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Martin Head-Gordon

Publications and source records attributed to Martin Head-Gordon.

At least 37 records · Page 2Linked to original sources
PubMed2005

A density functional theory study of the mechanism of free radical generation in the system vanadate/PCA/H2O2.

Experimental studies by Shul'pin and co-workers have shown that vanadate anions in combination with pyrazine-2-carboxylic acid (PCA identical with pcaH) produce an exceptionally active complex that promotes the oxidation of alkanes and other organic molecules. Reaction of this complex with H2O2 releases HOO* free radicals and generates V(IV) species, which are capable of generating HO* radicals by reaction with additional H2O2. The oxidation of alkanes is initiated by reaction with the HO* radicals. The mechanism of hydrocarbon oxidation with vanadate/PCA/H2O2 catalyst has been studied using density functional theory. The proposed model reproduces the major experimental observations. It is found that a vanadium complex with one pca (PCA identical with pcaH) and one H2O2 ligand is the precursor to the species responsible for HOO* generation. It is also found that species containing two pca ligands and an H2O2 molecule do not exist in the solution, in contradiction to previous interpretations of experimental observations. Calculated dependences of the oxidation rate on initial concentrations of PCA and H2O2 have characteristic maxima, the shapes of which are determined by the equilibrium concentration of the active species. Conversion of the precursors requires hydrogen transfer from H2O2 to a vanadyl group. Our calculations show that direct transfer has a higher barrier than pca-assisted indirect transfer. Indirect transfer occurs by migration of hydrogen from coordinated H2O2 to the oxygen of a pca ligand connected to the vanadium atom. The proposed mechanism demonstrates the important role of the cocatalyst in the reaction and explains why H2O2 complexes without pca are less active. Our work shows that the generation of HOO* radicals cannot occur via cleavage of a V-OOH bond in the complex formed directly from the precursors, as proposed before. The activation barrier for this process is too high. Instead, HOO* radicals are formed via a sequence of additional steps involving lower activation barriers. The new mechanism for free radical generation underestimates the observed rate of hexane oxidation by less than an order of magnitude; however, the calculated activation energy (67-81 kJ/mol) agrees well with that determined experimentally (63-80 kJ/mol).

Adsorption↗
PubMed2005

Search for stratospheric bromine reservoir species: theoretical study of the photostability of mono-, tri-, and pentacoordinated bromine compounds.

Previous work has shown that pentacoordinated bromine compounds have their lowest excited electronic states shifted to the blue relative to monocoordinated bromine molecules, and that this shift may be large enough to render them photostable in the lower stratosphere. Our earlier work has also shown that certain pentacoordinated bromine compounds are thermodynamically stable relative to their mono- or tricoordinated isomers, suggesting that if a bromine stratospheric reservoir species exists, it may be a pentacoordinated compound. In this study we have examined the singlet and triplet excited electronic states of several bromine compounds, using time dependent density functional theory, to assess their photostability under stratospheric conditions and in order to elucidate the nature of lowest excited states in mono-, tri-, and pentacoordinated bromine molecules. The triplet states have been included due to the strong spin-orbit mixing in bromine. We have found several pentacoordinated bromine/oxygen compounds that could be photostable in the lower stratosphere, but we have also found that monovalent bromine compounds where the bromine atom is bonded to an atom with no lone-pair p-electrons is far and away the most photostable. Attachment/detachment electron density plots have been useful in ascertaining the nature of the excited electronic states and their likely path to photodissociation.

Bromine↗
PubMed2005

Fast localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates.

We present here an algorithm for computing stable, well-defined localized orthonormal virtual orbitals which depend smoothly on nuclear coordinates. The algorithm is very fast, limited only by diagonalization of two matrices with dimension the size of the number of virtual orbitals. Furthermore, we require no more than quadratic (in the number of electrons) storage. The basic premise behind our algorithm is that one can decompose any given atomic-orbital (AO) vector space as a minimal basis space (which includes the occupied and valence virtual spaces) and a hard-virtual (HV) space (which includes everything else). The valence virtual space localizes easily with standard methods, while the hard-virtual space is constructed to be atom centered and automatically local. The orbitals presented here may be computed almost as quickly as projecting the AO basis onto the virtual space and are almost as local (according to orbital variance), while our orbitals are orthonormal (rather than redundant and nonorthogonal). We expect this algorithm to find use in local-correlation methods.

Algorithms↗
PubMed2005

Simulated quantum computation of molecular energies.

The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.

Journal Article↗
PubMed2005

Scaled opposite spin second order Møller-Plesset theory with improved physical description of long-range dispersion interactions.

