Cool clusters correctly correlated

This work describes the applications of ab-initio quantum chemical methods to the studies of atomic clusters. In Chapter 1 a general description of quantum chemical methods, used to solve the stationary Schrodinger equation in subsequent parts of the dissertation, is given. In Chapter 2 the adsorption of oxygen molecules on small neutral and anionic gold clusters is studied. It is shown that O2 binds better to clusters with an odd number of electrons than to clusters with an even number of electrons. DFT results are found to be in significant disagreement with high-level ab-initio CCSD(T) results. Chapter 3 describes the study of reaction mechanisms of molecular hydrogen with small neutral and anionic gold clusters. The binding energies of one and two H2 molecules are calculated. The transition states of H2 dissociation on gold clusters are located. In contrast to O2 absorption, DFT produces reasonable results for the H2 binding energies and the barriers to H2 dissociation. The study of the stability of different isomers of C36 carbon clusters is presented in Chapter 4. It is shown that the singlet state of the lowest energy D6h isomer has significant diradical character. The experimental data is explained based on multireference perturbation theory calculations. It is shown that strong electron correlation is responsible for the high stability of D6h isomer observed in experiments. In Chapter 5 the mixed metal-carbon Ti8C12 cluster is studied with the main goal to determine the geometry and ground electronic state of this cluster. It is shown that the Td structure with a 1E ground state is a subject to Jahn-Teller distortion. The distorted D2d and C3v structures are studied with multireference configuration interaction and coupled cluster methods. The D2d structure with a singlet ground state suggested as a ground state of the Ti8C12 cluster. A new approach for solving the many electron Schrodinger equation is proposed in Chapter 6. In contrast to the wave function or the density functional theory approaches, the proposed method uses the first-order reduced density matrix and the diagonal part (density) of the cumulant of the second-order reduced density matrix

Ab initio calculations of spectroscopic constants and vibrational state lifetimes of diatomic alkali-alkaline-earth cations

We investigate the lifetimes of vibrational states of diatomic alkali-alkaline-earth cations to determine their suitability for ultracold experiments where long decoherence time and controllability by an external electric field are desirable. The potential energy and permanent dipole moment curves for the ground electronic states of LiBe+, LiMg+, NaBe+, and NaMg+ are obtained using the coupled cluster with singles doubles and triples and multireference configuration interaction methods in combination with large all-electron cc-pCVQZ and aug-cc-pCV5Z basis sets. The energies and wave functions of all vibrational states are obtained by solving the Schrodinger equation for nuclei with the B-spline basis set method. To predict the lifetimes of vibrational states, the transition dipole moments, as well as the Einstein coefficients describing spontaneous emission, and the stimulated absorption and emission induced by black body radiation are calculated. Surprisingly, in all studied ions, the lifetimes of the highest excited vibrational states are similar to the lifetimes of the ground vibrational states indicating that highly vibrationally excited ions could be useful for the ultracold experiments requiring long decoherence time. Published by AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Fedorov, D. A., Barnes, D. K., & Varganov, S. A. (2017). Ab initio calculations of spectroscopic constants and vibrational state lifetimes of diatomic alkali-alkaline-earth cations. The Journal of chemical physics, 147(12), 124304. and may be found at https://doi.org/10.1063/1.4986818

Multireference Second-Order Perturbation Theory: How Size Consistent is “Almost Size Consistent”

A systematic study of the deviation from size consistency of the multireference second-order Møller-Plesset perturbation theory (MRMP2) method is presented. The size-consistency error is shown to depend on the number of monomers in a supermolecule calculation, size of basis set, number of correlated valence electrons, and size of active space. HF, F2, and N2 are used as test cases, with stretched bonds, to include simple, well-defined multireference character. This is essential in ensuring that MRMP2 is being tested as a multireference method. It is concluded that the MRMP2 and other multireference perturbation theory methods can exhibit significant size-consistency errors, and that the size of the error depends on the manner in which the perturbation theory is implemented

