Corrections to the Born-Oppenheimer Approximation in the Calculation of Isotope Effects on Equilibrium Constants

1975 ◽  
pp. 64-76 ◽  
Author(s):  
MAX WOLFSBERG ◽  
LAWRENCE I. KLEINMAN
Keyword(s):  
Isotope Effects ◽  
Equilibrium Constants ◽  
Oppenheimer Approximation

Isotope Effects on Chemical Equilibria. Part II. Some Further Secondary Isotope Effects of the Second Kind

1974 ◽  
Vol 52 (10) ◽  
pp. 1966-1972 ◽  
Author(s):  
Douglas James Barnes ◽  
Peter David Golding ◽  
John Marshall William Scott
Keyword(s):  
Isotope Effect ◽  
Dissociation Constants ◽  
Isotope Effects ◽  
Equilibrium Constants ◽  
Chemical Equilibria

The ratio of the dissociation constants Ka(H)/Ka(D) has been measured conductimetrically for the isotopic pairs XCH2COOH/XCD2COOH where X = Cl, PhO, and PhS. Methods of calculating the ratio of the equilibrium constants are considered in some detail. Since the isotope effect varies with the nature of the X substituent it is concluded that the simple inductive description of these effects is not tenable.

Full-dimensional analytical potential energy surface describing the gas-phase Cl + C2H6 reaction and kinetics study of rate constants and kinetic isotope effects

2018 ◽  
Vol 20 (6) ◽  
pp. 3925-3938 ◽  
Author(s):  
Cipriano Rangel ◽  
Joaquin Espinosa-Garcia
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Gas Phase ◽  
Energy Surface ◽  
Isotope Effects ◽  
Hydrogen Abstraction ◽  
System P ◽  
Abstraction Reaction ◽  
Analytical Potential ◽  
Oppenheimer Approximation

Within the Born–Oppenheimer approximation a full-dimensional analytical potential energy surface, PES-2017, was developed for the gas-phase hydrogen abstraction reaction between the chlorine atom and ethane, which is a nine body system.

Etude comparée des constantes moléculaires de HBr et de DBr : Application à la détermination des constantes moléculaires de TBr

1977 ◽  
Vol 55 (11) ◽  
pp. 1016-1024 ◽  
Author(s):  
P. Bernage ◽  
P. Niay
Keyword(s):  
Equilibrium Constants ◽  
Oppenheimer Approximation

In this paper, the adiabatic and non-adiabatic corrections to the Born–Oppenheimer approximation are numerically determined for Dunham's equilibrium constants Y10 and Y01 of H Br and DBr molecules.In the case of the Y20, Y11, and Y02 constants, only the adiabatic corrections are significant.The correct isotopic relations using these corrections allow the TBr equilibrium constants calculation from the HBr and DBr ones.

RKR-type inversion of the diatomic energy shifts due to breakdown of the Born–Oppenheimer approximation

2004 ◽  
Vol 82 (6) ◽  
pp. 820-825 ◽  
Author(s):  
James KG Watson
Keyword(s):  
Diatomic Molecule ◽  
Internuclear Distance ◽  
Diatomic Molecules ◽  
Isotope Effects ◽  
Electron Mass ◽  
Effective Hamiltonian ◽  
Expectation Values ◽  
Oppenheimer Approximation ◽  
Vibration Rotation

The principal effects of the breakdown of the Born–Oppenheimer approximation on the vibration–rotation energies of a diatomic molecule can be represented by the expectation values of terms to order (me/Mi) in the effective Hamiltonian, where me is the electron mass and Mi is the mass of atom i. This paper examines the possibility of inverting these expectation values to obtain the correction functions as functions of the internuclear distance r, using a generalization of the semiclassical Rydberg–Klein–Rees method. It is shown that the correction functions are not completely determinable from the inversion, and the form of the determinable combinations is obtained.Key words: diatomic molecules, vibration–rotation energies, isotope effects, Born–Oppenheimer breakdown, Rydberg–Klein–Rees method.

