The Kinetics of the Anation Reaction of Aquopentaamminerhodium(III) lon by Oxalate in Aqueous Acidic Solution

The anation reaction of aquopentaamminerhodium(III) by oxalate has been studied in the temperature range 51–69°C and acidity range 0 ≤ pH ≤ 4.5 for oxalate concentrations up to 0.25 M and at ionic strength 1.0 M. The kinetic results provide evidence for the formation of an ion-pair between the complex ion and HC₂O(Q₁) and C₂O₄^2?(Q₂), where Q₁ = 2.3 M^?1 and Q₂ = 8.1 M^?1 at 60°C, but no evidence for an ion-pair with H₂C₂O₄ exists. The values of the rate constants at 60°C for anation by H₂C₂O₄, HC₂O and C₂O₄^2? are k₀ = 1.5 · 10^?4 M^?1 sec^?1, k₁ = 1.4 · 10^?4 sec^?1 and k₂ = 1.2 · 10^?4 sec^?1. The corresponding values for ΔH≠ and ΔS≠ are reported and the results discussed with reference to analogous reactions of Rh(III) and Co(III).     

Aquation of chloropentaamminecobalt(III) Perchlorate in chloride-ion containing water–nonaqueous solvent mixtures

The equilibrium quotients for the formation of Co(NH₃)₅Cl²⁺ from Co(NH₃)₅OH₂³⁺ and Cl^? were 3.74±0.25 M^?1 and 6.07±0.54 M^?1 at 45.0°C in 10:1 mole ratio water: dimethyl sulfoxide and in 25 w/w % aqueous ethanol, respectively, and those forthe formation of the ion pair Co(NH₃)₅OH₂³⁺ . Cl^? were 1.21±0.20 M^?1 and 1.58±0.17 M^?1, respectively, in the same solvents. The aquation and anation rateconstants were determined at 45.0°C for these two solvents over the range of chloride-ion concentrations 0.0 ≤ [Cl^?] ≤ 0.9 M. The aquation rate constant was essentially independent of chloride-ion concentration in each solvent over this range. The inverse of the pseudo-first-order anation rate constant was linearly dependent on the inverse of the chloride-ion concentration in each solvent. The least squares relationships between (1/k_an) and (1/[Cl^?]) gave intercepts and ratios of intercept to slope which were analyzed interms of I_d and D mechanisms. It was concluded that the data were not satisfied by a D mechanism, but that they were consistent with an I_d mechanism.     

Solvation of ligandopentaamminecobalt (III) complexes in dimethyl sulfoxide–water mixtures

The rate constants for the replacement of water from the inner-coordination shell of Co(NH₃)₅OH₂³⁺, I, by dimethyl sulfoxide (DMSO) as DMSO gradually replaced water in the solvation shell of I were found to approach, and finally equal, the water-exchange rate constant of I in aqueous media in accordance with expectation for a dissociative mechanism. Also the rate constants for the replacement of DMSO from the innercoordination shell of Co(NH₃)₅DMSO³⁺, II, by water as water replaced DMSO in the solvation shell of II were found to approach, and approximately equal, the DMSO-exchange rate constant for II in liquid DMSO in accordance with expectation for a dissociative mechanism. The DMSO-exchange rate constant for II in liquid DMSO was determined and found to be equal to (3.6 ± 0.8) × 10^?4 sec^?1 at 45°C. The dissociation quotient, [II] [NO₃^?]/[Co(NH₃)₅NO₃²⁺], was found to be equal to 0.28 ± 0.11 M at 45°C by NMR methods. The pseudo first-order rate constants for anation of II by NO₃^? and the solvation of Co(NH₃)₅NO₃ ²⁺ by DMSO were determined at various temperatures.     

