Showing papers by "Martin Head-Gordon published in 2006"

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

Abstract: 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.

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

Abstract: 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.

Linear scaling density fitting.

Abstract: 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.

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

Abstract: 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.

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

Abstract: 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 π interaction, π and π*, 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 π 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...

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

Abstract: Vertical electron detachment energies (VDEs) are calculated for a variety of (H2O)n− and (HF)n− isomers, using different electronic structure methodologies but focusing in particular on a comparison between second-order Moller–Plesset perturbation theory (MP2) and coupled-cluster theory with noniterative triples, CCSD(T). For the surface-bound electrons that characterize small (H2O)n− clusters (n ≤ 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 (H2O)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 (H2O)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 (H2O)20− and (H2O)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.

Steric modulations in the reversible dimerizations of phenalenyl radicals via unusually weak carbon-centered pi- and sigma-bonds.

Abstract: [reaction: see text] Spontaneous self-associations of various tricyclic phenalenyl radicals lead reversibly to either pi- or sigma-dimers, depending on alkyl-substitution patterns at the alpha- and beta-positions. Thus, the sterically encumbered all-beta-substituted tri-tert-butylphenalenyl radical (2*) affords only the long-bonded pi-dimer in dichloromethane solutions, under conditions in which the parent phenalenyl radical (1*) leads to only the sigma-dimer. Further encumbrances of 1* with a pair of alpha, beta- or beta, beta- tert-butyl substituents and additional methyl and ethyl groups (as in sterically hindered phenalenyl radicals 3* - 6*) do not inhibit sigma-dimerization. ESR spectroscopy is successfully employed to monitor the formation of both diamagnetic (2-electron) dimers; and UV-vis spectroscopy specifically identifies the pi-dimer by its intense near-IR band. The different temperature-dependent spectral (ESR and UV-vis) behaviors of these phenalenyl radicals allow the quantitative evaluation of the bond enthalpy of 12 +/- 2 kcal mol(-1) for sigma-dimers, in which the unusually low value has been theoretically accounted for by the large loss of phenalenyl (aromatic) pi-resonance energy attendant upon such bond formation.

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

Abstract: A new implementation of the scaled opposite spin Moller–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 π-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.

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

Abstract: The origin of O−H vibrational red-shifts observed experimentally in (H2 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 σ* orbitals on a nearby water molecule in a double hydrogen-bond-acceptor (“AA”) configuration. The extent of e- → σ* charge transfer is comparable to the n → σ* 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 (H2 is not energetically accessible; thus, the O−H stretching modes of the AA water are reasonably harmonic, and their red-shifts ...

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

Abstract: 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.

Mulliken–Hush elucidation of the encounter (precursor) complex in intermolecular electron transfer via self-exchange of tetracyanoethylene anion-radical

Abstract: The paramagnetic [1:1] encounter complex ( TCNE ) 2 - is established as the important precursor in the kinetics and mechanism of electron-transfer for the self-exchange between tetracyanoethylene acceptor (TCNE) and its radical-anion as the donor. Spectroscopic observation of the dimeric complex ( TCNE ) 2 - by its intervalence absorption band at the solvent-dependent wavelength of λIV ∼ 1500 nm facilitates the application of Mulliken–Hush theory which reveals the significant electronic interaction extant between the pair of cofacial TCNE moieties with the sizable coupling of HDA = 1000 cm−1. The transient existence of such an encounter complex provides the critical link in the electron-transfer kinetics by lowering the classical Marcus reorganization barrier by the amount of HDA in this strongly adiabatic system. Ab initio quantum-mechanical methods as applied to independent theoretical computations of both the reorganization energy (λ) and the electronic coupling element (HDA) confirm the essential correctness of the Mulliken–Hush formalism for fast electron transfer via strongly coupled donor/acceptor encounter complexes.

A Fast Implementation of Perfect Pairing and Imperfect Pairing Using the Resolution of the Identity Approximation.

Abstract: We present an efficient implementation of the perfect pairing and imperfect pairing coupled-cluster methods, as well as their nuclear gradients, using the resolution of the identity approximation to calculate two-electron integrals. The perfect pairing and imperfect pairing equations may be solved rapidly, making integral evaluation the bottleneck step. The method's efficiency is demonstrated for a series of linear alkanes, for which we show significant speed-ups (of approximately a factor of 10) with negligible error. We also apply the imperfect pairing method to a model of a recently synthesized stable singlet biradicaloid based on a planar Ge-N-Ge-N ring, confirming its biradical character, which appears to be remarkably high.

The localizability of valence space electron–electron correlations in pair-based coupled cluster models

Abstract: Inspired by the success of very restrictive local active space approaches like Generalized Valence Bond Perfect Pairing (GVB-PP) and Imperfect Pairing (IP), we investigate the localizability of valence correlation in the context of electron pair models. In particular, the role of two-center local excitations in local active space coupled cluster doubles models is examined in the context of a variety of chemical applications. The full two spatial center pairing model is found to recover the majority of the correlation effects missed by GVB-PP and IP, recovering up to 95% of the untruncated valence correlation energy, and could provide an inexpensive reference wave function for the treatment of additional electron–electron correlations. All of these models improve noticeably upon the Hartree–Fock wave function and can be computed for very large systems due to their only cubic computational cost. Their main weakness is a tendency to exhibit symmetry breaking in systems with multiple resonance structures.

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

Abstract: 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.