Showing papers by "Martin Head-Gordon published in 2002"

Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group

Abstract: We study the recently developed Density Matrix Renormalization Group (DMRG) algorithm in the context of quantum chemistry In contrast to traditional approaches, this algorithm is believed to yield arbitrarily high accuracy in the energy with only polynomial computational effort We describe in some detail how this is achieved We begin by introducing the principles of the renormalization procedure, and how one formulates an algorithm for use in quantum chemistry The renormalization group algorithm is then interpreted in terms of familiar quantum chemical concepts, and its numerical behavior, including its convergence and computational cost, are studied using both model and real systems The asymptotic convergence of the algorithm is derived Finally, we examine the performance of the DMRG on widely studied chemical problems, such as the water molecule, the twisting barrier of ethene, and the dissociation of nitrogen In all cases, the results compare favorably with the best existing quantum chemical methods, and particularly so when the nondynamical correlation is strong Some perspectives for future development are given

A geometric approach to direct minimization

Abstract: The approach presented, geometric direct minimization (GDM), is derived from purely geometrical arguments, and is designed to minimize a function of a set of orthonormal orbitals. The optimization steps consist of sequential unitary transformations of the orbitals, and convergence is accelerated using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) approach in the iterative subspace, together with a diagonal approximation to the Hessian for the remaining degrees of freedom. The approach is tested by implementing the solution of the self-consistent field (SCF) equations and comparing results with the standard direct inversion in the iterative subspace (DIIS) method. It is found that GDM is very robust and converges in every system studied, including several cases in which DIIS fails to find a solution. For main group compounds, GDM convergence is nearly as rapid as DIIS, whereas for transition metal-containing systems we find that GDM is significantly slower than DIIS. A hybrid procedure where DIIS is used for...

Characterization of the relevant excited states in the photodissociation of CO-ligated hemoglobin and myoglobin.

Abstract: The relevant excited states in the rapid photodissociation process of hemoglobin and myoglobin are examined by means of time-dependent density functional theory. Our calculations clearly show that the photodissociation is mediated by two repulsive states (5 A‘ ‘ and 3 A‘) which cross the lowest excited states (1 A‘ and 1 A‘ ‘) at an internuclear Fe−C distance of about 2 A. Electron detachment/attachment density plots nicely explain the repulsive nature of the 5 A‘ ‘ and 3 A‘ states.

Implementation of generalized valence bond-inspired coupled cluster theories

Abstract: We present an implementation of the recently proposed imperfect pairing (IP) and generalized valence bond restricted coupled cluster (GVB-RCC) methods. Our algorithm centers on repeated construction of Coulomb and exchange matrices. These operations are the computational bottleneck, scaling with the third power of system size for large systems. Robust optimization of the valence orbitals is attained using a geometrically consistent form of direct minimization. Analytic gradients of the IP and GVB-RCC energies are also obtained by a simple modification of the energy optimization scheme. As an illustration of the potential of these new methods, we use IP to compute the equilibrium geometry and energetics of a Si9H12 cluster that is a crude model for silicon dimerization on the Si(001) surface. We thus demonstrate a valuable role for IP and GVB-RCC as a diagnostic for the accuracy of reduced active space calculations as compared to their full valence analogs.

Modeling base voltammetry and CO electrooxidation at the Pt(111)-electrolyte interface: Monte Carlo simulations including anion adsorption

Abstract: We perform dynamic Monte Carlo simulations to understand the effect of anion adsorption on CO oxidation at the Pt(111)–electrolyte (sulfuric acid) interface. Our simulations are performed on a model for CO electrooxidation, where oxygen-containing species (adsorbed OH) formed on the Pt surface reacts with adsorbed CO by a Langmuir–Hinshelwood mechanism to form CO2. In our site-blocking model, discharged anions adsorb on fcc and hcp sites, while CO and OH occupy the atop sites. Our simulations of blank voltammograms show a disorder to order phase transition for HSO4 adsorption on Pt(111) surfaces near 0.4 V, RHE. This transition is observed when the difference in binding energy of HSO4 on hcp and fcc sites, Δe ≫ kBT. Here T is the temperature and kB is the Boltzmann constant. We attribute this transition to the formation of the sulfate ‘butterfly’ observed in experimental base voltammograms. The ordered state () is composed of antiphase anion islands separated by domain walls. OH adsorption is observed at a potential near 0.75 V along the atop sites near the domain walls. Our simulations indicate the quenching of this phase transition for relatively high rates of OH adsorption. This phenomena is also observed in experiments for small concentrations of sulfuric acid solutions. For CO oxidation stripping voltammetry in the limit of slow CO diffusion, our simulations show a prewave (slow CO oxidation) followed by a sharp peak (rapid CO oxidation). The observed features are the result of strongly correlated kinetic events, and is explained using a nucleation–growth model. In the limit of fast diffusion, CO moving rapidly on the electrode surface washes out these effects resulting in a voltammogram with no prewave.