KINETICS OF FORMATION AND STABILITY CONSTANTS OF MONO AND BIS l-TYROSINE COMPLEXES OF Cu(II), Co(II), AND Ni(II)

Abstract

The kinetics and stability constants of l-tyrosine complexation with copper(II), cobalt(II) and nickel(II) have been studied in aqueous solution at 25° and ionic strength 0.1 M. The reactions are of the type M(HL)^(3-n)+ _n-1 + HL- ? M(HL)^(2-n)+_n(k_n, forward rate constant; k_-n, reverse rate constant); where M=Cu, Co or Ni, HL^? refers to the anionic form of the ligand in which the hydroxyl group is protonated, and n=1 or 2. The stability constants (K_n=k_n/k_-n) of the mono and bis complexes of Cu²⁺, Co²⁺ and Ni²⁺ with l-tyrosine, determined by potentiometric pH titration are: Cu²⁺, log K₁=7.90 ± 0.02, log K₂=7.27 ± 0.03; Co²⁺, log K₁=4.05 ± 0.02, log K₂=3.78 ± 0.04; Ni²⁺, log K₁=5.14 ± 0.02, log K₂=4.41 ± 0.01. Kinetic measurements were made using the temperature-jump relaxation technique. The rate constants are: Cu²⁺, k₁=(1.1 ± 0.1) × 10⁹ M ^?1 sec^?1, k_-1=(14 ± 3) sec^?1, k₂=(3.1 ± 0.6) × 10⁸ M ^?1 sec^?1, k^?2=(16 ± 4) sec^?1; Co²⁺, k₁=(1.3 ± 0.2) × 10⁶ M ^?1 sec^?1, k_-1=(1.1 ± 0.2) × 10² sec^?1, k₂=(1.5 ± 0.2) × 10⁶ M ^?1 sec^?1, k_-2=(2.5 ± 0.6) × 10² sec^?1; Ni²⁺, k₁=(1.4 ± 0.2) × 10⁴ M ^?1 sec^?1, k_-1=(0.10 ± 0.02) sec^?1, k₂=(2.4 ± 0.3) × 10⁴ M ^?1 sec^?1, k_-2=(0.94 ± 0.17) sec^?1. It is concluded that l-tyrosine substitution reactions are normal. The presence of the phenyl hydroxyl group in l-tyrosine has no primary detectable influence on the forward rate constant, while its influence on the reverse rate constant is partially attributed to substituent effects on the basicity of the amine terminus.     

Kinetics of the Reductions of (Ethylenediaminetetraacetato)cobaltate(III) by 4,4-Dipyridylamine Complexes of Pentacyanoferrate(II) and Pentaammineruthenium(II)

The reactions of Fe(CN)₅dpa^3? and Ru(NH₃)₅dpa²⁺ (dpa = 4,4′-dipyridylamine) with Co(edta)^? have been investigated kinetically. For Fe(CN)₅dpa^3? complex, a linear relationship was observed between the pseudo-First-order rate constants and the concentrations of Co(edta) which leads to a specific rate 0.876 ± 0.006 M^?1S^?1 at T = 25°C., μ = 0.10 M and pH = 8.0. For the Ru(NH₃)₅dpa²⁺ system, the plots k_obs vs [Co(edta)^?] become nonlinear at concentrations of Co(edta) greater than 0.01 M and the reaction is interpreted on the basis of a mechanism involving the formation of an ion pair between Ru(NH₃)₅dpa²⁺ and Co(edta)^? followed by electron transfer from Ru(II) to Co(III). The nonlinear least squares fit of the kinetic results shows that Q_ip = 10.6 ± 0.7 M^?1 and k_et = 93.9 ± 0.7 s^?1 at pH = 8.0,μ = 0.10 M and T = 25°C.     

The relaxation spectra of nickel(II) and cobalt(II) arginine complexes

The temperature-jump method has been used to determine the nickel(II)- and cobalt(II)-arginine complexation kinetics. In the pH range studied, the neutral form of the ligand, HL, is the attacking, as well as the complexed, ligand species. The reactions reported on are of the type where n = 1, 2, 3 and M is Ni or Co. At 25° and ionic strength 0.1M the association rate constants are: for nickel(II) k₁ = 2.3 × 10³(±20%), k₂ = 2.4 × 10⁴(±20%), k₃ = 3.5 × 10⁴(±40%) M^?1 sec^?1; for cobalt(II) k₁ = 1.5 × 10⁵(±20%), k₂ = 8.7 × 10⁵(±20%), k₃ = 2.0 × 10⁵(±40%) M^?1 sec^?1. Arginine binds to metal ions less well than homologous chelating agents due to the electrostatic repulsion arising from the positively charged terminus of the zwitterion. Kinetically, the effect appears in the association rate constants with nickel reactions more strongly influenced than cobalt.     

