Abstracts of the Kathmandu Workshop 2012

This page is in preparation.

Newari art

The abstracts are in the alphabetical order of the author names.

Helen van Aggelen

Ghent University

Variational optimization of second order density matrices for chemistry

A myriad of ab initio methods uses simple mathematical objects to describe a chemical system in order to avoid the ‘exponential wall’ inherent to the wavefunction. This talk evaluates the use of variational second order density matrix methods for chemistry and identifies the major theoretical and computational challenges that need to be overcome to make it successful for chemical applications.

Its major theoretical challenges originate from the need for the second order density matrix to be N-representable: it must be derivable from an ensemble of N-electron states. Our calculations have pointed out major drawbacks of commonly used necessary N-representability conditions, such as incorrect dissociation into fractionally charged products and size-inconsistency, as well as flaws in the description of spin properties. We have derived subspace energy constraints that fix these problems, albeit in an ad-hoc manner.

Its major computational challenges originate from the method’s formulation as a vast semidefinite optimization problem. We have implemented and compared several algorithms that exploit the specific structure of the problem. Even so, their slow speed remains prohibitive. Both the second order methods and the zeroth order boundary point method that we tried performed quite similar, which suggests that the underlying problem responsible for their slow convergence, ill-conditioning due to the singularity of the optimal matrix, manifests itself in all these algorithms even though it is most explicit in the barrier method.

Significant progress in these two areas is needed to make the variational second order density matrix method competitive to comparable wavefunction based methods.

Paul Ayers

McMaster University

What Should One Do When Electronic Structure Methods Aren’t Good Enough? Machine-Learning Methods for Molecular Properties

Thermodynamic properties like equilibrium and rate constants are exquisitely sensitive to errors in the relative free energies of the chemical species involved. For example, experimental measurements of acidity in molecules and proteins are often accurate to .1 pKa unit; in order to compute pKa’s to this accuracy, one must compute the Gibbs free energy of deprotonation to within .5 kJ/mol (2 × 10–4 a.u.). This level of computational accuracy is inaccessible for small molecules in the gas phase and unfathomable for large molecules in solution.

Fortunately, the errors in computational models tend to be systematic. It is thus possible to correct the errors in the computations with statistical methods. This talk will show how a hybrid approach, wherein computational models are reparameterized to agree with experimental data, can provide computational models for pKa’s that approach experimental accuracy. The primary tools are multiple regression (with great care taken to avoid overfitting); the residual errors can be removed, at least in part, using a machine learning method called Gaussian process regression (kriging). These methods are applied to a diverse set of acids, including molecular acids (carboxylic acids, alcohols, and amines) and proteins. While experimental accuracy is not attainable, root-mean-square errors that are significantly less than one pKa unit are attainable.

Roi Baer

The Hebrew University of Jerusalem

Dogmatic and Pragmatic Spirits in Density Functional Theory

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Daniel Borgis

CNRS and Ecole Normale Supérieure

Classical Density Functional Theory and its Application to Chemistry

We will ask how the concepts developed for electronic DFT in quantum chemistry and classical DFT in statistical mechanics can nourish from each other and lead to a practical application of classical DFT to problems of chemical interest: Molecular solvation, complex interfaces, molecular recognition, ...

Benoît Braida

Université Pierre et Marie Curie

Recent trends in ab initio Valence Bond methods

Ab initio Valence Bond (VB) methods based on strictly local (one-center atomic) orbitals are able to combine a unique chemical interpretability, with, when electronic correlation is properly included, reasonable accuracy of the computed quantities.[1] How to grasp electronic correlation (static and dynamic) in a VB wave function will be discussed. To illustrate the merit of such methods, application of a recently proposed mixed Valence Bond / Quantum Monte Carlo method [2] on the elucidation of the nature of bonding in tetracyano-ethylene anion dimer will be presented.

