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E. Bright Wilson

Bio: E. Bright Wilson is an academic researcher from Harvard University. The author has contributed to research in topics: Rotational spectroscopy & Dipole. The author has an hindex of 47, co-authored 124 publications receiving 8600 citations.


Papers
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Journal ArticleDOI
TL;DR: In this article, a general rule for writing down the coefficients of the transformation to symmetry coordinates is derived together with a method of obtaining the kinetic energy reciprocal matrix (G) in terms of symmetry coordinates with a minimum of algebra.
Abstract: Developments which reduce the labor of calculating the vibration frequencies of complex molecules are described. In particular a vectorial scheme is given for obtaining the reciprocal of the matrix of the kinetic energy in terms of valence‐type coordinates. A general rule for writing down the coefficients of the transformation to symmetry coordinates is derived together with a method of obtaining the kinetic energy reciprocal matrix (G) in terms of symmetry coordinates with a minimum of algebra. A treatment of redundant coordinates is developed. In addition, reduction of the secular equation by the splitting out of high frequencies, a new type of isotope product rule, and the determination of normal coordinates are discussed. The molecule CH3Cl is worked out as an illustration.

685 citations

Journal ArticleDOI
TL;DR: In this paper, a method for obtaining the secular equation for the vibration frequencies of a molecule directly in expanded form, i.e. as an algebraic rather than a determinantal equation, is described.
Abstract: A method is described for obtaining the secular equation for the vibration frequencies of a molecule directly in expanded form, i.e. as an algebraic rather than a determinantal equation. The force constants occur literally and the masses may occur either literally or numerically, as desired. The symmetry may be employed as usual to factor the secular equation. Several methods of obtaining approximate roots are described for which the expanded form is particularly suitable. Finally, an example, the nonlinear general triatomic molecule, is worked out algebraically.

651 citations

Book
01 Jan 1952

360 citations

Journal ArticleDOI
TL;DR: In this article, a perturbation method is introduced which permits the change of moment of inertia with vibration, the coupling of rotation and vibration, and the centrifugal stretching effects to be taken into account.
Abstract: The exact classical kinetic energy for a system of point masses is obtained. From this the correct form for the quantum‐mechanical Hamiltonian operator is derived. If the assumption of small vibrations is applied to this operator, the familiar approximation of a rigid top plus normal coordinate vibrator is obtained. In order to secure better approximations, in which larger amplitudes of vibration are admitted, a perturbation method is introduced which permits the change of moment of inertia with vibration, the coupling of rotation and vibration, and the centrifugal stretching effects to be taken into account. If the stretching terms alone are neglected, it is possible to reduce the secular equation for the rotational energy levels to the Wang form, except that ``effective moments of inertia'' must be used whose magnitude depends on the vibrational quantum state. The relation of these quantities to the equilibrium moments of inertia or to the instantaneous moments of inertia averaged over the vibrational motion is not simple, although the numerical deviation from them may not be great. In addition, for molecules with less than orthorhombic symmetry there is the further possibility that the orientation of the principal axes of inertia will vary with the vibrational quantum number. It is also pointed out that the Wang equation should not fit the data when a nearby vibrational state perturbs the state under examination or when the centrifugal effects are large. A method is indicated whereby the latter terms may in principle be calculated.

356 citations

Journal ArticleDOI
TL;DR: In this paper, the rotational energy of a nonrigid asymmetric rotor was derived for the first order treatment of a first-order treatment and the relation W = W0+A1W02+A2W0J(J+1)+A3J2(J + 1)2+A4J(j+1)
Abstract: A first‐order treatment yields the relation W=W0+A1W02+A2W0J(J+1)+A3J2(J+1)2+A4J(J+1)〈Pz2〉+A5〈Pz4〉+A6W0〈Pz2〉 for the rotational energy W of a nonrigid asymmetric rotor. The A's are constants independent of the rotational quantum numbers (J, K−1, K+1) while W0 is the rigid‐rotor energy. Pz is the operator for the component of angular momentum along the axis of quantization. Formulas are given for 〈Pz2〉 and 〈Pz4〉, based on continued fractions, as well as expansions useful for nearly symmetric cases. As a special case, the corrections are derived for transitions between the components of asymmetry doublets.

