Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session P19: Focus Session: Frontiers in Electronic Structure Theory IV |
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Sponsoring Units: DCP DCOMP Chair: Troy van Voonhis, Massachusetts Institute of Technology Room: Colorado Convention Center 104 |
Wednesday, March 7, 2007 11:15AM - 11:51AM |
P19.00001: Ab-initio DMRG and Canonical Transformation Theories of Electronic Structure Invited Speaker: I will talk about two complementary methods that are under development in our group: (1) Ab-initio Density Matrix Renormalization Group: The Density Matrix Renormalization Group (DMRG) is a natural multireference method. Recently, we have implemented a quadratic-scaling DMRG algorithm which opens up the description of multireference (strongly interacting) correlation in large quasi-one-dimensional systems [1]. I will report calculations using this technique on conjugated oligomers correlating exactly, in the sense of Full-CI, complete pi-active spaces with up to 100 electrons in 100 orbitals (100, 100). (2) Canonical Transformation Theory: We have been developing a canonical transformation method to incorporate dynamical correlation on top of a multireference starting point. Our theory, termed Canonical Transformation Theory (CT) [2] is based on an exponential ansatz and is size-consistent. It retains the accuracy of coupled cluster theory at equilibrium bond geometries, but extends this accuracy to the full potential energy surface. The cost of the calculation is the same as for single-reference coupled cluster theory. I will report calculations using this technique for bond-breaking and excited states. I will also describe our recent efforts in developing a reduced-scaling version of the theory for large molecules. [1] J. Chem. Phys. 125, 144101 (2006) [2] J. Chem. Phys. 124, 194106 (2006) [Preview Abstract] |
Wednesday, March 7, 2007 11:51AM - 12:27PM |
P19.00002: Real-time {\it ab initio} simulations of excited-state dynamics in nanostructures Invited Speaker: Combining time-dependent {\em ab initio} density functional calculations for electrons with molecular dynamics simulations for ions, we investigate the effect of excited-state dynamics in nanostructures. In carbon nanotubes, we find electronic excitations to last for a large fraction of a picosecond.\footnote{Yoshiyuki Miyamoto, Angel Rubio, and David Tomanek, Phys.\ Rev.\ Lett.\ {\bf 97}, 126104 (2006).} The de-excitation process is dominated by coupling to other electronic degrees of freedom during the first few hundred femtoseconds. Later, the de-excitation process becomes dominated by coupling to ionic motion. The onset point and damping rate in that regime change with initial ion velocities, a manifestation of temperature dependent electron-phonon coupling. Considering the fact that the force field in the electronically excited state differs significantly from the ground state, as reflected in the Franck-Condon effect, atomic bonds can easily be broken or restored during the relatively long lifetime of electronic excitations. This effect can be utilized in a ``photo-surgery" of nanotubes, causing structural self-healing at vacancy sites\footnote{Yoshiyuki Miyamoto, Savas Berber, Mina Yoon, Angel Rubio, and David Tomanek, Chem.\ Phys.\ Lett.\ {\bf 392}, 209 (2004).} or selective de-oxidation processes induced by photo-absorption.\footnote{Yoshiyuki Miyamoto, Noboru Jinbo, Hisashi Nakamura, Angel Rubio, and David Tomanek, Phys.\ Rev.\ B {\bf 70}, 233408 (2004).} Also, electronic excitations are a key ingredient for the understanding of sputtering processes in nanostructures, induced by energetic collisions with ions.\footnote{Yoshiyuki Miyamoto, Arkady Krasheninnikov, and David Tomanek (in preparation).} [Preview Abstract] |
Wednesday, March 7, 2007 12:27PM - 12:39PM |
P19.00003: First principles spectroscopy of confined water. Manu Sharma, Giulia Galli In order to characterize the changes in hydrogen bonding in water confined at the nanoscale, and to understand the effect of the interface between water and the confining medium, we carried out a spectroscopic investigation using first principles calculations. In particular, we computed the infrared (IR) spectrum of liquid water confined between two sheets of graphite. While the far IR region of the spectrum contains features characterizing the H-bond dynamics in water, we find a significant overlap of this region with the vibrational modes of graphite. We also find modes in the near IR region $\sim $2500 cm$^{-1}$, associated to the OH stretching mode, which while present in the kinematical (power) spectrum are absent from the computed IR spectrum. We demonstrate that these modes arise due to a dynamical charge transfer between water molecules and the p -- orbitals of the graphite surface. [Preview Abstract] |
Wednesday, March 7, 2007 12:39PM - 12:51PM |
