Accurate evaluation of internal energy level sums and densities including anharmonic oscillators and hindered rotors

Abstract

The calculation of molecular energy level sums and densities is necessary for the treatment of many physical and chemical problems including reaction rates. An extension of Beyer and Swinehart's algorithm for directly computing harmonic oscillator eigenstate sums and densities is described. With this new algorithm it is possible to compute exact or near-exact energy level sums and densities for degrees of freedom such as free and hindered rotors and anharmonic oscillators so long as the energy levels for each degree of freedom can be specified. Computer calculation by this technique is practical even for large molecules up to all chemically interesting energies and error is confined to small rounding errors. Results by this algorithm are compared to values of energy level sums that have been given in the literature by various alternative approximate treatments and permit more rigorous testing of the latter and assessment of the approximations involved.

Photodissociation of benzene under collision-free conditions: An ab initio/Rice–Ramsperger–Kassel–Marcus study

“…We used the harmonic approximation to calculate the total number and density of states employing the direct count method. 36 In the calculations of the number of states for transition states we incorporated tunneling corrections using Miller's scheme where the shape of the barrier is approximated either by parabolic or Eckart potential. 37 For the radical product channels, such as C 6 H 5 ϩH, C 3 H 3 ϩC 3 H 3 , C 5 H 3 ϩCH 3 , or C 4 H 3 ϩC 2 H 3 , normally, no distinct transition state exists on the PES for the last reaction step, as it is a simple bond cleavage process.…”

Sodium Cation Affinities of Commonly Used MALDI Matrices Determined by Guided Ion Beam Tandem Mass Spectrometry

“…The relative reactivity of all ro-vibrational states, as reflected by σ 0 and n, is assumed to be equivalent. The Beyer-Swinehart algorithm [69][70][71] is used to evaluate the density of the ro-vibrational states and the relative populations, g i , are calculated for a MaxwellBoltzmann distribution at 298 K, the internal temperature of the reactants. The average internal energy of the groundstate conformations of the neutral MALDI matrices and Na + (MALDI) complexes are also included in the Supplementary Information, Table 1S.…”

On the time scale of internal energy relaxation of AP-MALDI and nano-ESI Ions in a quadrupole ion trap

“…The referenced study described the vibrational relaxation of N 2 ϩ· through collisions with a variety of noble gases, in which the cooling process with He was least efficient [15]. However, it would be an over-simplification to assume that the collision induced vibrational relaxation behavior of N 2 ϩ· , which has one vibrational degree of freedom and a vibrational density of states of 1 per cm Ϫ1 at room temperature, could be used as an accurate predictor of the collision induced vibrational relaxation behavior of a medium sized peptide such as leucine enkephalin (YGGFL), which has 228 degrees of freedom and a vibrational density of states of 3.4 ϫ 10 36 per cm Ϫ1 at room temperature, calculated with the direct count method [16] As our group has an interest in the mechanisms and kinetics of internal energy-transfer processes in mass spectrometry experiments, the study described here undertakes a re-examination of the cited work.…”