335 citations


Cited by
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Journal ArticleDOI
TL;DR: The new HITRAN is greatly extended in terms of accuracy, spectral coverage, additional absorption phenomena, added line-shape formalisms, and validity, and molecules, isotopologues, and perturbing gases have been added that address the issues of atmospheres beyond the Earth.
Abstract: This paper describes the contents of the 2016 edition of the HITRAN molecular spectroscopic compilation. The new edition replaces the previous HITRAN edition of 2012 and its updates during the intervening years. The HITRAN molecular absorption compilation is composed of five major components: the traditional line-by-line spectroscopic parameters required for high-resolution radiative-transfer codes, infrared absorption cross-sections for molecules not yet amenable to representation in a line-by-line form, collision-induced absorption data, aerosol indices of refraction, and general tables such as partition sums that apply globally to the data. The new HITRAN is greatly extended in terms of accuracy, spectral coverage, additional absorption phenomena, added line-shape formalisms, and validity. Moreover, molecules, isotopologues, and perturbing gases have been added that address the issues of atmospheres beyond the Earth. Of considerable note, experimental IR cross-sections for almost 300 additional molecules important in different areas of atmospheric science have been added to the database. The compilation can be accessed through www.hitran.org. Most of the HITRAN data have now been cast into an underlying relational database structure that offers many advantages over the long-standing sequential text-based structure. The new structure empowers the user in many ways. It enables the incorporation of an extended set of fundamental parameters per transition, sophisticated line-shape formalisms, easy user-defined output formats, and very convenient searching, filtering, and plotting of data. A powerful application programming interface making use of structured query language (SQL) features for higher-level applications of HITRAN is also provided.

7,638 citations

Journal ArticleDOI
David R. Janero1
TL;DR: The conclusion is reached that MDA determination and the TBA test can offer, at best, a narrow and somewhat empirical window on the complex process of lipid peroxidation.

2,540 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that if the total electronic state of orbital and spin motion is degenerate, then a non-linear configuration of the molecule will be unstable unless the degeneracy is the special twofold one (discussed by Kramers 1930) which can occur only when the molecule contains an odd number of electrons.
Abstract: In a previous paper (Jahn and Teller 1937) the following theorem was established: A configuration of a polyatomic molecule for an electronic state having orbital degeneracy cannot be stable with respect to all displacements of the nuclei unless in the original configuration the nuclei all lie on a straight line. The proof given of this theorem took no account of the electronic spin, and in the present paper the justification of this is investigated. An extension of the theorem to cover additional degeneracy arising from the spin is established, which shows that if the total electronic state of orbital and spin motion is degenerate, then a non-linear configuration of the molecule will be unstable unless the degeneracy is the special twofold one (discussed by Kramers 1930) which can occur only when the molecule contains an odd number of electrons. The additional instability caused by the spin degeneracy alone, however, is shown to be very small and its effect for all practical purposes negligible. The possibility of spin forces stabilizing a non-linear configuration which is unstable owing to orbital degeneracy is also investigated, and it is shown that this is not possible except perhaps for molecules containing heavy atoms for which the spin forces are large. Thus whilst a symmetrical nuclear configuration in a degenerate orbital state might under exceptional circumstances be rendered stable by spin forces, it is not possible for the spin-orbit interaction to cause instability of an orbitally stable state. 1—General theorem for molecules with spin Just as before we must see how the symmetry of the molecular framework determines whether the energy of a degenerate electronic state with spin depends linearly upon nuclear displacements. This is again determined by the existence of non-vanishing perturbation matrix elements which are linear in the nuclear displacements. These matrix elements are integrals involving the electronic wave functions with spin and the nuclear dis­placements, and we deduce as before from their transformation properties whether for a given molecular symmetry they can be different from zero.

2,539 citations

Journal ArticleDOI
TL;DR: In this article, it is suggested that force constants should be calculated by differentiating the forces numerically, which is numerically more accurate and requires less computation than the customary one of differentiating energy numerically twice.
Abstract: The general expression for the exact forces on the nuclei (negative derivatives of the total energy with respect to the nuclear coordinates) is applied for Hartree-Fock wavefunctions. It is suggested that force constants should be calculated by differentiating the forces numerically. This method, called the force method, is numerically more accurate and requires less computation than the customary one of differentiating the energy numerically twice. It permits the quick determination of the equilibrium geometry by relaxing the nuclear coordinates until the forces vanish. The unreliability of the methods using the Hellmann-Feynman forces is re-emphasized. The question of which force constants can be best calculated ab initio is discussed.

2,106 citations