Separate scaling of the same-spin and opposite spin contributions to the second-order Møller-Plesset energy can yield statistically improved performance for a variety of chemical problems. If only the opposite spin contribution is scaled, it is also possible to reduce the computational complexity from fifth order to fourth order in system size, with very little degradation of the results. However neither of these scaled MP2 energies recovers the full MP2 result for the dispersion energy of nonoverlapping systems. This deficiency is addressed in this work by using a distance-dependent scaling of the opposite spin correlation energy. The resulting method is compared against the previously proposed scaled MP2 methods on a range of problems involving both short and long-range interactions.

Algorithms↗
PubMed2005

Accelerated, energy-conserving Born-Oppenheimer molecular dynamics via Fock matrix extrapolation.

Born-Oppenheimer molecular dynamics calculations, especially those that exploit information retained from previous time steps in order to accelerate convergence of the electronic structure calculations, can suffer from systematic error in the energy gradient that manifests as a drift in the microcanonical energy. Here, we demonstrate that this is only the case when the self-consistent field (SCF) convergence criterion is set too low; using only a marginally tighter threshold (still two orders of magnitude lower than what is standard for geometry optimizations), the drift disappears completely, for a time scale of several picoseconds. Using a Fock matrix extrapolation technique, SCF convergence is achieved in as few as three iterations per time step, without sacrificing energy conservation. In test calculations for C2F4, (H2O4-, (H2O6, and [Fe(H2O6]2+, we demonstrate energy-conserving Fock matrix extrapolation that reduces the number of SCF cycles by up to 70% and reduces the computer time per molecular dynamics step by 45-55%, relative to simulations performed without extrapolation.

Algorithms↗
PubMed2005

A local correlation model that yields intrinsically smooth potential-energy surfaces.

We demonstrate an algorithm for computing local coupled-cluster doubles (LCCD) energies that form rigorously smooth potential-energy surfaces and which should be fast enough for application to large systems in the future. Like previous LCCD algorithms, our method solves iteratively for only a limited number of correlation amplitudes, treating the remaining amplitudes with second-order perturbation theory. However, by employing bump functions, our method smoothes the transition from iteratively solved amplitude to perturbation-treated amplitude, invoking the implicit function theorem to prove that our LCCD energy is an infinitely differentiable function of nuclear coordinates. We make no explicit amplitude domains nor do we rely on the existence of atom-centered, redundant orbitals in order to get smooth potential-energy curves. In fact, our algorithm employs only localized orthonormal occupied and virtual orbitals. Our approach should be applicable to many other electron correlation methods.

Journal Article↗
PubMed2005

Nitrogen activation via three-coordinate molybdenum complexes: comparison of density functional theory performance with wave function based methods.

Obtaining an accurate theoretical model for the activation of dinitrogen by three-coordinate molybdenum amide complexes (e.g. Mo(NH2)3) is difficult due to the interaction of various high- and low-spin open-shell complexes along the reaction coordinate which must be treated with comparable levels of accuracy in order to obtain reasonable potential energy surfaces. Density functional theory with present-day functionals is a popular choice in this situation; however, the dinitrogen activation reaction energetics vary substantially with the choice of functional. An assessment of the reaction using specialized wave function based methods indicates that although current density functionals in general agree qualitatively on the mechanistic details of the reaction, a variety of high-level electron correlation methods (including CCSD(T), OD(T), CCSD(2), KS-CCSD(T), and spin-flip CCSD) provide a consistent but slightly different representation of the system.

Journal Article↗
PubMed2005

Calculation of electron detachment energies for water cluster anions: an appraisal of electronic structure methods, with application to (H2O)20- AND (H2O)24-.

We present benchmark calculations of vertical electron detachment energies (VDEs) for various conformers of (H2O)n-, using both wave function and density functional methods, in sequences of increasingly diffuse Gaussian basis sets. For small clusters (n < or = 6), a systematic examination of VDE convergence reveals that it is possible to converge this quantity to within approximately 0.01 eV of the complete-basis limit, using a highly diffuse but otherwise economical Pople-style basis set of double-zeta quality, with 28 atom-centered basis functions per water molecule. Floating-center basis functions can be useful but are not required to obtain accurate VDEs. Second-order Møller-Plesset perturbation (MP2) theory suffices to obtain VDEs that are within 0.05 eV of the results from both experiment and coupled-cluster theory, and which always err toward underbinding the extra electron. In contrast to these consistent predictions, VDEs calculated using density functional theory (DFT) vary widely, according to the fraction of Hartree-Fock exchange in a given functional. Common functionals such as BLYP and B3LYP overestimate the VDE by 0.2-0.5 eV, whereas a variant of Becke's "half and half" functional is much closer to coupled-cluster predictions. Exploratory calculations for (H2O)20- and (H2O)24- cast considerable doubt on earlier calculations that were used to assign the photoelectron spectra of these species to particular cluster isomers.