Ria Broer

Zernike Institute for Advanced Materials

First principles Studies of Magnetic Interactions in Molecules and Solids

An important task for Theoretical Chemistry is to develop and apply methods for the accurate computation of electronic and magnetic properties of molecules and solids, to complement experimental observations. An equally important task is to analyze the accurate results, therewith enabling interpretation in terms of useful physical and chemical concepts. In the case of magnetic interactions we have now gained much experience with the prediction of relative energies and electron distributions of states with different electron spin couplings. The results are often conveniently interpreted in terms of phenomenological spin hamiltonians, like the Heisenberg Hamiltonian that includes only isotropic couplings, which can be extended with anisotropic terms in case the latter turn out to be important. The mechanisms of transitions between one spin state and another as occur for example in light induced excited-spin state trapping (LIESST) are still not well understood, but current research is devoted to this problem. In this contribution I will give an overview of methods used to approach the scientific problems mentioned above and discuss their merits and limitations.

Patrick Bultick

Ghent University

Chemical verification of new quantum chemical methods

When new quantum chemical methods are introduced, or even old ones revived, much attention is paid to the energy obtained. Especially for a variational method, the adagium is that lower is better as this is closer to the Full CI energy. However, energy does not always suffice as a criterion. Although often not considered based on firm theoretical considerations, different sorts of chemical concepts can often help in interpreting failures of methods or reveal quite unexpected flaws.

In this talk useful concepts are sketched, including Atoms in Molecules models with the accompanying atomic charges, Fermi hole analysis etc. Simple chemical reasoning based on electronegativity and ionization energies, for instance, allow one to predict what a potential energy surface (PES) for diatomic species should look like. Even fairly simple experiments give important information on the stability of triplets versus singlets etc. If a new method does not match the results of these basic facts, this warrants the question whether there are no hidden problems in the method.

As an illustration, variational second order density matrices are discussed under a limited set of so-called N-representability constraints. Although this method has been introduced quite a while ago, its dramatic failure for potential energy surfaces has only been shown recently thanks to taking a look at Mulliken and Hirshfeld-I populations near dissociation. Molecules are split in fragments with fractional occupancies, which is clearly unphysical. Moreover, subspace constraints could be introduced that fix this problem but leave the problem of incorrect ordering of PES for different spin multiplicities untouched.

Patrizia Calaminici

Departamento de Química, CINVESTAV

Finite Systems Properties from Born-Oppenheimer Molecular Dynamics

Density functional theory (DFT) Born-Oppenheimer molecular dynamics (BOMD) simulations of �nite systems such as metal clusters are presented. The calculations have been performed with the deMon2k [1] code employing all-electron basis sets and local and non-local functionals. The capability of reasonable long (~100 ps) �rst-principle BOMD simulations to explore potential energy landscape of metallic clusters will be presented. The evolution of the cluster structures and properties such as polarizabilty and heat capacity, at di�erent temperatures, will be discussed.

Carlos Cárdenas

Universidad de Chile

Navigating the Hard-Soft Acids-Bases Principle.

Hard-soft acids-bases (HSAB) principle of Pearson establishes that when the strength of the acids and bases involved in the reaction is similar, hard acid prefer binding to hard bases an soft acids prefer binding to soft bases. For years the hardness of molecules lacked of a mathematical definition and a numerical scale of hardness was unavailable. However, in 1983 Parr and Pearson identified the hardness as the derivative of electronic chemical potential (the Lagrange multiplier in Euler equation of DFT) with respect to the number of electrons. This definition orders correctly the hardness of molecules and it is in agreement with many physical properties empirically associated to hardness. Nevertheless, there is not a complete proof of HSAB in terms of this definition of hardness. Such proof seems impossible as HSAB operates differently in different reactions. However, much can be learned and proofed when one studies relevant cases. I will review most of available theoretical evidence in favor of HSAB and, significantly, recent contributions we have done in understanding the validity of HSAB in a situation as general as can be double exchange acid-base reactions. Both, mathematical proofs and Monte Carlo-like experiment will be shown.

