Biomedical subjects

David A Mazziotti

Publications and source records attributed to David A Mazziotti.

18 recordsLinked to original sources

PubMed2007

Molecular properties from variational reduced-density-matrix theory with three-particle N-representability conditions.

Molecular ground-state energies and two-electron reduced density matrices (2-RDMs) have recently been computed without the many-electron wave function by constraining the 2-RDM to satisfy a complete set of three-positivity conditions for N representability [D. A. Mazziotti, Phys. Rev. A 74, 032501 (2006)]. Energies at both equilibrium and nonequilibrium geometries are obtained within 0.3% of the correlation energy. In this paper the authors extend this work to examine the accuracy of molecular properties, including multipole moments and components of the ground-state energy, relative to full configuration interaction (FCI). Comparisons are also made with 2-RDM methods with two-positivity conditions and two-positivity plus the generalized T1T2 conditions as well as several approximate wave function methods. Using the 2-RDM method with three-positivity conditions, the authors obtain dipole, quadrupole, and octupole moments for BeH2, BH, H2O, CO, and NH3 at equilibrium geometries that are within 0.04% of their FCI values. In addition, for the potential energy surface of N2, the 2-RDM method with three-positivity yields not only accurate total ground-state energies but also accurate expectation values of the kinetic energy operator, the electron-nuclei potential, and electron-electron repulsion.

Algorithms↗

PubMed2006

The cumulant two-particle reduced density matrix as a measure of electron correlation and entanglement.

Several measures of electron correlation are compared based on two criteria: (i) the presence of a unique mapping between the reduced variables in the measure and the many-electron wave function and (ii) the linear scaling of the measure and its variables with system size. We propose the squared Frobenius norm of the cumulant part of the two-particle reduced density matrix (2-RDM) as a measure of electron correlation that satisfies these criteria. An advantage of this cumulant-based norm is its ability to measure the correlation from spin entanglement, which is not contained in the correlation energy. Alternative measures based on the 2-RDM, such as the von Neumann entropy, do not scale linearly with system size. Properties of the measures are demonstrated with Be, F(2), HF, N(2), and a hydrogen chain.

Algorithms↗

PubMed2006

Computation of dipole, quadrupole, and octupole surfaces from the variational two-electron reduced density matrix method.

Recent advances in the direct determination of the two-electron reduced density matrix (2-RDM) by imposing known N-representability conditions have mostly focused on the accuracy of molecular potential energy surfaces where multireference effects are significant. While the norm of the 2-RDM's deviation from full configuration interaction has been computed, few properties have been carefully investigated as a function of molecular geometry. Here the dipole, quadrupole, and octupole moments are computed for a range of molecular geometries. The addition of Erdahl's T2 condition [Int. J. Quantum Chem. 13, 697 (1978)] to the D, Q, and G conditions produces dipole and multipole moments that agree with full configuration interaction in a double-zeta basis set at all internuclear distances.

Journal Article↗

PubMed2006

Anti-hermitian contracted schrödinger equation: direct determination of the two-electron reduced density matrices of many-electron molecules.

Two-electron reduced density matrices (2-RDMs) of many-electron molecules are directly determined without calculation of their wave functions by solving the anti-Hermitian contracted Schrödinger equation. Approximation of the 3-RDM in the anti-Hermitian contracted Schrödinger equation by a corrected cumulant expansion [Mazziotti, Phys. Rev. A 60, 3618 (1999)] permits the direct calculation of the energy and 2-RDM with many high-order correlation effects included. The method is illustrated for the molecules BeH2, H2O, NH3, CH4, and CO as well as the dissociation of BH. Correlation energies are obtained within 95%-100% of full-configuration interaction, and 2-RDMs very nearly satisfy known N-representability conditions.

Journal Article↗

PubMed2006

Modeling the influence of a laser pulse on the potential energy surface in optimal molecular control theory.

Understanding and modeling the interaction between light and matter is essential to the theory of optical molecular control. While the effect of the electric field on a molecule's electronic structure is often not included in control theory, it can be modeled in an optimal control algorithm by a set or toolkit of potential energy surfaces indexed by discrete values of the electric field strength where the surfaces are generated by Born-Oppenheimer electronic structure calculations that directly include the electric field. Using a new optimal control algorithm with a trigonometric mapping to limit the maximum field strength explicitly, we apply the surface-toolkit method to control the hydrogen fluoride molecule. Potential energy surfaces in the presence and absence of the electric field are created with two-electron reduced-density-matrix techniques. The population dynamics show that adjusting for changes in the electronic structure of the molecule beyond the static dipole approximation can be significant for designing a field that drives a realistic quantum system to its target observable.

Journal Article↗

PubMed2006

Variational reduced-density-matrix theory applied to the potential energy surfaces of carbon monoxide in the presence of electric fields.