An absolute measurement of the rate constant for ethyl radical combination

An absolute value of k_r of ethyl radicals at 860 ± 17°K of 4.5 × 10⁹ M^?1·sec^?1 was determined under VLPP conditions, where the value of k_r/k_r^∞ should be about 1/2. Thus k_r^∞(M^?1·sec^?1) ～ 10¹⁰ at 860°K. An error of as much as a factor of 2 in k_r would be surprising, but possible. The value of 10¹⁰M^?1·sec^?1 seems to be a factor of from 2 to 5 too high to be compatible with extensive data on the reverse reaction and the accepted thermochemistry. Changes in the heat of formation and entropy of the ethyl radical can change the situation somewhat, but even these changes when applied to the work of Hiatt and Benson [3] indicate that ethyl combination should be ～ 10^9.3 M^?1·sec^?1. More work is necessary if a better value is desired.     

The reaction of OH with NO2 and the deactivation of O(1D) by CO

NO₂ was photolyzed with 2288 Å radiation at 300° and 423°K in the presence of H₂O, CO, and in some cases excess He. The photolysis produces O(¹D) atoms which react with H₂O to give HO radicals or are deactivated by CO to O(³P) atoms The ratio k₅/k₃ is temperature dependent, being 0.33 at 300°K and 0.60 at 423°K. From these two points, the Arrhenius expression is estimated to be k₅/k₃ = 2.6 exp(?1200/RT) where R is in cal/mole – °K. The OH radical is either removed by NO₂ or reacts with CO The ratio k₂/k^α is 0.019 at 300°K and 0.027 at 423°K, and the ratio k₂/k⁰ is 1.65 × 10^?5M at 300°K and 2.84 × 10^?5M at 423°K, with H₂O as the chaperone gas, where k^α = k₁ in the high-pressure limit and k⁰[M] = k₁ in the low-pressure limit. When combined with the value of k₂ = 4.2 × 10⁸ exp(?1100/RT) M^?1sec^?1, k^α = 6.3 × 10⁹ exp (?340/RT)M^?1sec^?1 and k⁰ = 4.0 × 10¹²M^?2sec^?1, independent of temperature for H₂O as the chaperone gas. He is about 1/8 as efficient as H₂O.     

The decomposition of dimethyl peroxide and the rate constant for CH3O + O2 → CH2O + HO2

The decomposition of dimethyl peroxide (DMP) was studied in the presence and absence of added NO₂ to determine rate constants k₁ and k₂ in the temperature range of 391–432°K: The results reconcile the studies by Takezaki and Takeuchi, Hanst and Calvert, and Batt and McCulloch, giving log k₁(sec^?1) = (15.7 ± 0.5) - (37.1 ± 0.9)/2.3 RT and k₂ ≈ 5 × 10⁴M^?1· sec^?1. The disproportionation/recombination ratio k_7b/k_7a = 0.30 ± 0.05 was also determined: When O₂ was added to DMP mixtures containing NO₂, relative rate constants k₁₂/k_7a were obtained over the temperature range of 396–442°K: A review of literature data produced k_7a = 10^9.8±0.5M^?1·sec^?1, giving log k₁₂(M^?1·sec^?1) = (8.5 ± 1.5) - (4.0 ± 2.8)/2.3 RT, where most of the uncertainty is due to the limited temperature range of the experiments.     

The very-low-pressure pyrolysis (VLPP) of n-propyl nitrate,tert-butyl nitrite,and methyl nitrite. Rate constants for some alkoxy radical reactions

The pyrolysis of n-propyl nitrate and tert-butyl nitrite at very low pressures (VLPP technique) is reported. For the reaction the high-pressure rate expression at 300°K, log k₁ (sec^?1) = 16.5 ? 40.0 kcal/mole/2.3 RT, is derived. The reaction was studied and the high-pressure parameters at 300°K are log k₂(sec^?1) = 15.8 ? 39.3 kcal/mole/2.3 RT. From ΔS_1,?1⁰ and ΔS_2,?2⁰ and the assumption E_?1 and E_?2 ? 0, we derive log k_?1(M^?1·sec^?1) (300°K) = 9.5 and log k_?2 (M^?1·sec^?1) (300°K) = 9.8. In contrast, the pyrolysis of methyl nitrite and methyl d₃ nitrite afford NO and HNO and DNO, respectively, in what appears to be a heterogeneous process. The values of k_?1 and k_?2 in conjunction with independent measurements imply a value at 300°K for of 3.5 × 10⁵ M^?1·sec^?1, which is two orders of magnitude greater than currently accepted values. In the high-pressure static pyrolysis of dimethyl peroxide in the presence of NO₂, the yield of methyl nitrate indicates that the combination of methoxy radicals with NO₂ is in the high-pressure limit at atmospheric pressure.     