Vibrational and Electronic Spectroscopy of the Fluorene Cation

Abstract: The fluorene cations, C13H10+ and C13D10+, have been formed by both electron impact ionization and vacuum ultraviolet photoionization, deposited in an argon matrix at 12K and studied via Fourier transform infrared and ultraviolet/visible absorption spectroscopy. Harmonic vibrational frequencies have been calculated using density functional theory (B3LYP/6-31G(d,p)) and vibrational band assignments made. Good agreement is found. Dramatic differences have been observed in the infrared band intensities of the cations compared to their neutral parents. Two excited electronic band systems have been observed and compared with previous photoelectron spectroscopic results. New calculations of the fluorene cation excited states have been performed using configuration interaction singles (CIS), CIS with a doubles correlation correction (CIS(D)), time-dependent Hartree−Fock (TDHF), and time-dependent density functional theory (TDDFT) with SVWN, BLYP, and B3LYP functionals. Theoretically, 12 low-lying excited states ...

Quadratic coupled-cluster doubles: Implementation and assessment of perfect pairing optimized geometries

Abstract: We present orbital amplitude and orbital gradient equations for the quadratic coupled-cluster doubles (QCCD) theory. These expressions are size extensive and can be solved in O(N 6 ) time with the use of O(N 4 ) intermediates, which are efficiently defined. The optimized orbital formalism is naturally suited for excitations in only a valence space to describe nondynamical correlation. This also minimizes the additional cost relative to conventional CCD. The resulting valence QCCD is used to study the effects of correlation on equilibrium geometries of a range of small molecules in the perfect pairing active space. This enables comparison with generalized valence bond perfect pairing calculations on the same systems. Additionally, the use of valence QCCD as a supplement to complete active space (CAS) methods is illustrated with calculations of the transition structure for addition of hydrogen to trans-diazene (N 2 H 2 ).

Parallelization of analytical Hartree—Fock and density functional theory Hessian calculations. Part I: parallelization of coupled-perturbed Hartree—Fock equations

Abstract: Solving the coupled-perturbed Hartree-Fock (CPHF) equations is the most time consuming part in the analytical computation of second derivatives of the molecular energy with respect to the nuclei. This paper describes a unique parallelization approach for solving the CPHF equations. The computational load is divided by the nuclear perturbations and distributed evenly among the computing nodes. The parallel algorithm is scalable with respect to the size of the molecule, i.e. the larger the molecule, the greater the parallel speedup. The memory storage requirements are also distributed among the processors, with little communication among the processors. The method is implemented in the Q-Chem software package and its performance is discussed. This work represents the first step in a research project to parallelize analytical frequency calculations at Hartree-Fock and density functional theory levels.

Can coupled cluster singles and doubles be approximated by a valence active space model

Abstract: A new, efficient approximation for coupled cluster singles and doubles (CCSD) is proposed in which a CCSD calculation is performed in a valence active space followed by a second-order perturbative correction to account for the inactive singles and doubles cluster amplitudes. This method, denoted VCCSD(SD), satisfactorily reproduces CCSD results in a variety of test cases, including spectroscopic constants of diatomic molecules, reaction energies, the Cope rearrangement, and other relative energies. Use of VCCSD alone is significantly less satisfactory. Formally, the O2V4 scaling of CCSD is reduced to o2v2V2, where o is the number of active occupied orbitals, v is the number of active virtual orbitals, and V is the total number of virtual orbitals. We also investigate the role of orbital optimizations and the appropriate choice of an active space in such methods.

Geometric direct minimization of hartree–fock calculations involving open shell wavefunctions with spin restricted orbitals

Abstract: Recently, we have introduced a method based on geometric considerations, termed geometric direct minimization (GDM), to achieve robust convergence of self consistent field calculations. GDM was limited to calculations involving either spin-unrestricted orbitals or closed shell systems. We report the extension of the GDM method to treat open shell systems involving spin-restricted orbitals. Open shell systems pose a challenge for achieving robust convergence of the calculation. We compare the convergence using the GDM method to the convergence achieved by the well known direct inversion in the iterative space (DIIS) technique. This comparison demonstrates the ability of the GDM method to achieve robust convergence. Additionally we assess the importance of geometric considerations by comparing against an alternative direct minimization method that is not geometrically correct.