Biomedical subjects

Martin Head-Gordon

Publications and source records attributed to Martin Head-Gordon.

At least 19 recordsLinked to original sources

PubMed2007

An improved algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory: application to alanine tetrapeptide conformational analysis.

We present a new algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory (RI-MP2) and thoroughly assess its computational performance and chemical accuracy. This algorithm addresses the potential I/O bottlenecks associated with disk-based storage and access of the RI-MP2 t-amplitudes by utilizing a semi-direct batching approach and yields computational speed-ups of approximately 2-3 over the best conventional MP2 analytical gradient algorithms. In addition, we attempt to provide a straightforward guide to performing reliable and cost-efficient geometry optimizations at the RI-MP2 level of theory. By computing relative atomization energies for the G3/99 set and optimizing a test set of 136 equilibrium molecular structures, we demonstrate that satisfactory relative accuracy and significant computational savings can be obtained using Pople-style atomic orbital basis sets with the existing auxiliary basis expansions for RI-MP2 computations. We also show that RI-MP2 geometry optimizations reproduce molecular equilibrium structures with no significant deviations (>0.1 pm) from the predictions of conventional MP2 theory. As a chemical application, we computed the extended-globular conformational energy gap in alanine tetrapeptide at the extrapolated RI-MP2/cc-pV(TQ)Z level as 2.884, 4.414, and 4.994 kcal/mol for structures optimized using the HF, DFT (B3LYP), and RI-MP2 methodologies and the cc-pVTZ basis set, respectively. These marked energetic discrepancies originate from differential intramolecular hydrogen bonding present in the globular conformation optimized at these levels of theory and clearly demonstrate the importance of long-range correlation effects in polypeptide conformational analysis.

Alanine↗

PubMed2006

Dual-basis analytic gradients. 1. Self-consistent field theory.

Analytic gradients of dual-basis Hartree-Fock and density functional theory energies have been derived and implemented, which provide the opportunity for capturing large basis-set gradient effects at reduced cost. Suggested pairings for gradient calculations are 6-31G/6-31G**, dual[-f,-d]/cc-pVTZ, and 6-311G*/6-311 + +G(3df,3pd). Equilibrium geometries are produced within 0.0005 A of large-basis results for the latter two pairings. Though a single, iterative SCF response equation must be solved (unlike standard SCF gradients), it may be obtained in the smaller basis set, and integral screening further reduces the cost for well-chosen subsets. Total nuclear force calculations exhibit up to 75% savings, relative to large-basis calculations.

Journal Article↗

PubMed2006

Linear scaling density fitting.

Two modifications of the resolution of the identity (RI)/density fitting (DF) approximations are presented. First, we apply linear scaling and J-engine techniques to speed up traditional DF. Second, we develop an algorithm that produces local, accurate fits with effort that scales linearly with system size. The fits produced are continuous, differentiable, well-defined, and do not require preset fitting domains. This metric-independent technique for producing a priori local fits is shown to be accurate and robust even for large systems. Timings are presented for linear scaling RI/DF calculations on large one-, two-, and three-dimensional carbon systems.

Algorithms↗

PubMed2006

Charge penetration and the origin of large O-H vibrational red-shifts in hydrated-electron clusters, (H2O)n-.

The origin of O-H vibrational red-shifts observed experimentally in (H2O)n(-) clusters is analyzed using electronic structure calculations, including natural bond orbital analysis. The red-shifts are shown to arise from significant charge transfer and strong donor-acceptor stabilization between the unpaired electron and O-H sigma* orbitals on a nearby water molecule in a double hydrogen-bond-acceptor ("AA") configuration. The extent of e(-) --> sigma* charge transfer is comparable to the n --> sigma* charge transfer in the most strongly hydrogen-bonded X(-)(H2O) complexes (e.g., X = F, O, OH), even though the latter systems exhibit much larger vibrational red-shifts. In X(-)(H2O), the proton affinity of X(-) induces a low-energy XH...(-)OH diabatic state that becomes accessible in v = 1 of the shared-proton stretch, leading to substantial anharmonicity in this mode. In contrast, the H + (-)OH(H2O)(n-1) diabat of (H2O)n(-) is not energetically accessible; thus, the O-H stretching modes of the AA water are reasonably harmonic, and their red-shifts are less dramatic. Only a small amount of charge penetrates beyond the AA water molecule, even upon vibrational excitation of these AA modes. Implications for modeling of the aqueous electron are discussed.