Equilibrium,kinetics, and mechanism of the malonic acid–iodine reaction

The equilibrium constant for the reaction CH₂(COOH)₂ + I₃^? ? CHI(COOH)₂ + 2I^? + H⁺, measured spectrophotometrically at 25°C and ionic strength 1.00M (NaClO₄), is (2.79 ± 0.48) × 10^?4M². Stopped-flow kinetic measurements at 25°C and ionic strength 1.00M with [H⁺] = (2.09-95.0) × 10^?3M and [I^?] = (1.23-26.1) × 10^?3M indicate that the rate of the forward reaction is given by (k₁[I₂] + k₃[I₃^?]) [HOOCCH₂COO^?] + (k₂[I₂] + k₄[I₃^?]) [CH(COOH)₂] + k₅[H⁺] [I₃^?] [CH₂(COOH)₂]. The values of the rate constants k₁-k₅ are (1.21 ± 0.31) × 10², (2.41 ± 0.15) × 10¹, (1.16 ± 0.33) × 10¹, (8.7 ± 4.5) × 10^?1M^?1·sec^?1, and (3.20 ± 0.56) × 10¹M^?2·sec^?1, respectively. The rate of enolization of malonic acid, measured by the bromine scavenging technique, is given by k_en[CH₂(COOH)₂], with k_en = 2.0 × 10^?3 + 1.0 × 10^?2 [CH₂(COOH)₂]. An intramolecular mechanism, featuring a six-member cyclic transition state, is postulated to account for the results on the enolization of malonic acid. The reactions of the enol, enolate ion, and protonated enol with iodine and/or triodide ion are proposed to account for the various rate terms.     

Vinyl polymerization. 361. Polymerization of 2,2,4-trimethyl-3-on-1-pentyl methacrylate

2,2,4-Trimethyl-3-on-1-pentyl methacrylate (TMPM) was first synthesized from the condensation reaction of 2,2,4-trimethyl-1-pentanol-3-on with methacrylic acid. Second, the polymerization of TMPM and the copolymerization of TMPM with styrene (St) were carried out in benzene at 60°C, using 2,2′-azobisisobutyronitrile (AIBN) as an initiator. As the result of kinetic investigation, the rate of polymerization (R_p) could be expressed by: R_p = k[AIBN]^0.5 [TMPM]^1.0. Kinetic constants of polymerization of TMPM were obtained as follows: k_p/k = 0.27 dm^3/2 mole^?1/2 sec^?1/2, 2fk_d = 1.23 × 10^?5 sec^?1, f = 0.73, C_m = 2.6 × 10^?5, C_s = 1.1 × 10^?5. From the results the reactivity of TMPM was found to be larger than that of methyl methacrylate. The overall activation energy was calculated to be 110 kJ mole^?1. The following monomer reactivity ratios and Q, e values were obtained: TMPM(M₁) ? St(M₂): r₁ = 1.50, r₂ = 0.14, Q₁ = 2.63, E₁ = 0.45.     

Kinetic Studies of the Catalytic Effect of Cobalt(II) Ions on the Substitution Reactions of the Ethylenediaminetetraacetatocobalt(III) Complex

The rate for the substitution reaction of Co(edta)^? with ethylenediamine was greatly enhanced by the presence of an excess of Co(II) ion in solution. The rate constant is (13±2) M^?-sec^?1 at μi=0.10M LiClO₄, pH=11.1, [en]=0.10M and T=25°C. The mechanism for the reaction is discussed on the basis of the Marcus theory for outer-sphere processes corrected for electrostatic effects. This catalytic effect was not observed when the Co(II) was present in small amount due to the stability of the Co(edta)^?2 complex toward substitution. The rate constant for direct substitution of Co(edta)^? under the same conditions has also been measured and the value is (3.66±0.40)×10^?4sec^?.     