Stephane Carniato

Université Pierre et Marie Curie

How RIXS and theory can be combined to measure the electronegativity

Polarization-dependent resonant inelastic x-ray scattering (RIXS) is a new probe [1] of molecular-field effects on the electronic structure of isolated molecules. A combined experimental and theoretical analysis explains the linear dichroism observed in Cl 2p RIXS following Cl 1s excitation in HCl due tomolecular-field effects, including singlet-triplet exchange, indicating polarized-RIXS provides a direct probe of spin-orbit-state populations applicable to any molecule. It will be shown how theory-experiments can be helpful to predict the electronegativity of radical species and why it is challenging for a better description of the chemical bond in core excited species.

Mauro Causá

Universitá di Napoli Federico II

Locality and non-locality. It is possible to cut a system governed by quntum mechanics

The embedding schemes, for treating large quantum systems by small parts, are briefly revised. Some hypothesis about the reason why the embedding problem remains an open problem are presented to the discussion.

Guanhua Chen

University of Hong Kong

Penetrating Potential Barrier One Hundred Percent

It is known that a quantum particle may tunnel through a potential barrier. However, the overall transmission coefficient is less than one. We consider an infinite chain of atoms. Applying an external field to raise the potential energy of a few atoms in the middle, we find that under certain condition an incoming electron may go through the potential barrier completely. Numerical simulation of transient current, evaluating of steady state current and as well as analytic result of a model system will be present. The precise condition for such a complete tunneling will be discussed.

Henry Chermette

Université Lyon1

The Gradient-Regulated Connection of Generalized Gradient Exchange Functionals: Interest and Limitations

The Gradient-Regulated Connection (GRAC) has been introduced a few years ago by Baerends et al. in order to build a density functional potential model satisfying theoretical conditions and providing Kohn-Sham orbitals. Recently the GRAC has been used to build an exchange functional able to mix performances of a modified PBE for the bulk region, to those of the PW91 for the asymptotic one. This exchange functional, coupled with the TCA correlation functional, was able to significantly improve the modeling of weak interacting systems, while keeping a good accuracy for the atomization energies. The interest and the limitations of this approach is discussed.

Jerzy Cioslowski

University of Szczecin

All you always wanted to know about many-electron harmonium atoms

Recent theoretical and numerical developments on electronic structures of harmonium atoms with more than two electrons are reviewed, including FCI and Monte Carlo results, as well as a new accurate representations for the total anergy and its components in terms of a transformed coupling strength.

Claude A. Daul

University of Fribourg

Prediction of single-molecular magnets with open d- or f-shells by theoretical calculations

Preliminary summary: Most single-molecule magnets (SMMs) are transition metal clusters of exchanged-coupled metal ions with high-spin ground states and large uniaxial anisotropy (1). They have attracted a lot of attention in recent time because of their potential application as nanometer-scale memory devices. The unusually slow magnetic relaxation and the resultant superparamagnetic behaviour of these polynuclear complexes are explained by the characteristic electronic structure of their ground multiplets where by zero-field splitting the spin-up (Sz = S) and spin-down (Sz = - S) states have the lowest energy. Here, S is the spin quantum number. The long magnetization relaxation time are explained by the presence of a potential barrier between the spin-up and spin-down states.

Etienne Derat

Université Pierre et Marie Curie

Models for complex bioinorganic systems: a tool for future design?

Enzymes are fascinating molecular objects, designed by nature to perform chemical reactions with high turn-over, regioselectivity and stereoselectivity. Therefore, they represent a "Holy Grail" for most bio-organic chemists. But when a metal is included in the enzymatic structure, they also represent a difficult challenge for theoretical chemists: most if not all force-fields were designed for organic only species, QM methods are not always robust with transition metals, and sometimes to add even more difficulties, reactions are performed in the excited state, or with open-shell wavefunctions. In our days, solving such a problem has been in some way tackled: choose your favorite QM/MM scheme, and run CCSD(T)/CASPT2/MRCI/BOVB calculations on top of it. But modeling a chemical system is not only choosing the best (and most expensive) calculations, modeling is creating a tool that can be used by others to understand/design/play with their own chemically related systems. In this talk, archetypical enzymatic systems will be shown that illustrate the fact that rationalizing them using theoretical chemistry tools can help to design new structures with improved functionalities or new chemical reactivities.