Journal Article↗
PubMed2005

Auxiliary basis expansions for large-scale electronic structure calculations.

One way to reduce the computational cost of electronic structure calculations is to use auxiliary basis expansions to approximate four-center integrals in terms of two- and three-center integrals, usually by using the variationally optimum Coulomb metric to determine the expansion coefficients. However, the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric fitting equations also involve divergent matrix elements for extended systems treated with periodic boundary conditions. An attenuated Coulomb metric that is short-range can eliminate these oddities without substantially degrading calculated relative energies. The sparsity of the fit coefficients is assessed on simple hydrocarbon molecules and shows quite early onset of linear growth in the number of significant coefficients with system size using the attenuated Coulomb metric. Hence it is possible to design linear scaling auxiliary basis methods without additional approximations to treat large systems.

Alkanes↗
PubMed2005

Viscosity of the aqueous liquid/vapor interfacial region: 2D electrochemical measurements with a piperidine nitroxy radical probe.

Surface partitioning of 2,2,6,6-tetramethyl-1-piperidynyloxy radical (Tempo) to the air/water interface follows a Langmuir isotherm. The partition constant was obtained by the surface tension measurements in the concentration range of 1.0 x 10(-4)-2.4 x 10(-3) M yielding K = 640 +/- 99 M(-1). The lateral mobility of Tempo at the air/water interface was measured electrochemically in the surface concentration range of 2.0 x 10(-11)-1.4 x 10(-10) mol/cm2, corresponding to ca. 7.3-50% full monolayer coverage. The measurements employed cyclic voltammetry with line microelectrodes touching the air/water interface. The Tempo lateral diffusion constant of (1.5 +/- 0.7) x 10(-4) cm2/s is independent of surface concentration below 4.0 x 10(-11) mol/cm2. The extent of Tempo water interactions was assessed by the electronic structure calculations. These calculations showed that, at most, two water molecules can hydrogen bond with the oxygen atom of the nitroxyl group of Tempo, and that a single water molecule forms a hydrogen bond that is ca. 30% stronger than the H2O-H2O hydrogen bond. These calculations led to a postulate that Tempo diffuses along the interface largely unimmersed, and that it is coupled to the interfacial water via hydrogen bonding with H2O. In view of this postulate, the viscosity of the aqueous liquid/vapor interfacial region obtained by interpreting the Tempo diffusion constant in the low concentration region is as much as 4 times smaller than that of bulk liquid water.

Journal Article↗
PubMed2005

A localized basis that allows fast and accurate second-order Moller-Plesset calculations.

We present a method for computing a basis of localized orthonormal orbitals (both occupied and virtual), in whose representation the Fock matrix is extremely diagonal dominant. The existence of these orbitals is shown empirically to be sufficient for achieving highly accurate second-order Moller-Plesset (MP2) energies, calculated according to Kapuy's method. This method (which we abbreviate KMP2) involves a different partitioning of the n-electron Hamiltonian and scales at most quadratically, with potential for linearity, in the number of electrons. As such, we believe the KMP2 algorithm presented here could be the basis of a viable approach to local-correlation calculations.

Journal Article↗
PubMed2004

Curvy-steps approach to constraint-free extended-Lagrangian ab initio molecular dynamics, using atom-centered basis functions: convergence toward Born-Oppenheimer trajectories.

A dynamical extension of the "curvy-steps" approach to linear-scaling self-consistent field calculations is presented, which yields an extended-Lagrangian formulation of ab initio molecular dynamics. An exponential parametrization of the one-electron density matrix, expressed in terms of atom-centered Gaussian basis functions, facilitates propagation along the manifold of density matrices in a geometrically correct fashion that automatically enforces idempotency constraints. The extended Lagrangian itself is constraint free, thus neither density matrix purification nor expensive, iterative solution for Lagrange multipliers is required. Propagation is highly efficient, and time steps compare favorably to those used in Car-Parrinello molecular dynamics simulations. The behavior of the method, especially with regard to the maintenance of adiabatic decoupling of nuclei and electrons, is examined for a sequence of diatomic molecules, and comparison is made to trajectories propagated on the converged Born-Oppenheimer surface. Certain claims to the contrary notwithstanding, our results demonstrate that vibrational frequencies may depend on the value of the fictitious mass parameter, even in an atom-centered basis. Light-atom stretching frequencies can be significantly redshifted, even when the nuclear and electronic energy scales are well separated. With a sufficiently small fictitious mass and a short time step, accurate frequencies can be obtained; we characterize appropriate values of these parameters for a wide range of vibrational frequencies.

Journal Article↗
PubMed2004

Scaled opposite-spin second order Møller-Plesset correlation energy: an economical electronic structure method.

