Molecular quantum gases

From the general quantum-statistical standpoint, Bose-Einstein condensation can be achieved with both atoms and molecules. However the realization of BEC with a molecular gas is a much more formidable task because of the difficulties involved in the deep cooling of molecules. 

5 Bohr magnetons. A measurement of the expansion energies of the molecular cloud gave energies of a few nK, which is evidence of a macroscopic molecular matter wave. 

The first step was the production of ultracold molecules from a quantum-degenerate Fermi gas of atoms at a temperature below 150 nK (Regal et al. 2003). The low binding energy of the molecules was controlled by detuning the magnetic field away from the Feshbach resonance. Clear evidence of diatomic molecules was achieved through direct, radio-frequency spectroscopic detection of molecules. 

It seems that these seminal experiments have marked only the very beginning of the progress of ultracold-matter physics, so that one can expect other remarkable discoveries to be made while this book is being published. 

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From laser-cooled and trapped atoms to atomic and molecular quantum gases... 

The most interesting implementations and applications of laser-induced photoassociation of ultracold atoms have emerged in experiments with quantum gases (BECs and Fermi-degenerate gases). These experiments made it possible to obtain and investigate molecular quantum gases. They are briefly discussed in Section 8.5. 

Herbig J, Kraemer T, Mark M, Weber T, Chin C, Nagerl H-C, Grimm R. (2003) Preparation of a pure molecular quantum gas. Science 301 1510-1513. 

The foundations of the modem tireory of elementary gas-phase reactions lie in the time-dependent molecular quantum dynamics and molecular scattering theory, which provides the link between time-dependent quantum dynamics and chemical kinetics (see also chapter A3.11). A brief outline of the steps hr the development is as follows [27],... 

When structural and dynamical information about the solvent molecules themselves is not of primary interest, the solute-solvent system may be made simpler by modeling the secondary subsystem as an infinite (usually isotropic) medium characterized by the same dielecttic constant as the bulk solvent, that is, a dielectric continuum. Theoretical interpretation of chemical reaction rates has a long history already. Until recently, however, only the chemical reactions of systems containing a few atoms in the gas phase could be studied using molecular quantum mechanics due to computational expense. Fortunately, very important advances have been made in the power of computer-simulation techniques for chemical reactions in the condensed phase, accompanied by an impressive progress in computer speed (Gonzalez-Lafont et al., 1996). 

The details were significant. In July 1924 Einstein read a paper before the Prussian Academy in which he applied the Bose statistical method to an ideal gas and drew an analogy between a quantum gas and a molecular gas. Over the following few months, Einstein wrote what Martin Klein has called another of his masterful works, which was published in January 1925. In this paper, Einstein predicted that the particles of an ideal quantum gas could collect together in the lowest energy state and form what is now called a Bose-Einstein condensate. At the time, physicists regarded Einstein s prediction as a curiosity with litde or no physical significance. 

The quantum gases (e.g., hydrogen, helium, and neon) do not conform to the same corresponding-states behavior as do normal fluids. Prausnitz, Lichtenthaler, and de Azevedo [Molecular Thermodynamics of Fluid-Phase Equilibria, 3d ed., pp. 172—173, Prentice-Hall PTR, Upper Saddle River, N.J. (1999)] propose the use of temperature-dependent effective critical parameters. For hydrogen, the quantum gas most commonly found in chemical prcxjessing, the recommended equations are... 

Molecular quantum chemistry and quantum mechanical simulation of solids have followed substantially independent paths and strategies for many years, with almost no reciprocal influence. In the implementation of computational schemes and formalisms, they started from different elementary models either the hydrogen or helium atom like, for example, the parameterization of a correlation functional based on accurate He atom calculations by Colle and Salvetti, or the electron gas, which is the reference system of the local density approximation "" (LDA) to density functional theory (DFT). Moreover, if we compare the simplest real crystals, like lithium metal or sodium chloride, with the smallest molecule, H2, the much greater complexity of the solid system is... 

A reader is probably interested in finding answers to the following questions What additional basic information is needed for proper use of periodic codes by a scientist with a molecular quantum chemistry background Are there features peculiar to the solid state, with no analogy to the gas phase In this chapter, we shall provide answers to these questions as well as provide a tutorial for the nonspecialist wanting to learn about solid state calculations. 

For simplicity consider a gas sample containing just three identical molecules. A quantum state of the whole system will be specified by saying how many moleciiles there are in each of the molecular quantum states, but without seeking to distinguish between these molecules, which is impossible. An expression for the probability of this state hets already been obtained in equation (11 42). For example, the probability that one molecule is the zeroth molecular quantum state, a second also in the zeroth, and the third in the ith is... 

The field of applications of molecular quantum dynamics covers broad areas of science not only in chemistry but also in physics and biology. Historically, due to the fact that the full quantum-mechanical simulation of molecular processes is limited to small systems, molecular quantum dynamics has given rise mainly to important applications of astrophysical and atmospheric relevance. In the interstellar medium or the Earth atmosphere, molecules are generally in the gas phase. Since many accurate spectroscopic data are available, these media have provided various prototype systems to study quantum effects in molecules and to calibrate the theoretical methods used to simulate these effects. In this context, it is not surprising that much theoretical effort is still directed toward modeling the full quantum-mechanical treatment of small molecules. Among others, one can cite the studies of the spectroscopy of water [159-161], and of the spectroscopy, photodissociation. 

Althorpe SC, Worth GA (2004) Collaborative computational project on molecular quantum dynamics (CCP6). Daresbury Laboratory, Daresbury... 

In order to consolidate the bases of theoretical treatments and understand clearly the effective limits of approximate models, molecular beam gas-phase experiments are an ideal choice to study molecular systems under well-controlled conditions [1]. They allow making a clear picture of isolated system properties and then introducing the perturbation due to the environment in a controlled way. Given the characteristics of the supersonic expansion, it is possible to obtain cold isolated molecules distributed in very few quantum states as well as complexes that are held together by weak interactions including clusters that are not stable under the usual static gas-cell... 

Leitner D M 1999 influence of quantum energy flow and localization on molecular isomerization in gas and condensed phases Int. J. Quant. Chem. 75 523-31... 

The scope of this section restricts the discussion. One omitted topic is the collision and interaction of molecules with surfaces (see [20, 21] and section A3.9). This topic coimects quantum molecular dynamics in gas and condensed phases. Depending on the time scales of the interaction of a molecule witli a surface, the... 

Singh, U.C., Kollman, P.A. A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems Applications to the CH3CI 4- Cl exchange reaction and gas phase protonation of polyethers. J. Comput. Chem. 7 (1986) 718-730. 

Singh U C and P A Kollman 1986. A Combined Ab Initio Quantum Mechanical and Molecule Mechanical Method for Carrying out Simulations on Complex Molecular Systems Applicatior to the CHsQ + Cr Exchange Reaction and Gas Phase Protonation of Polyethers. Journal Computational Chemistry 7 718-730. 

The molecular mechanics calculations discussed so far have been concerned with predictions of the possible equilibrium geometries of molecules in vacuo and at OK. Because of the classical treatment, there is no zero-point energy (which is a pure quantum-mechanical effect), and so the molecules are completely at rest at 0 K. There are therefore two problems that I have carefully avoided. First of all, I have not treated dynamical processes. Neither have I mentioned the effect of temperature, and for that matter, how do molecules know the temperature Secondly, very few scientists are interested in isolated molecules in the gas phase. Chemical reactions usually take place in solution and so we should ask how to tackle the solvent. We will pick up these problems in future chapters. 

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