Rotational partition functions for symmetric-top molecules

Journal Article · Wed Aug 15 00:00:00 EDT 1990 · Journal of Chemical Physics; (USA)

DOI:https://doi.org/10.1063/1.458865· OSTI ID:6547593

McDowell, R S ^[1]

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1. University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (USA)

A simple, accurate closed-form expression for the rotational partition functions of symmetric-top molecules is derived, which includes the effects of nuclear-spin statistics (significant at very low temperatures), quartic and sextic centrifugal distortion terms (moderate and high temperatures), and inversion (all temperatures): {ital Q}{sub {ital r}}{congruent}{sigma}*({pi}{ital m}){sup {1/2}} exp({beta}(4{minus}m)/12){beta}{sup {minus}3/2}(1+{beta}{sup 2}(1{minus}{ital m}){sup 2}/90+{center dot}{center dot}{center dot})(1+{delta}) (1+{rho}{sub 1}{beta}{sup {minus}1}+{rho}{sub 2}{beta}{sup {minus}2}+{rho}{sub 3}{beta}{sup {minus}3}), where {beta}{equivalent to}{ital hcB}/{ital kT}, {ital m}{equivalent to}{ital B}/{ital A} for prolate tops or {ital B}/{ital C} for oblate tops ({ital A}{gt}{ital B}{gt}{ital C} are the rotational constants), and {sigma}*{equivalent to}{Pi}{sub {ital i}}(2{ital I}{sub {ital i}}+1)/{sigma}, where {ital I}{sub {ital i}} is the spin of nucleus {ital i} and {sigma} is the classical symmetry number. For {ital C}{sub 3{ital v}}{ital XY}{sub 3} and {ital WXY}{sub 3} molecules, the low-temperature nuclear-spin correction is {delta}{approx}2(2{ital I}{sub {ital Y}}+1){sup {minus}2} exp({pi}{sup 2}{ital m}({beta}{ital m}{minus}6)/54{beta}); similar expressions are given for other molecular models. The {rho}'s are functions of the centrifugal distortion constants {ital D}{sub {ital J}}, {ital D}{sub {ital JK}}, {ital D}{sub {ital K}}, {ital H}{sub {ital J}}, etc. If inversion doubling occurs, with a splitting {Delta}{ital G} in the ground vibrational state, this expression for {ital Q}{sub {ital r}} is to be multiplied by (1{minus}{beta}{Delta}{ital G}/2{ital B}+{center dot}{center dot}{center dot}).

• OSTI ID: 6547593
• Journal Information: Journal of Chemical Physics; (USA), Vol. 93:4; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
36 MATERIALS SCIENCE
ALLENE
PARTITION FUNCTIONS
AMMONIA
METHANE
DEUTERIUM COMPOUNDS
HIGH TEMPERATURE
LOW TEMPERATURE
MEDIUM TEMPERATURE
MOLECULAR STRUCTURE
ROTATIONAL STATES
ULTRALOW TEMPERATURE
VERY HIGH TEMPERATURE
VERY LOW TEMPERATURE
ALKANES
DIENES
ENERGY LEVELS
EXCITED STATES
FUNCTIONS
HYDRIDES
HYDROCARBONS
HYDROGEN COMPOUNDS
NITROGEN COMPOUNDS
NITROGEN HYDRIDES
ORGANIC COMPOUNDS
POLYENES
400201* - Chemical & Physicochemical Properties
360603 - Materials- Properties