The variational optimization of the energy with respect to the two-electron reduced-density matrix (2-RDM), constrained by N-representability conditions, can determine the shape of molecular potential energy surfaces with useful accuracy. In this paper, we apply the 2-RDM method with a first-order optimization algorithm [Mazziotti, D. A. Phys. Rev. Lett. 2004, 93, 213001] to investigating the potential energy surfaces of carbon monoxide in the presence and absence of an electric field. Two beneficial characteristics of the 2-RDM method for computing potential energy surfaces include the following: (i) its ability to capture multireference effects without specifying any reference wave function or density matrix and (ii) its guarantee of a global energy minimum in the variational optimization. The 2-RDM method produces electronic ground-state energies with similar accuracy at equilibrium and nonequilibrium geometries in both the presence and the absence of the electric field. Computed dipole moments are similar in accuracy to the values from the computationally expensive configuration interaction with single, double, triple, and quadruple excitations. These surfaces have important applications in quantum molecular control theory.

Carbon Monoxide↗

PubMed2006

Quantum chemistry without wave functions: two-electron reduced density matrices.

For 50 years, progress toward the direct calculation of the ground-state two-electron reduced density matrix (2-RDM) was stymied from an inability to constrain the 2-RDM to represent an N-electron wave function. Recent advances in theory and optimization have realized the direct calculation of the 2-RDM. A variational 2-RDM procedure, using first-order semidefinite programming, has been shown to capture multireference correlation effects important at nonequilibrium geometries [Mazziotti, Phys. Rev. Lett. 2004, 93, No. 213001]. This method emerged from research on a nonvariational calculation of the 2-RDM by the contracted Schrödinger equation. Both approaches will be discussed and illustrated.

Journal Article↗

PubMed2005

Quantum chemical design of hydroxyurea derivatives for the treatment of sickle-cell anemia.

Treatment of sickle-cell anemia by hydroxyurea has been shown to decrease patient mortality by 40%. In a rate-limiting step, hydroxyurea reacts with hemoglobin to form the nitroxide radical, which then decomposes to yield nitric oxide (NO). In this paper, we examine derivatives of hydroxyurea and their radicals by quantum chemical methods to identify derivatives that generate NO-producing radicals at a faster rate than hydroxyurea. The molecules are treated with Hartree-Fock theory, correlated wave function methods such as perturbation theory and coupled-cluster methods, and density functional theory. We observe that the inclusion of the correlation energy is important for an accurate comparison of the energy changes associated with modifications of the hydroxyurea molecule and its radical. The computational results are compared with available experimental data. All 19 derivatives of hydroxyurea, including a new medication for asthma Zileuton, manifest changes in their electronic energies that mark them as candidates for a faster formation of NO-producing radicals.

Anemia, Sickle Cell↗

PubMed2005

Application of variational reduced-density-matrix theory to the potential energy surfaces of the nitrogen and carbon dimers.

The acceleration of the variational two-electron reduced-density-matrix (2-RDM) method, using a new first-order algorithm [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)], has shown its usefulness in the accurate description of potential energy surfaces in nontrivial basis sets. Here we apply the first-order 2-RDM method to the potential energy surfaces of the nitrogen and carbon dimers in polarized valence double-zeta basis sets for which benchmark full-configuration-interaction calculations exist. In a wave function formalism accurately stretching the triple bond of the nitrogen dimer requires at least six-particle excitations from the Hartree-Fock reference. Furthermore, cleaving the double bond of C2 should produce a "non-Morse"-like potential curve because the ground state near equilibrium (X 1sigma(g)+) has an avoided crossing with the second excited state (B' 1sigma(g)+) and a level crossing with the first excited state (B 1delta(g)). Because the 2-RDM method variationally optimizes the energy over correlated 2-RDMs on the two-electron space without parametrization of the many-electron wave function, it captures multireference correlations that are difficult to describe with approximate wave functions. The 2-RDM method yields for N2 a potential energy surface with features and spectroscopic constants that are more accurate than those from single-reference methods and similar in accuracy to multireference techniques, and it describes the non-Morse-like behavior of C2 which is not captured by single-reference methods.

Journal Article↗

PubMed2005

Improved perturbative treatment of electronic energies from a minimal-norm approach to many-body perturbation theory.

We propose a zeroth-order Hamiltonian for many-body perturbation theory based on the unitary decomposition of the two-particle reduced Hamiltonian. For the zeroth-order Hamiltonian constrained to be diagonal in the Hartree-Fock basis set, the two-particle reduced perturbation matrix is chosen to have a minimal Frobenius norm. When compared with the Møller-Plesset partitioning, the method yields more accurate second-order energies.

Journal Article↗

PubMed2005

Application of variational reduced-density-matrix theory to organic molecules.

Variational calculation of the two-electron reduced-density matrix (2-RDM), using a new first-order algorithm [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)], is applied to medium-sized organic molecules. The calculations reveal systematic trends in the accuracy of the energy with well-known chemical concepts such as hybridization, electronegativity, and atomic size. Furthermore, correlation energies from hydrocarbon chains indicate that the calculation of the 2-RDM subject to two-positivity conditions is size extensive, that is, the energy grows linearly with the number of electrons. Because organic molecules have a well-defined set of functional groups, we employ the trends in energy accuracy of the functional groups to design a correction to the 2-RDM energy for an arbitrary organic molecule. We apply the 2-RDM calculations with the functional-group correction to a large set of organic molecules with different functional groups. Energies with millihartree accuracy are obtained both at equilibrium and nonequilibrium geometries.