P19.00004: Quadratic Scaling Local Canonical Transformation Method. Debashree Ghosh, Takeshi Yanai, Garnet Kin-Lic Chan Canonical transformation theory [1] can be used to describe the detailed dynamic correlation in bonding situations where there is significant non-dynamic, i.e. multireference character. This theory uses an exponential ansatz and is size-consistent. The computational cost of this method scales as N$^{6}$ which is about the same as in a single reference coupled cluster theory. We have devised a local Canonical transformation method for large systems. For large systems, we have been able to obtain quadratic scaling with the size of the system. Reduced and linear scaling algorithms for methods like MP2 and coupled cluster are well known. However, all these reduced scaling algorithms have been primarily developed for single reference correlation calculations. By combining the local canonical transformation method with, e.g. the quadratic scaling ab-initio Density Matrix Renormalization Group theory, we can now obtain a reduced-scaling description of dynamical and non-dynamical correlation in large multireference problems. [1] Takeshi Yanai, Garnet K.L. Chan, J. Chem. Phys. \textbf{124}, 194106, 2006. [Preview Abstract] |
Wednesday, March 7, 2007 12:51PM - 1:03PM |
P19.00005: Representing molecules as atomic-scale electrical circuits with fluctuating-charge models Jiahao Chen, Todd Mart\'Inez Fluctuating-charge models (FCMs), also known as chemical potential equilibration models, can describe charge transfer in molecular mechanics (MM). Examples of FCMs are QEq [1], \textit{fluc}-q (FQ) [2], and our recently proposed PE-CC-QVB2 [3] and QTPIE [4]. FCMs describe the accumulation and depletion of atomic charges with electronegativities and chemical hardnesses. We show that this description of atoms maps molecular systems onto electrical circuits. Unlike other models [1, 2], our models correctly model a diatomic molecule in the dissociation limit; we explain how this is reflected in its circuit representation. FCMs hence establish a new connection between the statistical mechanics of molecular electronic structure [5] and classical circuit theory. [1] A. K. Rappe, and W. A. Goddard III, \textit{J. Phys. Chem.} \textbf{95}, 3358 (1991). [2] S. W. Rick, S. J. Stuart, and B. J. Berne, \textit{J. Chem. Phys.} \textbf{101}, 6141 (1994). [3] J. Morales, and T. J. Mart\'{\i}nez, \textit{J. Phys. Chem.} \textbf{108A}, 3076 (2004). [4] J. Chen, and T. J. Mart\'{\i}nez, \textit{Chem. Phys. Lett.} submitted (2006). [5] J. Morales, and T. J. Mart\'{\i}nez, \textit{J. Phys. Chem.} \textbf{105A}, 2842 (2001). [Preview Abstract] |
Wednesday, March 7, 2007 1:03PM - 1:15PM |
P19.00006: Partition-of-unity finite element method for large, accurate electronic-structure calculations John Pask, Natarajan Sukumar Over the past few decades, the planewave pseudopotential (PW) method has established itself as the method of choice for large, accurate, density-functional calculations in condensed matter. However, due to its global Fourier basis, the PW method suffers from substantial inefficiencies in parallel implementation and problems involving localized states. Modern real-space approaches, such as finite-difference (FD) and finite-element (FE) methods, resolve these problems but have until now required much larger bases to attain the required accuracy. Here, we present a new real-space FE based method which employs modern partition-of-unity FE techniques to substantially reduce the number of basis functions required. Initial results show order-of-magnitude improvements relative to current state-of-the-art PW and adaptive-mesh FE methods for systems involving localized states such as d- and f-electron metals. [Preview Abstract] |
Wednesday, March 7, 2007 1:15PM - 1:27PM |
P19.00007: Anti-Hermitian Contracted Schr{\"o}dinger Equation for the Determination of Ground-state Energies and Two-electron Reduced-density-matrices without Wavefunctions David Mazziotti A recent advance in the theory of the contracted Schr{\"o}dinger equation (CSE), in which only the anti-Hermitian part of the equation is solved, permits the direct determination of ground-state two-electron reduced density matrices (2-RDMs) that yield 95-100\% of the correlation energy of atoms and molecules [Mazziotti, Phys. Rev. Lett. {\bf 97}, 143002 (2006)]. Here we discuss in detail the anti-Hermitian contracted Schr{\"o}dinger equation (ACSE) and its comparison to the CSE with regard to cumulant reconstruction of RDMs, the role of Nakatsuji's theorem, and the structure of the wavefunction. The ACSE is also formulated in the Heisenberg representation and related to canonical diagonalization. The solution of the ACSE is illustrated with a variety of molecules. The computed 2-RDMs very closely satisfy known $N$-representability conditions. [Preview Abstract] |