A simplified approach to treating the electron correlation energy is suggested in which only the alpha-beta component of the second order Møller-Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled opposite-spin second order energy (SOS-MP2), where MP2 is Møller-Plesset theory, yields results for relative energies and derivative properties that are statistically improved over the conventional MP2 method. Furthermore, the SOS-MP2 energy can be evaluated without the fifth order computational steps associated with MP2 theory, even without exploiting any spatial locality. A fourth order algorithm is given for evaluating the opposite spin MP2 energy using auxiliary basis expansions, and a Laplace approach, and timing comparisons are given.

Algorithms↗
PubMed2004

An efficient method for calculating maxima of homogeneous functions of orthogonal matrices: applications to localized occupied orbitals.

We present here three new algorithms (one purely iterative and two DIIS-like [Direct Inversion in the Iteractive Subspace]) to compute maxima of homogeneous functions of orthogonal matrices. These algorithms revolve around the mathematical lemma that, given an invertible matrix A, the function f(U)=Tr(AU) has exactly one local (and global) maximum for U special orthogonal [i.e., UU(T)=1 and det(U)=1]. This is proved in the Appendix. One application of these algorithms is the computation of localized orbitals, including, for example, Boys and Edmiston-Ruedenberg (ER) orbitals. The Boys orbitals are defined as the set of orthonormal orbitals which, for a given vector space of orbitals, maximize the sum of the distances between orbital centers. The ER orbitals maximize total self-interaction energy. The algorithm presented here computes Boys orbitals roughly as fast as the traditional method (Jacobi sweeps), while, for large systems, it finds ER orbitals potentially much more quickly than traditional Jacobi sweeps. In fact, the required time for convergence of our algorithm scales quadratically in the region of a few hundred basis functions (though cubicly asymptotically), while Jacobi sweeps for the ER orbitals traditionally scale as the number of occupied orbitals to the fifth power. As an example of the utility of the method, we provide below the ER orbitals of nitrated and nitrosated benzene, and we discuss the chemical implications.

Journal Article↗
PubMed2004

Intermolecular pi-to-pi bonding between stacked aromatic dyads. Experimental and theoretical binding energies and near-IR optical transitions for phenalenyl radical/radical versus radical/cation dimerizations.

The high symmetry and stability of phenalenyl systems, both as the planar pi-radical (P*) and as the pi-cation (P+), are desirable characteristics of prototypical aromatic donor/acceptor pairs that encourage their use as (binary) models for the study of intermolecular interactions extant in stacked molecular arrays. Thus, quantitative ESR spectroscopy of the paramagnetic P* identifies its spontaneous self-association to the diamagnetic P2, previously characterized as the stacked pi-dimer by X-ray crystallography. Likewise, the rapid cross-association of P* with the closed-shell P+ leads to the stacked pi-dimer cation P2*+ with the "doubled" ESR spectrum diagnostic of complete (odd) electron delocalization. These pi-associations are confirmed by UV-vis studies that reveal diagnostic near-IR bands of both P2 and P2*+-strongly reminiscent of intermolecular charge-transfer absorptions in related aromatic (donor/acceptor) pi-associations. Ab initio molecular-orbital calculations for the pi-dimer P2 predict a binding energy of DeltaED = -11 kcal mol(-1), which is in accord with the experimental enthalpy change of DeltaHD = -9.5 kcal mol(-1) in dichloromethane solution. Most importantly, the calculations reproduce the intermonomer spacings and reveal the delicate interplay of attractive covalent and dispersion forces, balanced against the repulsions between filled orbitals. For comparison, the binding energy in the structurally related cationic pi-pimer P2*+ is calculated to be significantly larger with DeltaEP approximately -20 kcal mol(-1) (gas phase), owing to favorable electrostatic interactions not present in the neutral pi-dimer (which outweigh the partial loss of covalent interactions). As a result, our theoretical formulation can correctly account for the experimental enthalpy change in solution of DeltaHP = -6.5 kcal mol(-1) by the inclusion of differential ionic solvation in the formation of the pi-pimer.

Journal Article↗
PubMed2004

Extracting dominant pair correlations from many-body wave functions.

The singular value decomposition of the n-particle excitation operator as determined by coupled cluster or perturbation theory is used to extract the dominant and interesting electron-electron correlations from complex molecular wave functions. As an example of the very general formalism, the decomposition of the T(2) operator obtained from coupled cluster doubles calculations is used to analyze the strength and character of pair correlations in a variety of molecules with interesting electronic structure. The magnitude of the largest singular value(s) determines the strength of the correlation(s), and the corresponding right- and left-hand singular vectors characterize the physical and spatial nature of the correlations. The primary advantage of this tool over natural orbital analysis is that it provides direct associations between the occupied and virtual geminals involved in the correlations.

Journal Article↗