A generalized Poisson equation and short-range self-interaction energies

We generalize the Poisson equation to attenuated Newtonian potentials. If the attenuation is at least exponential, the equation provides a local mapping between the density and its potential. We use this to derive several density functionals for the short-range self-interaction energy

Privacy-Preserving Aggregation of Time-Series Data

The conference paper can be viewed at: http://www.isoc.org/isoc/conferences/ndss/11/proceedings.shtmlSession 9: PrivacyWe consider how an untrusted data aggregator can learn desired statistics over multiple participants’ data, without compromising each individual’s privacy. We propose a construction that allows a group of participants to periodically upload encrypted values to a data aggregator, such that the aggregator is able to compute the sum of all participants’ values in every time period, but is unable to learn anything else. We achieve strong privacy guarantees using two main techniques. First, we show how to utilize applied cryptographic techniques to allow the aggregator to decrypt the sum from multiple ciphertexts encrypted under different user keys. Second, we describe a distributed data randomization procedure that guarantees the differential privacy of the outcome statistic, even when a subset of participants might be compromised.published_or_final_versio

Interfacing the Ab Initio Multiple Spawning Method with Electronic Structure Methods in GAMESS: Photodecay of trans-Azomethane

This work presents a nonadiabatic molecular dynamics study of the nonradiative decay of photoexcited trans-azomethane, using the ab initio multiple spawning (AIMS) program that has been interfaced with the General Atomic and Molecular Electronic Structure System (GAMESS) quantum chemistry package for on-the-fly electronic structure evaluation. The interface strategy is discussed, and the capabilities of the combined programs are demonstrated with a nonadiabatic molecular dynamics study of the nonradiative decay of photoexcited trans-azomethane. Energies, gradients, and nonadiabatic coupling matrix elements were obtained with the state-averaged complete active space self-consistent field method, as implemented in GAMESS. The influence of initial vibrational excitation on the outcome of the photoinduced isomerization is explored. Increased vibrational excitation in the CNNC torsional mode shortens the excited state lifetime. Depending on the degree of vibrational excitation, the excited state lifetime varies from ∼60–200 fs. These short lifetimes are in agreement with time-resolved photoionization mass spectroscopy experiments

Resolutions of the Coulomb operator

We discuss a generalization of the resolution of the identity by considering one-body resolutions of two-body operators, with particular emphasis on the Coulomb operator. We introduce a set of functions that are orthonormal with respect to 1∕r₁₂ and propose that the resulting “resolution of the Coulomb operator,” r₁₂⁻¹=∣ϕi><ϕi∣, may be useful for the treatment of large systems due to the separation of two-body interactions. We validate our approach by using it to compute the Coulomb energy of large systems of point charges

The interaction of oxygen with small gold clusters

Presented in this work are the results of a quantum chemical study of oxygen adsorption on small Aun and Au−n (n=2,3) clusters. Density functional theory(DFT), second order perturbation theory (MP2), and singles and doubles coupled clustertheory with perturbative triples [CCSD(T)] methods have been used to determine the geometry and the binding energy of oxygen to Aun. The multireference character of the wave functions has been studied using the complete active space self-consistent field method. There is considerable disagreement between the oxygen binding energies provided by CCSD(T) calculations and those obtained with DFT. The disagreement is often qualitative, with DFT predicting strong bonds where CCSD(T) predicts no bonds or structures that are bonded but have energies that exceed those of the separated components. The CCSD(T) results are consistent with experimental measurements, while DFT calculations show, at best, a qualitative agreement. Finally, the lack of a regular pattern in the size and the sign of the errors [as compared to CCSD(T)] is a disappointing feature of the DFT results for the present system: it is not possible to give a simple rule for correcting the DFT predictions (e.g., a useful rule would be that DFT predicts stronger binding of O2 by about 0.3 eV). It is likely that the errors in DFT appear not because of gold, but because oxygen binding to a metal cluster is a particularly difficult problem.This work was supported by AFOSR through a DURINT grant