John Dobson

Griffith University

Dispersion Forces

The dispersion energy is a long-ranged part of the correlation energy, but there are many ways to understand it. A summary will be given of various approaches to the theory of dispersion forces, including some very old and some very new ones.

Matthias Ernzerhof

University of Montreal

Non-Hermitian quantum mechanics and density functional theory

It is usually assumed that the conservation of the wave-function normalization upon time evolution requires a Hermitian Hamiltonian. However, we show that certain types of non-Hermitian Hamiltonians also yield a time evolution with conserved normalization. The particular type of non-Hermitian Hamiltonian we are interested in can be used to describe open systems. It enables one to model the time evolution of sub systems that exchange current density with the environment. Numerical examples of various time evolutions are presented which illustrate how electrons are transferred through molecules. Non-Hermitian Hamiltonians are also suitable to model stationary, time-independent states of open systems. We demonstrate this by deriving a generalized Hartree-Fock theory and a generalized Kohn-Sham density functional theory for non-Hermitian Hamiltonians. Applications of these methods to electron transport through molecules and to the calculation of the life time of metastable systems are presented.

Patricio Fuentealba

Universidad de Chile

The richness of the dynamic of clusters and molecules

Ab initio molecular dynamics for a variety of atomic clusters and molecules will be shown and discussed. In systems as small as M3 (M= alkali metal atom) there are some interesting phenomena like pseudorotation and transposing. The dynamics will be characterized by some geometric parameters and also energetic considerations. In some cases, especially Na7 , it was also possible to identify a transition state for the conversion between the two main isomers. In molecules of the type MCN (M: alkali metal atom) it will be shown how the alkali metal atom orbits around the cyano ion.

Irek Grabowski

Nicolaus Copernicus University, Torun

Impact of the correlation effects on the KS DFT potentials, energies and densities.

Direct comparison of the correlation potentials, electron densities and correlation energies, generated from few variants of correlated Optimized Effective Potential Method (OEP), standard Density Functional Theory (DFT) and from ab initio Wave Function Theory Methods (WFT), has been employed for analyzing the impact of the correlation effects on those quantities. These methods have been applied to a few atomic and molecular systems.

The correlation potentials, energies and densities generated from correlated OEP - OEP2-sc [1], OEP-ccpt2 [2] and from WFT methods - Coupled Cluster and second-order Many Body Perturbation Theory show very similar and systematic behaviour, reconfirming the correctness of the ab initio DFT (OEP2) methods [3,4].

In a contrast it has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial correlation effects on the KS-correlation potentials [3,4] and electron density [5], whereas these effects are well represented by the orbital dependent OEP correlation functionals. In the same time for the local, generalized-gradient, and hybrid functionals it has been found that the dynamic correlation effects are to a large extend accounted for by densities resulting from exchange-only calculations. Additional calculations with self-interaction corrected exchange potentials indicate that this finding cannot be explained as an artifact caused by the self-interaction error or non dynamic correlation effect.

The usefulness of such kind of analysis in a context of development new exchange correlation functionals in DFT will be also discussed.

Ante Graovac

Faculty of Science, Nikole Tesle 12, HR-21000 Split, Croatia

On topology versus geometry in molecules

Graphs can be drawn in an infinite number of ways. However, by analysis of eigenvectors of adjacency and Laplacian matrices of molecular graphs one is able to get drawings which reproduce rather well geometries in some classes of molecules like fullerenes, nanotubes and their junctions. The results obtained up to now will be discussed and possible new routes to generalize graph drawing techniques will be discussed.

This presentation is a result of collaboration with Istvan Laszlo (Budapest) and Tomaz Pisanski (Ljubljana).

Frank E. Harris

University of Florida

Fully Correlated Wavefunctions for Small Atoms

While this work includes a lot that is new, I would expect to give a talk that is general enough to place the new developments in the context of the line of work that was started by Robert Hill and was advanced significantly by Rebane (St. Petersburg), with some further contributions from our laboratory and from others.