Journal Article↗

PubMed2006

First-principles, quantum-mechanical simulations of electron solvation by a water cluster.

Despite numerous experiments and static electronic structure calculations, the nature of hydrated-electron clusters, (H2O)(n)(-), remains poorly understood. Here, we introduce a hybrid ab initio molecular dynamics scheme, balancing accuracy against feasibility, to simulate vibrational and photoelectron spectra of (H(2)O)(n)(-), treating all electrons quantum-mechanically. This methodology provides a computational tool for understanding the spectra of weakly bound and supramolecular anions and for elucidating the fingerprint of dynamics in these spectra. Simulations of (H2O)(4)(-) provide quantitative agreement with experimental spectra and furnish direct evidence of the nonequilibrium nature of the cluster ensemble that is probed experimentally. The simulations also provide an estimate of the cluster temperature (T approximately 150-200 K) that is not available from experiment alone. The "double acceptor" electron-binding motif is found to be highly stable with respect to thermal fluctuations, even at T = 300 K, whereas the extra electron stabilizes what would otherwise be unfavorable water configurations.

Journal Article↗

PubMed2006

Dual-basis second-order Moller-Plesset perturbation theory: A reduced-cost reference for correlation calculations.

The resolution-of-the-identity (RI) approximation has placed the onus of the cost of a second-order Moller-Plesset (MP2) calculation on the underlying self-consistent field (SCF) calculation for many moderately sized molecules. A dual-basis approach to the SCF calculation, based on previous methods demonstrated for density functional theory, is combined with RI-MP2 calculations, and small basis subsets for cc-pVTZ, cc-pVQZ, and 6-311++G(3df,3pd) are presented. These subsets provide time savings of greater than 90%, with negligible errors in absolute and relative energies, compared to the associated full-basis counterpart. The method is tested with a series of rotational barriers, relative conformational energies of alanine tetrapeptides, as well as the full G3/99 molecular set. RI-MP2 calculations on alanine octapeptides (40 heavy atoms, 3460 basis functions), using cc-pVQZ, are presented. Results improve upon previous methods that diagonalize the virtual space separately.

Journal Article↗

PubMed2006

A near linear-scaling smooth local coupled cluster algorithm for electronic structure.

We demonstrate near linear scaling of a new algorithm for computing smooth local coupled-cluster singles-doubles (LCCSD) correlation energies of quantum mechanical systems. The theory behind our approach has been described previously, [J. Subotnik and M. Head-Gordon, J. Chem. Phys. 123, 064108 (2005)], and requires appropriately multiplying standard iterative amplitude equations by a bump function, creating local amplitude equations (which are smooth according to the implicit function theorem). Here, we provide an example that this theory works in practice: we show that our algorithm leads to smooth potential energy surfaces and yields large computational savings. As an example, we apply our LCCSD approach to measure the post-MP2 correction to the energetic gap between two different alanine tetrapeptide conformations.

Algorithms↗

PubMed2006

On the nature of unrestricted orbitals in variational active space wave functions.

Active space coupled cluster methods exhibit unusual, nonsmooth spin symmetry-breaking behavior where the unrestricted minimum lies higher in energy at short bond distances and crosses below the restricted solution at longer distances. The restricted solution is also observed to be a stable minimum slightly beyond the symmetry-breaking point. This behavior arises due to differences in the optimal active spaces defining the restricted and unrestricted wave functions and results in unrestricted wave functions that are not strictly size consistent. We suggest a new, size-consistent model that allows the orbitals to break spin symmetry only within the active space.

Journal Article↗

PubMed2006

Advances in methods and algorithms in a modern quantum chemistry program package.

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

Algorithms↗

PubMed2006

Ab initio quantum chemistry calculations on the electronic structure of heavier alkyne congeners: diradical character and reactivity.

The electronic structure of the heavier congeners of alkynes has been studied with emphasis on characterizing their extent of diradical character. Four orbitals play a crucial role in determining the electronic structure in planar trans-bent geometries. Two are associated with an out-of-plane pi interaction, pi and pi, and two are associated with in-plane interactions and/or in-plane lone pairs, LP(n-) and LP(n+). The ordering of these orbitals can change depending upon geometry. One extreme, corresponding to the local minimum for Si-Si and Ge-Ge, is a diradicaloid multiple-bonding configuration where LP and pi are nominally occupied. Another extreme, corresponding to a local minimum for Sn-Sn, is a relatively closed-shell single-bond configuration where LP and LP are nominally occupied. This ordering leads to predicted bond shortening upon excitation from singlet to triplet state. For the heavier elements, there appears to be very little energy penalty for large geometric distortions that convert from one ordering to the other on the singlet surface. The implications of these results with respect to experimental observations are discussed.