Kinetics of the reactions of 2,4,6-tri-t-butylphenoxyl with cumene hydroperoxide,cumylperoxyl radicals,and molecular oxygen

Reactions of 2,4,6-tri-t-butylphenoxyl (TBP) with cumene hydroperoxide (ROOH), cumylperoxyl radicals (RO₂), and molecular oxygen in benzene solution have been investigated kinetically by the ESR method. The rate constant of the reaction TBP + ROOH has been estimated in the temperature range 27°-75°C: log₁₀(k_?7/M^?1sec^?1) = (7.1 ± 0.4) - (10.9 ± 0.6 kcal mole^?1)/θ The ratio of the rate constants of reactions TBPH + RO₂ products has been determined from the experimental dependence of the rate constant of reaction TBP with ROOH on [TBPH]₀/[TBP]₀. Putting k₇ = 4.0 × 10³M^?1sec^?1, we obtain k₈ = (2.0 ± 0.2) × 10⁸M^?1sec^?1 at 30°C. The reaction of TBP with O₂ obeys the kinetic law ?d[TBP]/dt = k′[O₂][TBP]². This is in accordance with scheme TBP + O₂ ← TBP ?O₂ [I]; TBP ?O₂ + TBP · products, log₁₀ (k′/M^?2sec^?1) = (?14.5 ± 0.9) + (27.2 ± 1.4)/θ at 66°?78°C, where ° = 2.303RT.     

Kinetics and mechanisms of substitution reactions with sulfur-containing nucleophiles in aqueous acid solutions. I—rates of reactions of some tetrahalopalladate (II) anions with thiourea and selenourea

The activation energy parameters for the reaction of PdX (X=Cl^?, Br^?) in aqueous halide acid solution with thiourea (tu) and selenourea (seu) have been determined. High rates of reaction parallel low enthalpies and appreciable negative entropy of activation. The rate law in each case simplifies to k_obs=k[L] where L=tu or seu, and only ligand-dependent rate constants are observed at 25°C. The ligand-dependent rate constants for the first identifiable step in the PdCl + X system is (9.1±0.1) × 10³ M^?1 sec^?1 and (4.5±0.1) × 10⁴ M^?1 sec^?1 for X=tu and seu, respectively, while for the PdBr + X system it is (2.0±0.1) × 10⁴ M^?1 sec^?1 and (9.0±0.1) × 10⁴ M^?1 sec^?1 for X=tu and seu, respectively.     

The reaction of methoxy radicals with nitric oxide and nitrogen dioxide

By allowing dimethyl peroxide (10^?4M) to decompose in the presence of nitric oxide (4.5 × 10^?5M), nitrogen dioxide (6.5 × 10^?5M) and carbon tetrafluoride (500 Torr), it has been shown that the ratio k₂/k_2′ = 2.03 ± 0.47: CH₃O + NO → CH₃ONO (reaction 2) and CH₃O + NO₂ → CH₃ONO₂ (reaction 2′). Deviations from this value in this and previous work is ascribed to the pressure dependence of both these reactions and heterogeneity in reaction (2). In contrast no heterogeneous effects were found for reaction (2′) making it an ideal reference reaction for studying other reactions of the methoxy radical. We conclude that the ratio k₂/k_2′ is independent of temperature and from k₁ = 10^10.2±0.4M^?1 sec^?1 we calculate that k_2′ = 10^9.9±0.4M^?1 sec^?1. Both k₂ and k_2′ are pressure dependent but have reached their limiting high-pressure values in the presence of 500 Torr of carbon tetrafluoride. Preliminary results show that k₄ = 10.^9.0±0.6 10^?4.5±1.1/ΘM^?1 sec^?1 (Θ = 2.303RT kcal mole^?1) and by k₄ = 10^8.6±0.6 10^?2.4±1.1/ΘM^?1 sec^?1: CH₃O + O₂ → CH₂O + HO₂ (reaction 4) and CH₃O + t-BuH → CH₃OH + (t-Bu) (reaction 4′).     