Trygve Helgaker

University of Oslo

Density-functional theory in magnetic fields

I intend to discuss the universal density functional with emphasis on magnetic fields—in particular in relationship to the Lieb variation principle. We have generalized our scheme for the calculation of the universal density functional by Lieb maximization from full configuration interaction (FCI) wave functions to electrons in magnetic fields. As a first step, we will study the density functional in a finite field without introducing a current dependence, simply regarding the charge density as the conjugate to the scalar potential with a parametric dependence on the magnetic field. Subsequently, we intend to study the charge and current densities as conjugate to the scalar and vector potentials. Different formulations of the universal density functional in magnetic fields will be discussed.

Philippe Hiberty

Université de Paris 11

Valence Bond Theory and Reactivity: Correlation Between the Diradical Character of 1,3-Dipoles and their Reactivity Toward Ethylene and Acetylene.

Preliminary summary: The influence of the diradical character of 1,3-dipoles on the barrier to 1,3-dipolar cycloaddition is studied by means of ab initio valence bond theory. Each 1,3-dipole is described as a linear combination of three valence bond structures, two zwitterions and one diradical. The diradical character of 1,3-dipoles is shown to be a critical feature to favor 1,3-dipolar cycloaddition. Within each family of 1,3-dipoles, involving diazonium betaines, nitrilium betaines and azomethine betaines, a linear relationship is evidenced between the weight of the diradical structure in the 1,3-dipole and the barrier to cycloaddition to ethylene or acetylene. The barrier heights also correlate with the transition energies from ground state to pure diradical states of the 1,3-dipoles at equilibrium geometry. From these results, we propose a reaction mechanism in which the 1,3-dipole first distorts so as to reach a “reactive electronic state” that has a significant diradical character, then adds with little or no barrier to the dipolarophile. This mechanism is in line with the recently proposed distortion/interaction energy model of Ess and Houk2 and their finding that the barrier heights for the cycloaddition of a given 1,3-dipole to ethylene and acetylene are nearly the same, despite the exothermicity difference.

Leeor Kronik

Weizmann Institute of Science

Understanding photoelectron spectroscopy from first principles - progress and challenges

Preliminary summary: In this talk, I will discuss the pros, cons, progress made, and remaining limitations, of understanding photoelectron spectroscopy with density functional theory, using semi-local, conventional hybrid, and range split hybrid functionals. This will be achieved via judicious comparison with experiment and with the results of many-body perturbation theory calculations.

Wenjian Liu

College of Chemistry and Molecular Engineering, Peking University

Relativistic correlation

Fundamental breakthroughs have recently been achieved in relativistic quantum chemistry based on the no-pair Dirac-Coulomb-Breit Hamiltonian (for a recent review see Ref. [1]). However, there still exist two issues that require great attention, i.e., how to go beyond the no-pair approximation so as to account for the correlation contributions of negative energy states and how to do relativistic explicit correlation under the no-pair approximation. It turns out[2] that the QED prescription must be invoked for the former case while an extended no-pair projection has to be introduced for the latter case. Only under these understandings, the know-how correlation methods can be transplanted to relativistic quantum chemistry.

Jean-Paul Malrieu

Université de Toulouse

Scale changes and reduction of the degrees of freedom in wave-function calculations through contraction and real space renormalization techniques

Post-mean field calculations in principle have to work in a Hilbert space of huge dimension. Two tools should enable us to reduce this size problem.

The first one consists in contracting sets of excitations into a composite vector. Multi-reference CI approaches, either perturbative or variational, frequently make use of such contractions, the form of which is very flexible. Other methods may contract excitations from topological criteria, using a unique vector for the excitations from the same couple of occupied localized MOs, or from the same region of space.

