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Martin Head-Gordon

Publications and source records attributed to Martin Head-Gordon.

43 records · Page 3Linked to original sources
PubMed2004

An exact reformulation of the diagonalization step in electronic structure calculations as a set of second order nonlinear equations.

A new formulation of the diagonalization step in self-consistent-field (SCF) electronic structure calculations is presented. It exactly replaces the diagonalization of the effective Hamiltonian with the solution of a set of second order nonlinear equations. The density matrix and/or the new set of occupied orbitals can be directly obtained from the resulting solution. This formulation may offer interesting possibilities for new approaches to efficient SCF calculations. The working equations can be derived either from energy minimization with respect to a Cayley-type parametrization of a unitary matrix, or from a similarity transformation approach.

Algorithms↗
PubMed2004

Failure of time-dependent density functional theory for long-range charge-transfer excited states: the zincbacteriochlorin-bacteriochlorin and bacteriochlorophyll-spheroidene complexes.

It is well-known that time-dependent density functional theory (TDDFT) yields substantial errors for the excitation energies of charge-transfer (CT) excited states, when approximate standard exchange-correlation (xc) functionals are used, for example, SVWN, BLYP, or B3LYP. Also, the correct 1/R asymptotic behavior of CT states with respect to a distance coordinate R between the separated charges of the CT state is not reproduced by TDDFT employing these xc-functionals. Here, we demonstrate by analysis of the TDDFT equations that the first failure is due to the self-interaction error in the orbital energies from the ground-state DFT calculation, while the latter is a similar self-interaction error in TDDFT arising through the electron transfer in the CT state. Possible correction schemes, such as inclusion of exact Hartree-Fock or exact Kohn-Sham exchange, as well as aspects of the exact xc-functional are discussed in this context. Furthermore, a practical approach is proposed which combines the benefits of TDDFT and configuration interaction singles (CIS) and which does not suffer from electron-transfer self-interaction. The latter approach is applied to a (1,4)-phenylene-linked zincbacteriochlorin-bacteriochlorin complex and to a bacteriochlorophyll-spheroidene complex, in which CT states may play important roles in energy and electron-transfer processes. The errors of TDDFT alone for the CT states are demonstrated, and reasonable estimates for the true excitation energies of these states are given.

Bacteriochlorophylls↗
PubMed2004

Aromaticity of four-membered-ring 6pi-electron systems: N2S2 and Li2C4H4.

N(2)S(2) is a four-membered-ring system with 6pi electrons. While earlier proposals considered N(2)S(2) to be aromatic, recent electronic structure calculations claimed that N(2)S(2) is a singlet diradical. Our careful reexamination does not support this assertion. N(2)S(2) is closed shell and aromatic since it satisfies all three generally accepted criteria for aromaticity: energetic (stability), structural (planarity with equal bond lengths), and magnetic (negative nucleus-independent chemical shift due to the pi electrons). These characteristics as well as the electronic structure of N(2)S(2) are compared with those for an isoelectronic pi system, Li(2)C(4)H(4), motivated by theoretical and recent experimental investigations that confirmed its aromaticity. However, N(2)S(2) and Li(2)C(4)H(4) are both essentially 2pi-electron aromatic systems with a formal N-S (C-C) bond order of 1.25 even though they both have 6pi electrons. This is because four of the six pi electrons occupy the nonbonding pi HOMOs and only two electrons participate effectively in the aromatic stabilization. However, wave function analysis shows relatively large LUMO occupation numbers; this antibonding effect can be said to reduce the aromatic character by approximately 7% and 4% for N(2)S(2) and Li(2)C(4)H(4), respectively.

Journal Article↗
PubMed2003

Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks.

A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear-scaling methods with atom-centered basis functions. Compared to conventional element-by-element sparse matrix multiplication schemes, efficiency is gained by the use of the highly optimized basic linear algebra subroutines (BLAS). However, some sparsity is lost in the multiatom blocking scheme because these matrix blocks will in general contain negligible elements. As a result, an optimal block size that minimizes the CPU time by balancing these two effects is recovered. In calculations on linear alkanes, polyglycines, estane polymers, and water clusters the optimal block size is found to be between 40 and 100 basis functions, where about 55-75% of the machine peak performance was achieved on an IBM RS6000 workstation. In these calculations, the blocked sparse matrix multiplications can be 10 times faster than a standard element-by-element sparse matrix package.

Journal Article↗
PubMed2003

Charge-transfer mechanism for electrophilic aromatic nitration and nitrosation via the convergence of (ab initio) molecular-orbital and Marcus-Hush theories with experiments.

The highly disparate rates of aromatic nitrosation and nitration, despite the very similar (electrophilic) properties of the active species: NO(+) and NO(2)(+) in Chart 1, are quantitatively reconciled. First, the thorough mappings of the potential-energy surfaces by high level (ab initio) molecular-orbital methodologies involving extensive coupled-cluster CCSD(T)/6-31G optimizations establish the intervention of two reactive intermediates in nitration (Figure 8) but only one in nitrosation (Figure 7). Second, the same distinctive topologies involving double and single potential-energy minima (Figures 6 and 5) also emerge from the semiquantitative application of the Marcus-Hush theory to the transient spectral data. Such a striking convergence from quite different theoretical approaches indicates that the molecular-orbital and Marcus-Hush (potential-energy) surfaces are conceptually interchangeable. In the resultant charge-transfer mechanism, the bimolecular interactions of arene donors with both NO(+) and NO(2)(+) spontaneously lead (barrierless) to pi-complexes in which electron transfer is concurrent with complexation. Such a pi-complex in nitration is rapidly converted to the sigma-complex, whereas this Wheland adduct in nitrosation merely represents a high energy (transition-state) structure. Marcus-Hush analysis thus demonstrates how the strongly differentiated (arene) reactivities toward NO(+) and NO(2)(+) can actually be exploited in the quantitative development of a single coherent (electron-transfer) mechanism for both aromatic nitrosation and nitration.

Journal Article↗
PubMed2002

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

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.

Carbon Monoxide↗