; incorporation of mosaic terms prevents this from happening.Show more