The second strategy is based on the concept of Real Space Renormalization. It divides the space into blocks and builds the wave function in a reduced space, composed of products of low energy eigenstates of the blocks. The energies of the block states and of their interactions is evaluated from accurate calculations on block pairs or triads, through effective Hamiltonian theory. Such a strategy may be used to compute excitation energies of large or infinite periodic systems in a Renormalized Excitonic Method, which represents a local approach to delocalized excitations.

Alexis Markovits

Laboratoire de Chimie théorique UMR7616 UPMC/CNRS

THE ACTIVE ROLE OF THE SURFACE IN HETEROGENEOUS CATALYSIS

Reaction mechanisms studies in heterogeneous catalysis have been focusing on adsorbate’s behavior for many years. However, in recent years, the role of the surface itself has been emphasized. “Modern surface science techniques have shattered the myth of the rigid surface waiting for the reaction to occur [1], the molecule adsorbing strongly, reacting and desorbing.

Particle shape, size and faceting are already a proof of that. In my talk, I present several examples of the active role of the surface. Surface flexibility during hydrogenation processes is a key feature of catalysts. Ethylidyne is shown to have a crucial role even if it does not directly participate to the catalytic process. Being strongly bound, it remodels the active site. It moves on the metal surface allowing a high turnover. Even though this mobility has been evidenced, it contains an apparent contradiction with the strength of the binding between the adsorbate and the surface. Another very large surface reorganization is due to oxygen. Oxygen yields pinholes on the surface which are mandatory for catalysis.

Ángel Martín Pendás

Universidad de Oviedo. Spain

Fluctuation of electron populations and chemical bonding.

An interesting description of chemical bonds is emerging from the study of the fluctuations of the electron population in real space domains. The latter include the atoms of the Quantum Theory of Atoms in Molecules (QTAIM), as well as the different attraction basins of the Electron Localization Function (ELF). These lecture will present a didactic model of chemical bonding in an N-electron, m-nuclei molecule in terms of the probabilities of the different statistical events coming from distributing N balls in m cages.

Christian Minot

LCT, UPMC, ParisVI

Reducibility of metal oxides

The properties of metal oxides depend on the reducibility of the metal cation. When the cation oxidation states vary, the adsorption takes place on another site with a different force. The dissociation of H2 on reducible oxides is different from that of irreducible ones. We analyze the mechanisms of formation of gaps and O hydrogenation that reduces oxides. When the cations are reducible, they are the seats of the reduction. When the cations are not, the electrons are localized in the cavity, trapped by the Madelung field. The formation of the vacancy is more costly in energy and reduced the surface more reactive. The analysis is supported by VASP calculations.

Debashis Mukherjee

Indian Association for the Cultivation of Science

Reflections on interplay of dynamical and static correlations (and relativistic effects) : paradigms and approaches

I wish to share with the participants some of my recent thoughts on the interplay of dynamical and static correlations as shaped by various paradigms. I will argue that the separation of the total correlation into dynamical and static is one of the several paradigms and is by no means unique--a rigid adherance may in fact lead to physically irrelevant artifacts. The problem of consistently handling the positronic degrees of freedom is another issue which enmeshes with the correlation effects, and it is here that the static correlation effects has to be dealt with carefully. I will discuss my current thoughts on some of the recent approaches to electron correlation based on a combination of paradigms.

Anna Okopinska

Jan Kochanowski University

Entanglement in natural and artificial atoms and molecules.

The recent progress in nanoscale technology made possible to address single quantum objects. Very small clusters containing down to a few atoms, molecules or ions can be isolated in various kinds of electromagnetic and optical traps at ultracold temperatures. Apart of nature-made atoms and molecules, the artificial few-body quantum systems become available, such as superconducting circuits or semiconductor quantum dots, that can be also individually addressed. The correlation effects are crucial for determining the properties of such systems. Especially useful is the concept of entanglement which refers to the correlations that have no classical counterpart. The problem of measuring entanglement is very complex and different methods have been proposed for its quantification. I will review several measures that are being used to quantify entanglement in few-body systems and discuss their behavior for simple models of natural and artificial quantum systems.

