Wick products of the CCR algebra

The purpose of this paper is to put in a precise mathematical (algebraic) form the Wick products of the CCR algebra. We state in detail the reduction of ordinary product of Bose fields in terms of a finite sum of monomials in the creation and annihilation operators in which all creation operators occur to the left of all annihilation operators (Wick‐ordered) and the Fock (vacuum) state of the former. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Geometric methods for nonlinear many-body quantum systems

Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schrödinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. We provide several important properties of this topology and use them to write a simple proof of the famous HVZ theorem in the repulsive case. In the second step we recall the method of geometric localization in Fock space as proposed by Dereziński and Gérard, and we relate this tool to our weak topology. We then provide several applications. We start by studying the so-called finite-rank approximation which consists in imposing that the many-body wavefunction can be expanded using finitely many one-body functions. We thereby emphasize geometric properties of Hartree-Fock states and prove nonlinear versions of the HVZ theorem, in the spirit of works of Friesecke. In the last section we study translation-invariant many-body systems comprising a nonlinear term, which effectively describes the interactions with a second system. As an example, we prove the existence of the multi-polaron in the Pekar-Tomasevich approximation, for certain values of the coupling constant.     

Fock space on C∞ and Bose-Fock space

In this paper, we introduce the Fock space on ${\mathbb{C}}^{\infty }$ and obtain an isomorphism between the Fock space on ${\mathbb{C}}^{\infty }$ and Bose-Fock space. Based on this isomorphism, we obtain representations of some operators on the Bose-Fock space and answer a question in [2]. As a physical application, we study the Gibbs state.     

Efficient implementation of the analytical second derivatives of hartree–fock and hybrid DFT energies within the framework of the conductor-like polarizable continuum model

Calculation of vibrational frequencies for solvated systems is essential to study reactions in complex environments. In this paper, we report the implementation of the analytical self-consistent field Hessian at the Hartree–Fock and density functional theory levels in the framework of the conductor-like polarizable continuum model (C-PCM) into the ORCA quantum chemistry suite. The calculated vibrational frequencies agree very well with those computed through numerical differentiation of the analytical gradients. The deviation between both sets of data is smaller than 3 cm⁻¹ for frequencies larger than 200 cm⁻¹ and smaller than 5 cm⁻¹ for the low-frequency regime (100 cm⁻¹ < ω < 200 cm⁻¹). The accuracy of the frequencies is not significantly affected by the size of the density functional theory (DFT) integration grid, with a deviation lower than 0.5 cm⁻¹ between data computed with the smallest and that with the largest DFT grid size. The calculation of the analytical Hessian is between 3 and 12 times faster than its numerical counterpart. The C-PCM terms only add an overhead of 10–30% relative to the gas phase calculations. Finally, for acetone, the (B3LYP) values for the frequency shifts obtained in going from the gas phase to liquid acetone are in agreement with experiment. © 2019 Wiley Periodicals, Inc.     

Cu(I) camphor coordination polymers: Synthesis and study of the catalytic activity for cyclization of 4‐pentyn‐1‐oic acid

The number of CuCl units per camphor ligand in [{CuCl}₂L]_n was extended to three or four in [{CuCl}₃L]_n ( 2 ) or [{CuCl}₄L]_n ( 1 ). The Hartree‐Fock ab initio calculations support the polymeric structure of 1 and 2 that catalyze the cyclization of 4‐pentyn‐1‐oic acid ( A ) forming 5‐methylenedihydrofuran‐2(3H)‐one ( B ) and/or 2‐methyl‐5‐oxotetrahydrofuran‐2‐ylpent‐4‐ynoate ( C ). The catalytic activity of 1 , 2 and other polynuclear Cu(I) complexes ( 3–5 ) was evaluated under solvent free conditions and/or solution. In the absence of solvent, catalyst 2 displays the highest activity and selectivity (75.8/23.1, C to B ratio, at 5.4% loading) while 4 reaches the highest level of A → B conversion (97.5 %) in solution. Selected reactions were followed by NMR and the kinetic constants calculated. A mechanism is proposed based on the equations used for the calculations. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3316–3323     

Hyperfine anomaly for the ground state of 9Be+

The Fermi contact parameter which represents hyperfine structure (hfs) has been accurately calculated for the ground state of the ⁹Be⁺ ion in a previous paper. In the present paper, the calculated parameter is compared with a high precision measurement to derive the hfs anomaly (the Bohr-Weisskopf effect), which is caused by nuclear magnetization distribution. The obtained hfs anomaly shows a satisfactory agreement with the result of a nuclear shell model calculation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Solution conformation of longifolene and its precursor by NMR and ab initio calculations

We describe the conformation and stereospecific 1H and 13C chemical shift assignments of longifolene 1 and its penultimate precursor 2 through the combined use of ab initio calculations and experimental NMR techniques. The predicted stable conformation for both compounds was similar and adopts a twisted chair conformation at the seven-membered ring where C4 lies on top of the exocyclic double bond. The calculated chemical shifts for the stable conformation agree well with the experimental values.     

Comment on: “Estimating the Hartree–Fock limit from finite basis set calculations” [Jensen F (2005) Theor Chem Acc 113:267]

We demonstrate that a minor modification of the extrapolation proposed by Jensen [(2005): Theor Chem Acc 113: 267] yields very reliable estimates of the Hartree–Fock limit in conjunction with correlation consistent basis sets. Specifically, a two-point extrapolation of the form yields HF limits E _HF,∞ with an RMS error of 0.1 millihartree using aug-cc-pVQZ and aug-cc-pV5Z basis sets, and of 0.01 millihartree using aug-cc-pV5Z and aug-cc-pV6Z basis sets.     

Frequently hypercyclic operators

We investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators on separable complex -spaces: is frequently hypercyclic if there exists a vector such that for every nonempty open subset of , the set of integers such that belongs to has positive lower density. We give several criteria for frequent hypercyclicity, and this leads us in particular to study linear transformations from the point of view of ergodic theory. Several other topics which are classical in hypercyclicity theory are also investigated in the frequent hypercyclicity setting.