Journal Article↗

PubMed2005

Comparison of two genres for linear scaling in density functional theory: purification and density matrix minimization methods.

Two classes of linear-scaling methods to replace diagonalization of the one-particle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2-contracted Schrodinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)] are implemented in large systems.

Journal Article↗

PubMed2004

First-order semidefinite programming for the direct determination of two-electron reduced density matrices with application to many-electron atoms and molecules.

Direct variational calculation of two-electron reduced density matrices (2-RDMs) for many-electron atoms and molecules in nonminimal basis sets has recently been achieved through the use of first-order semidefinite programming [D. A. Mazziotti, Phys. Rev. Lett. (in press)]. With semidefinite programming, the electronic ground-state energy of a molecule is minimized with respect to the 2-RDM subject to N-representability constraints known as positivity conditions. Here we present a detailed account of the first-order algorithm for semidefinite programming and its comparison with the primal-dual interior-point algorithms employed in earlier variational 2-RDM calculations. The first-order semidefinite-programming algorithm, computations show, offers an orders-of-magnitude reduction in floating-point operations and storage in comparison with previous implementations. We also examine the ability of the positivity conditions to treat strong correlation and multireference effects through an analysis of the Hamiltonians for which the conditions are exact. Calculations are performed in nonminimal basis sets for a variety of atoms and molecules and the potential-energy curves for CO and H(2)O.

Journal Article↗

PubMed2004

Realization of quantum chemistry without wave functions through first-order semidefinite programming.

Determining the energy and properties of an N-electron molecule through a two-electron variational optimization has been a dream for more than half a century. While optimizations, using two-electron reduced density matrices constrained to represent N electrons, have recently been achieved, the computational costs are prohibitive. In this report an efficient algorithm with an order-of-magnitude reduction in floating-point operations and memory usage is presented. Because the optimization occurs on the space of two electrons, this method automatically treats strong, multireference correlation. Application is made to N2 and H6 where the method yields consistent accuracy at all geometries.

Journal Article↗

PubMed2004

Perturbation theory corrections to the two-particle reduced density matrix variational method.

In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen.

Journal Article↗

PubMed2004

Spectral difference Lanczos method for efficient time propagation in quantum control theory.

Spectral difference methods represent the real-space Hamiltonian of a quantum system as a banded matrix which possesses the accuracy of the discrete variable representation (DVR) and the efficiency of finite differences. When applied to time-dependent quantum mechanics, spectral differences enhance the efficiency of propagation methods for evolving the Schrodinger equation. We develop a spectral difference Lanczos method which is computationally more economical than the sinc-DVR Lanczos method, the split-operator technique, and even the fast-Fourier-Transform Lanczos method. Application of fast propagation is made to quantum control theory where chirped laser pulses are designed to dissociate both diatomic and polyatomic molecules. The specificity of the chirped laser fields is also tested as a possible method for molecular identification and discrimination.

Journal Article↗

PubMed2003

Towards idempotent reduced density matrices via particle-hole duality: McWeeny's purification and beyond.

Generalizations of McWeeny's purification formula are developed within the formalism of the particle-hole duality from the theory of reduced density matrices. Each of the generalized purification formulas is expressed as a sum of the one-particle reduced density matrix (1-RDM) and a finite series in the product of the one-particle and the one-hole RDMs, a product which vanishes in the limit that the 1-RDM is idempotent. Two categories of purification formulas are explored: (i) formulas which treat the "occupied" and the "virtual" occupation numbers equivalently and (ii) formulas which treat these occupation numbers differently. The latter category includes and extends the purification formulas derived in the context of the 1,2-contracted Schrödinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)]. While the McWeeny purification minimizes the absolute error in the occupation numbers quadratically, the generalized purification formulas exhibit faster than quadratic convergence of the 1-RDM towards idempotency. Application of these purification formulas in existing algorithms for linear scaling will be explored and discussed including illustrative calculations on sodium wires of length 10, 20, 30, and 40 atoms.

Journal Article↗

PubMed2002

Purification of correlated reduced density matrices.

The notion of purification is generalized to treat correlated reduced density matrices. Traditionally, purification denotes the process by which a one-particle reduced density matrix (1-RDM) is made idempotent, that is, its eigenvalues are mapped to either 0 or 1. Purification of correlated RDMs is defined as the iterative process by which an arbitrary RDM is forced to satisfy several necessary N-representability conditions. Using the unitary decomposition of RDMs and the positivity conditions, we develop an algorithm to purify the 2-RDM. The algorithm is applied within the solution of the contracted Schrödinger equation CSE for the 2-RDM [D. A. Mazziotti, Phys. Rev. A 57, 4219 (1998)]. Previous attempts to solve the CSE by powerlike methods have frequently produced divergent energies, but we show that the purification process eliminates the divergent behavior for systematic and reliable convergence of the contracted power method to the N-particle energy.

Journal Article↗