Sourav Pal

National Chemical Laboratory

Coupled cluster theory: stationary or non-stationary?

The coupled cluster theory has been viewed primarily as a non- stationary theory and is often formulated as a similarity-transformed form of the Hamiltonian. However, in this presentation, it will be shown that it is possible to have explicit stationary forms of this theory, which are more useful for various properties. There exist many alternate stationary forms of the theory. The merits and demerits of several such forms will be discussed and the new developments from our group will be presented.

Mario Piris

University of the Basque Country

Can NOFT bridge the gap between DFT and WFT?

Since the molecular Hamiltonian operator contains only one- and two-electron operators, the energy of a molecule can be determined exactly from the knowledge of the one- and two-particle reduced density matrices (1- and 2-RDMs). The most accurate electronic structure methods are based on N-particle wave functions. Given an N-particle wave function, we have the N-RDM, and by contraction the 1- and 2-RDMs can be derived. Unfortunately, the N-particle wave-function is a too complex object and its manipulation becomes cumbersome as the system grows larger. In 1964, Hohenberg and Kohn demonstrated that the ground state energy can be expressed as a functional of the one-electron density only. The density functional theory (DFT) has become very popular thanks to its relatively low computational cost. In the exact DFT, we should reconstruct the 1- and 2-RDMs from the density, however, most practical implementations of DFT are based on the Kohn-Sham formulation, in which the kinetic energy is not constructed as a functional of the density but rather from an auxiliary Slater determinant. The contribution from a part of the kinetic energy in the correlation potential is probably the main source of problems of present-day KS functionals. Another obstacle is the construction of a functional capable of describing the N-particle system. This functional N-representability is related to the N-representability of the 2-RDM. Even though DFT energies may lie quite close to the exact ones, it is not fully guaranteed not to be below the exact ones, as required by the variational principle. In 1974, Gilbert proved for the 1-RDMs an analogous theorem to the Hohenberg-Kohn theorem for the electron density. He suggested an alternative viewpoint regarding 1-RDM functional theory. One can employ the exact functional with an approximate 2-RDM that is built from the 1-RDM using a reconstruction functional. The major advantage of a 1-RDM formulation is that the kinetic energy is explicitly constructed and does not require a functional. Like for the density, the ensemble N-representability conditions of the 1-RDM are well-known, but naturally, this does not overcome the N-representability problem of the energy functional. The 1-RDM functional is called Natural Orbital Functional (NOF) when it is based upon the spectral expansion of the 1-RDM. A reconstruction of the 2-RDM has been achieved using the cumulant expansion leading to an approximate NOF known in the literature as PNOF. The PNOF is based on an explicit ansatz of the two-particle cumulant λ(Δ,Π) satisfying the D-, Q- and G-necessary positivity conditions for the 2-RDM. In this presentation, the theory behind the PNOF is outlined. Special emphasis will be put on the spin conserving NOF theory and on the recent proposed algorithm which yields the natural orbitals by an iterative diagonalization of a generalized pseudo-Fockian matrix. Some examples of strongly correlated systems, where density functionals yields pathological failures, are also presented to illustrate the potentiality of the NOF theory.

Nino Russo

Università della Calabria

How to choose the exchange-correlation potential for different systems or processes: menu à la carte ou menu du jour ?

In the last decade many new exchange-correlation functionals have been proposed and tested. Looking at the applications it seems that the best way to work is to choose the exchange-correlation functional on the basis of the system of the physical process under investigation. Establishing criteria could be useful to people that live in this Babel in order to avoid the philosophy of “one problem one XC”.

Dennis R. Salahub

University of Calgary

Electron transfer and other reactions in proteins – towards an understanding of the effects of quantum decoherence

We have embarked on a multistage research program on the multiscale theory, simulation, computation and understanding of electron transfer and other reactions in complex bio-systemsi.

