### Molecular Chemistry and Molecular Physics

DrClaude Mentor. Buffu said:. One more thing I don't understand is why we multiply degrees of freedom with gas constant? DrClaude said:.

Mapes Science Advisor. Gold Member. Contrary to what many introductory textbooks report, the specific heat of a gas is not a constant but rather depends strongly on temperature. Certain degrees of freedom can be "frozen out" at temperatures below a certain threshold and therefore cease to contribute to the count. This is one possible reason why the single value given in your book is less than expected. I find it mildly fascinating that so many educational materials present a single temperature-independent value for the heat capacity of gases and rarely add the caveat "if the modes described here are fully excited".

By similar simplified arguments, you could instruct students that the molar heat capacity of all condensed elements is 3R, for example, and this isn't a bad rule of thumb. But I've never seen this. A diatomic molecule may translate 3 rotate end-over-end 1 , and vibrate lengthwise 1 for 5dof. What I am suggesting is to look through the 7dof as they are reasoned out in the text, or online materials, and compare that reasoning, in detail, with how you got Then you can better approach why they left out some dof that you included.

That sounds about right - you get now what I was saying about how you count the degrees of freedom? The diatomic molecule has 3 translational dof even though there are 2 atoms, because the atoms are not free to be anywhere they like in relation to each other Ok I found a resource where it is stated that triatomic molecule have 7 dof.

Reasoning is this :- Like a diatomic molecule, a linear triatomic molecule has three translational and only two accessible rotational degrees of freedom There are two degrees of freedom for vibrational energy accessible at lower temperatures. Is this correct? Chestermiller Mentor. Insights Author. I don't think so.

## Symmetry of Polyatomic Molecular Orbitals

The best way to solve it is to look at actual data. The high-T limit is about 6. So yes, around room T, CO 2 has an effective 7 quadratic dofs, but I would still argue that you can't get that value from theoretical reasoning. Lets ask Chestermiller what he thinks about this. The method presented is generally suitable for molecules of significant size and complexity, as illustrated by several examples of molecules up to six atoms.

The polyad quantum number technique is very useful for assembling comprehensive basis sets for the matrix representation of the Hamiltonian after removal of all non-resonance terms by CVPT. In addition, the classification of anharmonic energy levels according to their polyad quantum numbers provides an additional means for the interpretation of observed vibrational spectra.

## Symmetry of Polyatomic Molecular Orbitals

Carbon dioxide has been produced from the impact of a monoenergetic O P-3 beam upon a surface cooled to 4. Using temperature-programmed desorption and mass spectrometer detection, we have detected increasing amounts of CO2 formation with O P-3 energies of 2, 5, 10, and 14 eV. This is the first measurement of polyatomic molecule formation on a surface with superthermal atoms.

The goal of this work is to detect other polyatomic species, such as CH3OH, which can be formed under conditions that simulate the grain temperature, surface coverage, and superthermal atoms present in shock-heated circumstellar and interstellar regions. Conventional photochemical experiments give no information about the partitioning of energy between translational recoil and internal excitation of the fragment molecules formed in photodissociation of a polyatomic molecule. In a molecular beam experiment, it becomes possible to determine the energy partition from the form of the laboratory angular distribution of one of the photodissociation products.

A general kinematic analysis is worked out in detail, and the uncertainty introduced by the finite angular resolution of the apparatus and the velocity spread in the parent beam is examined.

The experimental requirements are evaluated for he photolysis of methyl iodide by the angstrom Hg line. Final Report. This report describes research on the theory of isotope separation produced by the illumination of polyatomic molecules by intense infrared laser radiation.

## String-like model for linear polyatomic molecules and polymers

This potential gives the correct symmetry of the molecule , the equilibrium configuration, the frequencies of the six distinct normal modes of oscillation and the correct or assumed value of the total potential energy of the molecule. Other conditions can easily be imposed in order to obtain a more refined potential energy function, for example, by making allowance for anharmonicity data.

A suitable expression was also obtained for the interaction energy between a laser field and the polyatomic molecule. The electromagnetic field is treated classically, and it would be easily possible to treat the cases of time dependent pulses, frequency modulation and noise. Benchmark quality total atomization energies of small polyatomic molecules. Sensitivity and resolution in frequency comb spectroscopy of buffer gas cooled polyatomic molecules. We discuss the use of cavity-enhanced direct frequency comb spectroscopy in the mid-infrared region with buffer gas cooling of polyatomic molecules for high-precision rovibrational absorption spectroscopy.

A frequency comb coupled to an optical enhancement cavity allows us to collect high-resolution, broad-bandwidth infrared spectra of translationally and rotationally cold K gas-phase molecules with high absorption sensitivity and fast acquisition times. The design and performance of the combined apparatus are discussed in detail.

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An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion. We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame.

It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule , which is suitable for developing a general program to study the spectra of many polyatomic systems. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates.

A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles.

Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results. We present a simple method for control of ro-vibrational populations in polyatomic molecules in the presence of inhomogeneous electric fields [1]. Cooling and trapping of heavy polar polyatomic molecules has become one of the frontier goals in high-resolution molecular spectroscopy, especially in the context of parity violation measurement in chiral compounds [2].

A key step toward reaching this goal would be development of a robust and efficient protocol for control of populations of ro-vibrational states in polyatomic , often floppy molecules. Here we demonstrate a modification of the stark-chirped rapid-adiabatic-passage technique SCRAP [3], designed for achieving high levels of control of ro-vibrational populations over a selected region in space. The new method employs inhomogeneous electric fields to generate space- and time- controlled Stark-shifts of energy levels in molecules.

Adiabatic passage between ro-vibrational states is enabled by the pump pulse, which raises the value of the Rabi frequency. This Stark-chirped population transfer can be used in manipulation of population differences between high-field-seeking and low-field-seeking states of molecules in the Stark decelerator [4].

Appropriate timing of voltages on electric rods located along the decelerator combined with a single pump laser renders our method as potentially more efficient than traditional Stark decelerator techniques. At the same time a high phase-space acceptance of the molecular packet is maintained. Zak, A. Yachmenev submitted. Medcraft, R. Wolf, M.

Schnell, Angew. Oberst, H. Munch, T. Halfman, PRL 99, Wohlfart, F. Filsinger, H. Haak, G. Meijer, J. A 77, R Bethlem, F. Crompvoets, R. Jongma, S. A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules. An analytic method to evaluate nuclear contributions to electrical properties of polyatomic molecules is presented. Such contributions control changes induced by an electric field on equilibrium geometry nuclear relaxation contribution and vibrational motion vibrational contribution of a molecular system.

Expressions to compute the nuclear contributions have been derived from a power series expansion of the potential energy. These contributions to the electrical properties are given in terms of energy derivatives with respect to normal coordinates, electric field intensity or both. Only one calculation of such derivatives at the field-free equilibrium geometry is required.

The results obtained are compared with previous theoretical calculations and with experimental values. Femtosecond response of polyatomic molecules to ultra-intense hard X-rays.

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