Wednesday, March 7, 2007 1:27PM - 1:39PM |
P19.00008: A Near Linear-Scaling Smooth Local Coupled Cluster Algorithm for Electronic Structure Joseph Subotnik, Alex Sodt, Martin Head-Gordon We demonstrate near linear-scaling of a new algorithm for computing smooth local coupled-cluster singles-doubles (LCCSD) correlation energies of quantum mechanical systems. Full CCSD provides an excellent, size-consistent treatment of electron correlation, but is computationally expensive, scaling formally as O($n^6$); by contrast, our LCCSD algorithm recovers more than 99\% of the CCSD correlation energy, while achieving near linear-scaling. Furthermore, previous domain-based LCCSD models had discontinuous potential-energy curves, with correspondingly infinite nuclear forces; by contrast, our domain-free algorithm's correlation energy is a rigorously differentiable function of nuclear coordinates, with correspondingly finite nuclear forces. Thus, our algorithm should allow, in the future, for the propagation of quantum dynamics on a highly correlated electron surface. We present applications to small polypeptide conformational energies, and demonstrate how one may smoothly dissociate two benchmark molecules (ethane and ketene) at the LCCSD level of electronic correlation using our algorithm. [Preview Abstract] |
Wednesday, March 7, 2007 1:39PM - 1:51PM |
P19.00009: Linear scaling integral fitting Alexander Sodt, Martin Head-Gordon In density (or integral) fitting methods, the density (or an orbital product) is replaced with a sum of atom-centered ``auxiliary'' functions, which are used to efficiently compute Coulomb interactions. In this work, we present a method for computing localized fit coefficients that scales linearly with system size, and introduces only extremely modest errors. We apply the algorithm to a variety of methods, including the J piece of the Fock matrix. [Preview Abstract] |
Wednesday, March 7, 2007 1:51PM - 2:03PM |
P19.00010: New many-body approach to photoemission and spectral functions Carl-Olof Almbladh, Claudio Verdozzi A new method for the description of photoemission and other spectra is presented. The key idea is to expand the transition amplitudes rather than the spectral function themselves. This leads to spectral intensities of a Golden-rule-like form. In the language of Keldysh path-ordered technique, contributions to ``lesser'' functions such as $G^<$ are classified into loss and no-loss diagrams, and in each diagram transition amplitudes can be identified. Conserving theories in the sense of Kadanoff and Baym exactly fulfill macroscopic conservation laws but may violate the positiveness of spectral functions. In contrast, the present scheme may violate conservation laws but it will always give positive spectra, thus being especially suitable for photoemission and other processes where spectral shapes are of primary interest. As examples, we will discuss the one-electron spectral function beyond GW theory and in presence of phonons. In both cases we find subtle interference effects between self-consistency and vertex corrections and a marked improvement of satellites. As a final example, photoemission beyond the sudden approximation will be discussed. [Preview Abstract] |
Wednesday, March 7, 2007 2:03PM - 2:15PM |
P19.00011: Targeting individual excited states in DMRG. Jonathan Dorando, Johannes Hachmann, Garnet Kin-Lic Chan The low-lying excited states of $\pi $-conjugated molecules are important for the development of novel devices such as lasers, light-emitting diodes, photovoltaic cells, and field-effect transistors [1,2]. The \textit{ab-intio} Density Matrix Renormalization Group (DMRG) provides a powerful way to explore the electronic structure of quasi-one-dimensional systems such as conjugated organic oligomers. However, DMRG is limited to targeting only low-lying excited states through state-averaged DMRG (SDMRG). There are several drawbacks; state-averaging degrades the accuracy of the excited states and is limited to at most a few of the low-lying states [3]. In this study, we present a new method for targeting higher individual excited states. Due to progress in the field of numerical analysis presented by Van Der Horst and others [4], we are able to target individual excited states of the Hamiltonian. This is accomplished by modifying the Jacobi-Davidson algorithm via a ``Harmonic Ritz'' procedure. We will present studies of oligoacenes and polyenes that compare the accuracy of SDMRG and Harmonic Davidson DMRG. [1] Burroughes, et al. , Nature 347, 539 (1990). [2] Shirota, J. Mater. Chem. 10, 1, (2000). [3] Ramasesha, Pati, Krishnamurthy, Shuai, Bredas, Phys. Rev. B. 54, 7598, (1997). [4] Bai, Demmel, Dongarra, Ruhe, Van Der Horst, Templates for the Solution of Algebraic Eigenvalue Problems, SIAM, 2000. [Preview Abstract] |
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