Our entry into the fieldi was our recent tunneling pathway analysis on molecular dynamics simulations of the methylamine dehydrogenase (MADH)—amicyanin (Am) redox pair. We found that the most frequently occurring molecular configurations afford superior electronic coupling, via a hydrogen-bonded “water bridge” between donor and acceptor. Surface residues are crucial to the recognition and dynamic docking of the proteins as well as the organisation of the aqueous environment at the active site, increasing the lifetime of the water bridge. Mutant complexes fail to achieve the same bridge stability.

A second contributionii reports our first attempts to understand the effects of quantum decoherence on the rates of chemical reactions. Multiple-state reaction rates can be estimated within semi-classical approaches provided the hopping probability between the quantum states is taken into account. This probability is intimately related to the transition from the fully quantum to the semi-classical description, but this issue is not adequately handled with kinetic models commonly in use that so far have treated this transition only in a perturbative manner. Quantum nuclear effects like decoherence and dephasing are not present in the rate constant expressions. Retaining the intuitive semi-classical picture, we included these effects through the introduction of a phenomenological quantum decoherence function. In addition to the electronic coupling term, a characteristic decoherence time tdec now also appears as a key parameter of the rate constant. The introduction of this new dimension may imply profound changes to our understanding of chemical reactivity. The new formula has been tested by means of Density Functional Theory molecular dynamics simulations for a triplet to singlet transition within a copper dioxygen adduct and for an electron-transfer model involving a Li donor and a Li+ acceptor, separated by up to five peptide units. We are now setting up to re-examine the MADH-Am with this new method, hence avoiding the empiricism of the pathway model.

Schwarz, W. H. E.

Tsinghua U Beijing & U Siegen Germany

Descriptive and Explanative Concepts of Theory for Chemistry or Unusual Bonding by the 5f-6d-6p-7s Valence Shell of Actinoids

?

Peter Schwerdtfeger

Massey University Auckland

High Pressure Simulations – Squeezing the Hell out of Atoms

The pressure range accessible to laboratory experiments exceeds now a remarkable 20 orders of magnitude, from ultra-high vacuum (< 1 nPa) to ultra-high pressures (> 100 GPa). With the development of high-pressure diamond-anvil cells we are now able to study materials at pressures equivalent to the pressure at the centre of our earth (350 GPa). In other planets and stars pressures beyond the TPa range are reached, which can only be explored by thermonuclear explosions or by theoretical methods. At high pressures unusual structures and materials properties are observed. It is, however, a formidable task to accurately derive equations of state (EOS), f(P,V,T)=0, and corresponding phase diagrams, for gases, liquids and the solid state up to high pressures and temperatures from first principles, that is from quantum theory and statistical physics. Our research group has just achieved that recently for neon, where the isotherms are in excellent agreement with experimental data. Fundamental questions we are currently exploring are, for example, if we can already understand the density-pressure relationship of simple atomic crystals (like helium or neon) from squeezing atoms. Is the EOS virial equation applicable for mercury in the gas phase? Can we obtain accurately melting temperatures up to the high-pressure range? Moving to more complex systems, we present new results on optical properties of ice under pressure, which is important for understanding the physics of icy planets. And finally, can we model the melting of mercury using first principle methods? Mercury is a notoriously difficult element to treat by quantum theoretical methods as not only electron correlation effects but also relativistic effects need to be considered, and the many-body expansion of the interaction energy between mercury atoms does not converge in the overlap region of the interaction.

Gustavo E. Scuseria

Rice University

Symmetry breaking & restoration

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.

Tomasz Wesolowski

University of Geneva

Joining seamlessly microscopic and macroscopic levels of description of matter: challenges and perspectives for modelling methods based on Frozen-Density Embedding Theory.

We target static properties of embedded systems. Using the formal framework of Frozen-Density Embedding Theory as the basis for numerical simulations of the multilevel type, hinges on a number of approximations, assumptions or even conjunctures of universal or system-specific nature. They will be overview taking into account our understanding of Frozen-Density Embedding Theory and numerical experience accumulated so far.

Weitao Yang

Duke University

Fukui functions: Analytic evaluation and new exact conditions from the flat plans

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Khumbu Icefall seen from the Everest Base Camp