The nature of the transition state in diarylmethyl cation – nucleophile combination reactions as probed by secondary α-deuterium isotope effects

2001 ◽  
Vol 79 (12) ◽  
pp. 1887-1897
Author(s):  
Thuy Van Pham ◽  
Robert A McClelland
Keyword(s):  
Transition State ◽  
Isotope Effect ◽  
Rate Constant ◽  
Rate Constants ◽  
Flash Photolysis ◽  
Isotope Effects ◽  
Equilibrium Constants ◽  
Bond Formation ◽  
Kinetic Isotope ◽  
Rate Limiting

Transition-state structures for the carbocation–nucleophile combination reactions of (4-substituted-4'- methoxydiphenyl)methyl cations with water, chloride, and bromide ions in acetonitrile–water mixtures have been investigated by measuring the secondary α-deuterium kinetic and equilibrium isotope effects. Rate constants in the combination direction were measured with laser flash photolysis. Equilibrium constants were measured for the water reaction by a comparison method in moderately concentrated sulfuric acid solutions, for the bromide reaction via the observation of reversible combination, and for the chloride reaction from the ratio of the combination rate constant and the rate constant for the ionization of the diarylmethyl chloride product. The fraction of bond making in the transition state has been calculated as the ratio log (kinetic isotope effect):log (equilibrium isotope effect). For the water reaction, there is 50–65% bond making in the transition state; this is also true for cations that are many orders of magnitude less reactive. The same conclusions, 50–65% bond formation in the transition state independent of reactivity, have previously been made in correlations of log kw vs. log KR. Thus, two quite different measures of transition structure provide the same result. The kH:kD values for the halide combinations in 100% acetonitrile are within experimental error of unity. This is consistent with suggestions that these reactions are occurring with diffusional encounter as the rate-limiting step. Addition of water has a dramatic retarding effect on the halide reactions, with rate constants decreasing steadily with increased water content. Small inverse kinetic isotope effects are observed (in 20% acetonitrile:80% water) indicating that carbon—halogen bond formation is rate-limiting. Comparison of the kinetic and equilibrium isotope effects shows ~25 and ~40% bond formation in the transition states for the reactions with bromide and chloride, respectively.Key words: carbocation, isotope effect, transition state, halide.

SULPHUR ISOTOPE EFFECTS IN THE BISULPHITE ADDITION REACTION OF ALDEHYDES AND KETONES: I. EQUILIBRIUM EFFECT AND THE STRUCTURE OF THE ADDITION PRODUCT

1954 ◽  
Vol 32 (1) ◽  
pp. 4-13 ◽  
Author(s):  
W. A. Sheppard ◽  
A. N. Bourns
Keyword(s):  
Isotopic Exchange ◽  
Addition Reaction ◽  
Isotope Effects ◽  
Equilibrium Constants ◽  
Addition Product ◽  
Sulphur Isotope ◽  
Isotopic Exchange Reaction ◽  
Small Constant ◽  
Aldehydes And Ketones ◽  
Equilibrium Effect

Equilibrium constants for the isotopic exchange reaction between bisulphite ion and the addition product of eight aldehydes and ketones have been measured.[Formula: see text]At 25 °C., values ranging from 1.021 for acetone to 1.010 for anisaldehyde have been observed. Since constants of this magnitude are to be expected only if the bonding of the sulphur atom is different in the bisulphite ion and the addition product, these results are considered to confirm the carbon-sulphur bond structure of the latter. This conclusion is supported by the small constant, 1.002, obtained for the diethyl sulphate and ethyl hydrogen sulphate isotopic exchange in which the bonding of sulphur is essentially the same in the two reacting species.

The proton transfer reaction between bis(2,4-dinitrophenyl)methane and nitrogen bases in dimethyl sulfoxide and toluene solvents

1991 ◽  
Vol 69 (3) ◽  
pp. 468-473 ◽  
Author(s):  
Arnold Jarczewski ◽  
Grzegorz Schroeder ◽  
Kenneth T. Leffek
Keyword(s):  
Proton Transfer ◽  
Dimethyl Sulfoxide ◽  
Isotope Effects ◽  
Equilibrium Constants ◽  
Activation Parameters ◽  
Kinetic Isotope Effects ◽  
Proton Transfer Reaction ◽  
Kinetic Isotope ◽  
Deuteron Transfer ◽  
Classical Region

Rate constants have been measured for the proton and deuteron transfer reactions of bis(2,4-dinitrophenyl)methane (1) with 1,1,3,3-tetramethylguanidine (TMG) and 1,5-diazabicyclo[5.4.0]undec-7-ene (DBU) in dimethyl sulfoxide (DMSO) and toluene solvents. Equilibrium constants, primary deuterium kinetic isotope effects, and activation parameters are reported. The reaction of 1 with DBU is faster than that with TMG by factors of 5 and 50 in toluene and DMSO respectively. The primary deuterium kinetic isotope effects, kH/kD = 7–9, which are independent of the polarity of the solvent, indicate an uncoupled mechanism of proton transfer and are in the "classical" region with little or no indication of a tunnelling contribution to the enthalpy of activation for these reactions. Key words: proton transfer, bis(2,4-dinitrophenyl)methane, deuterium isotope effects.

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