Kinetics and structural aspects of the cisplatin interactions with guanine: A quantum mechanical description

The interaction of cisplatin with guanine DNA bases has been investigated using ab initio Hartree–Fock (HF) and density functional levels of theory in gas phase and aqueous solution. The overall process was divided into three steps: the reaction of the monoaqua [Pt(NH₃)₂Cl(H₂O)]⁺ species with guanine (G) (reaction 1), the hydrolysis process yielding the adduct [Pt(NH₃)₂(G) (H₂O)]²⁺ (reaction 2) and the reaction with a second guanine leading to the product [Pt(NH₃)₂(G)₂]²⁺ (reaction 3). The functionals B3LYP, BHandH, and mPW1PW91 were used in the present study, to develop an understanding of the role of the distinct models. The geometries presented for the intermediate structures were obtained by IRC calculations from the transition state structure for each reaction. The structural analysis for the intermediates and transition states showed that hydrogen bonds with the guanine O6 atom play an important role in stabilizing these species. The geometries were not very sensitive to the level of theory applied with the HF level, giving a satisfactory overall performance. However, the energy barriers and the rate constants were found to be strongly dependent on the level of calculation and basis set, with the DFT calculations giving more accurate results. For reaction 1 the rate constant calculated in aqueous solution at PCM‐BHandH/6‐311G* (k₁ = 7.55 × 10^?1 M^?1 s^?1) was in good agreement with the experiment (5.4 × 10^?1 M^?1 s^?1). The BHandH/6‐31G* calculated gas phase rate constants for reactions 2 and 3 were: k₂ = 0.9 × 10^?6 M^?1 s^?1 and k₃ = 2.99 × 10^?4 M^?1 s^?1 in fairly good accordance with the experimental findings for reaction 2 (1.0 × 10^?6 M^?1 s^?1) and reaction 3 (3.0 × 10^?4 M^?1 s^?1). © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

The Reductions of Bis(terpyridyl) and Ethylenediaminetetraacetato Complexes of Cobalt(III) by Ascorbic Acid

The reductions of Co(terpy)₂³⁺ and Co(edta)^? complexes by ascorbic acid have been subjected to a detailed kinetic study in the range of pH =1–10.9. For each complex the rate law of the reaction is interpreted as a rate determining reaction between Co(III) complex and the ascorbic acid in the form of HA^? (k₁) and A^2? (k₂), depending on the pH of the solution, followed by a rapid scavenge of the ascorbic acid radicals by Co(III) complex. With given Ka₁ and Ka₂, the rate constants are k₁ = 0.25 and 9.87 × 10^?5 M^?1s^?1, k₂ = 1.28 × 10⁶ and 18.7 M^?1s^?1 for Co(terpy₎2³⁺and Co(edta)^? complexes, respectively, at T = 25 °C and μ = 0.50M (terpy)and 1.0 M (edta) HClO₄/LiClO₄. The mechanism of the reaction is discussed on the basis of Marcus theory for outer sphere electron transfer process. Spin change and charge effect, duly considered, account for the non‐adiabatic behavior in the reduction of Co(edta)^? complex.     

Thermal unimolecular isomerization of 1,4-dimethylbicyclo[2.2.0]hexane, 1,4-dimethylbicyclo[2.1.1]hexane,and 1,4-dimethylbicyclo[2.1.0]pentane

The thermal isomerization of the title compounds was studied in the vapor phase. Over the temperature range from 445.1 to 477.5°K, 1,4-dimethylbicyclo[2.2.0]hexane underwent a homogeneous unimolecular reaction to 2,5-dimethyl-1,5-hexadiene, the rate constants being represented by the equation: k = 1.86 × 10¹¹ exp (?31000 ± 1800/RT) sec^?1. Over the temperature range from 630.0 to 662.2°K, 1,4-dimethylbicyclo[2.1.1]-hexane also underwent a unimolecular isomerization to the same product, the rate constants being given by the equation: k = 8.91 × 10¹⁴ exp (?56000 ± 900/RT) sec^?1. The pyrolysis of 1,4-dimethylbicyclo[2.1.0]pentane gave 1,3-dimethylcyclopentene-1 and 2,4-dimethyl-1,4-pentadiene in the ratio of 9:1. The former reaction was influenced by surface effects but the latter was not. The rate constants for the formation of 2,4-dimethyl-1,4-pentadiene fitted the equation: k = 1.66 × 10¹⁷ exp (?57400 ± 3100/RT) sec^?1. The effect of the two methyl groups at the bridgehead positions in these molecules in influencing the rate of decomposition is discussed in terms of the non-bonded repulsive forces between the substituents.