Journal Article↗

PubMed2006

An efficient self-consistent field method for large systems of weakly interacting components.

An efficient method for removing the self-consistent field (SCF) diagonalization bottleneck is proposed for systems of weakly interacting components. The method is based on the equations of the locally projected SCF for molecular interactions (SCF MI) which utilize absolutely localized nonorthogonal molecular orbitals expanded in local subsets of the atomic basis set. A generalization of direct inversion in the iterative subspace for nonorthogonal molecular orbitals is formulated to increase the rate of convergence of the SCF MI equations. Single Roothaan step perturbative corrections are developed to improve the accuracy of the SCF MI energies. The resulting energies closely reproduce the conventional SCF energy. Extensive test calculations are performed on water clusters up to several hundred molecules. Compared to conventional SCF, speedups of the order of (N/O)2 have been achieved for the diagonalization step, where N is the size of the atomic orbital basis, and O is the number of occupied molecular orbitals.

Journal Article↗

PubMed2006

A fast correlated electronic structure method for computing interaction energies of large van der Waals complexes applied to the fullerene-porphyrin dimer.

A new implementation of the scaled opposite spin Møller-Plesset (SOS-MP2) method is briefly described, which exploits the locality and sparsity of expansion coefficients and as a result has computational costs that increase approximately quadratically with molecular size. The performance of SOS-MP2 for describing stacked pi-complexes is carefully investigated using the benzene, ethylene, uracil, and naphthalene dimers as model systems. It is demonstrated that counterpoise-corrected SOS-MP2 results, extrapolated towards the complete basis set (CBS) limit using a two-point extrapolation scheme, can yield association energies that are reasonably close to the best available numbers, when the single scale factor is chosen as 1.55 for extrapolating results at the cc-pVDZ and cc-pVTZ levels. This methodology yields an interaction energy for the fullerene-tetraphenylporphyrin dimer of -31.47 kcal mol(-1) while Hartree-Fock (HF) with the cc-pVTZ basis finds the dimer at the same geometry is unbound by +10.83 kcal mol(-1). This implies that the net binding is a result of substantial correlation effects, presumably long-range London dispersions.

Chemical Phenomena↗

PubMed2006

Second-order correction to perfect pairing: an inexpensive electronic structure method for the treatment of strong electron-electron correlations.

We have formulated a second-order perturbative correction for perfect-pairing wave functions [PP2] based on similarity-transformed perturbation techniques in coupled cluster theory. The perfect-pairing approximation is used to obtain a simple reference wave function which can qualitatively describe bond breaking, diradicals, and other highly correlated systems, and the perturbative correction accounts for the dynamical correlation. An efficient implementation of this correction using the resolution of the identity approximation enables PP2 to be computed at a cost only a few times larger than that of canonical MP2 for systems with hundreds of active electrons and tens of heavy atoms. PP2 significantly improves on MP2 predictions in various systems with a challenging electronic structure.

Journal Article↗

PubMed2006

Computational studies of molecular hydrogen binding affinities: the role of dispersion forces, electrostatics, and orbital interactions.

Intermolecular interactions between H2 and ligands, metals, and metal-ligand complexes determine the binding affinities of potential hydrogen storage materials (HSM), and thus their extent of potential for practical use. A brief survey of current activity on HSM is given. The key issue of binding strengths is examined from a basic perspective by surveying the distinct classes of interactions (dispersion, electrostatics, orbital interactions) in first a general way, and then in the context of calculated binding affinities for a range of model systems.

Greenhouse Effect↗

PubMed2005

Characterizing the dimerizations of phenalenyl radicals by ab initio calculations and spectroscopy: sigma-bond formation versus resonance pi-stabilization.

