Comparison of the anharmonicity correction to ρ for CH4 computed using Cartesian normal-mode and z-matrix coordinates.
(a) Relative standard deviation and (b) relative maximum error for W at three energies: 10 000 cm−1, 15 000 cm−1, and 20 000 cm−1 using both coordinate systems. Each point on the plot corresponds to the convergence metrics evaluated for one of the three energies using the specified coordinate system and for some value of M. The solid curves are the best fits of the data points to the form a · M b .
(a) One-dimensional state density for the H2C–C–H vibration for two choices of the bending coordinate and the harmonic approximation to it. The energy of the barrier between the two equivalent minima is shown as the pink vertical line. (b) The potential energy curves along two coordinates.
(a) Relative standard deviation and (b) relative maximum error for W at two energies, 5000 cm−1 and 10 000 cm−1, using both coordinate systems. The solid curves are the best fits of the data points to the form a · M −0.5.
Anharmonicity corrections to the (a) density of states and (b) partition function for the vinyl radical.
Comparison of vibrational partition functions obtained using the harmonic approximation, the Pitzer-Gwinn8 corrected harmonic partition function, and VCI. Results above 1500 K are not shown for VCI because it became difficult to converge sufficient vibrational states at high enough energies to converge Q.
Comparison of partition functions calculated with and without the inclusion of coupling between vibrations and rotations. All partition functions are calculated classically and numbers in square brackets correspond to powers of ten. The columns, respectively, are: the purely vibrational harmonic oscillator partition function, Q vib,har; the purely vibrational anharmonic sampled partition function, Q vib,anh; the rovibrational partition function using the harmonic vibrations and the rigid rotor approximation, Q rovib,anh–rr; the rovibrational partition function using the anharmonic sampled vibrations and the rigid rotor approximation, Q rovib,anh–rr; and the rovibrational partition function computed fully using the sampling algorithm, Q rovib,anh. The anharmonicity corrections are defined as f vib = Q vib,anh/Q vib,har, f rot = Q rovib,anh/Q rovib,anh–rr, and f rovib = Q rovib,anh/Q rovib,har–rr.
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