Electronic-structure calculations for the self-association of phenalenyl radical (P*) predict the formation of dimeric species (sigma-P2) in which both moieties are connected by a sigma-bond with rP-P approximately 1.59 A and bond dissociation enthalpy of DeltaH(D) approximately 16 kcal mol(-1). Such an unusually weak sigma-bond is related to the loss of aromatic stabilization energy of approximately 34 kcal mol(-1) per phenalenyl moiety, largely owing to rehybridization. Ab initio calculations also reveal that the corresponding (one-electron) bond between phenalenyl radical and its closed-shell cation in sigma-P2+* is unstable relative to dissociation. Time-dependent DFT computations indicate the absence of any (strongly allowed) electronic transition in the visible region of the absorption spectrum of phenalenyl sigma-dimer. Such theoretical predictions are supported by experimental (ESR and UV-NIR) spectroscopic studies, in which the availability of a series of sterically hindered phenalenyl radicals allows definitive separations of the sigma-dimerization process from interference by pi-dimerization. As such, the thermodynamic parameters (determined from the temperature dependence of the ESR signals) with DeltaH(D) = 14 kcal mol(-1) and DeltaS(D) = 52 e.u. can be assigned to the formation of the colorless sigma-dimer. Similar results are obtained for all phenalenyl derivatives (provided their substitution patterns allow sigma-bond formation) to confirm the energetic preference of sigma-dimerization over pi-dimerization.

Journal Article↗

PubMed2005

An efficient approach for self-consistent-field energy and energy second derivatives in the atomic-orbital basis.

Based on self-consistent-field (SCF) perturbation theory, we recast the SCF and the coupled-perturbed SCF (CPSCF) equations for time-independent molecular properties into the atomic-orbital basis. The density matrix and the perturbed density matrix are obtained iteratively by solving linear equations. Only matrix multiplications and additions are required, and this approach can exploit sparse matrix multiplications and thereby offer the possibility of evaluating second-order properties in computational effort that scales linearly with system size. Convergence properties are similar to conventional molecular-orbital-based CPSCF procedures, in terms of the number of derivative Fock matrices that must be constructed. We also carefully address the issue of the numerical accuracy of the calculated second derivatives of the energy, in order to specify the minimum precision necessary in the CPSCF procedure. It is found that much looser tolerances for the perturbed density matrices are adequate when using an expression for the second derivatives that is correct through second order in the CPSCF error.

Algorithms↗

PubMed2005

Accuracy and limitations of second-order many-body perturbation theory for predicting vertical detachment energies of solvated-electron clusters.

Vertical electron detachment energies (VDEs) are calculated for a variety of (H(2)O)(n)(-) and (HF)(n)(-) isomers, using different electronic structure methodologies but focusing in particular on a comparison between second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster theory with noniterative triples, CCSD(T). For the surface-bound electrons that characterize small (H(2)O)(n)(-) clusters (n< or = 7), the correlation energy associated with the unpaired electron grows linearly as a function of the VDE but is unrelated to the number of monomers, n. In every example considered here, including strongly-bound "cavity" isomers of (H(2)O)(24)(-), the correlation energy associated with the unpaired electron is significantly smaller than that associated with typical valence electrons. As a result, the error in the MP2 detachment energy, as a fraction of the CCSD(T) value, approaches a limit of about -7% for (H(2)O)(n)(-) clusters with VDEs larger than about 0.4 eV. CCSD(T) detachment energies are bounded from below by MP2 values and from above by VDEs calculated using second-order many-body perturbation theory with molecular orbitals obtained from density functional theory. For a variety of both strongly- and weakly-bound isomers of (H(2)O)(20)(-) and (H(2)O)(24)(-), including both surface states and cavity states, these bounds afford typical error bars of +/-0.1 eV. We have found only one case where the Hartree-Fock and density functional orbitals differ qualitatively; in this case the aforementioned bounds lie 0.4 eV apart, and second-order perturbation theory may not be reliable.

Electrons↗

PubMed2005

Unrestricted perfect pairing: the simplest wave-function-based model chemistry beyond mean field.

The perfect pairing (PP) approximation from generalized valence bond theory is formulated in an unrestricted fashion for both closed- and open-shell systems using a coupled cluster ansatz. In the model chemistry proposed here, active electron pairs are correlated, but the unpaired or radical electrons remain uncorrelated, leading to a linear number of decoupled cluster amplitudes which can be solved for analytically. The alpha and beta spatial orbitals are variationally optimized independently. This minimal treatment of electron-electron correlation noticeably improves upon symmetry-breaking problems and other pathologies in Hartree-Fock (HF) theory and may be computed using the resolution of the identity approximation at only a factor of several times more effort than HF itself. PP also generally predicts improved molecular structures over HF. This compact, correlated wave function potentially provides a useful starting point for dynamical correlation corrections.

Journal Article↗