Molecules

2014

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1576 KiB

Open AccessArticle

Chlorine Isotope Effects from Isotope Ratio Mass Spectrometry Suggest Intramolecular C-Cl Bond Competition in Trichloroethene (TCE) Reductive Dehalogenation

by Stefan Cretnik, Anat Bernstein, Orfan Shouakar-Stash, Frank Löffler and Martin Elsner

Molecules 2014, 19(5), 6450-6473; https://doi.org/10.3390/molecules19056450 - 20 May 2014

Cited by 43 | Viewed by 9783

Abstract

Chlorinated ethenes are prevalent groundwater contaminants. To better constrain (bio)chemical reaction mechanisms of reductive dechlorination, the position-specificity of reductive trichloroethene (TCE) dehalogenation was investigated. Selective biotransformation reactions (i) of tetrachloroethene (PCE) to TCE in cultures of Desulfitobacterium sp. strain Viet1; and (ii) of [...] Read more.

Chlorinated ethenes are prevalent groundwater contaminants. To better constrain (bio)chemical reaction mechanisms of reductive dechlorination, the position-specificity of reductive trichloroethene (TCE) dehalogenation was investigated. Selective biotransformation reactions (i) of tetrachloroethene (PCE) to TCE in cultures of Desulfitobacterium sp. strain Viet1; and (ii) of TCE to cis-1,2-dichloroethene (cis-DCE) in cultures of Geobacter lovleyi strain SZ were investigated. Compound-average carbon isotope effects were −19.0‰ ± 0.9‰ (PCE) and −12.2‰ ± 1.0‰ (TCE) (95% confidence intervals). Using instrumental advances in chlorine isotope analysis by continuous flow isotope ratio mass spectrometry, compound-average chorine isotope effects were measured for PCE (−5.0‰ ± 0.1‰) and TCE (−3.6‰ ± 0.2‰). In addition, position-specific kinetic chlorine isotope effects were determined from fits of reactant and product isotope ratios. In PCE biodegradation, primary chlorine isotope effects were substantially larger (by −16.3‰ ± 1.4‰ (standard error)) than secondary. In TCE biodegradation, in contrast, the product cis-DCE reflected an average isotope effect of −2.4‰ ± 0.3‰ and the product chloride an isotope effect of −6.5‰ ± 2.5‰, in the original positions of TCE from which the products were formed (95% confidence intervals). A greater difference would be expected for a position-specific reaction (chloride would exclusively reflect a primary isotope effect). These results therefore suggest that both vicinal chlorine substituents of TCE were reactive (intramolecular competition). This finding puts new constraints on mechanistic scenarios and favours either nucleophilic addition by Co(I) or single electron transfer as reductive dehalogenation mechanisms. Full article

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632 KiB

Open AccessArticle

Identifying Stereoisomers by ab-initio Calculation of Secondary Isotope Shifts on NMR Chemical Shieldings

by Karl-Heinz Böhm, Klaus Banert and Alexander A. Auer

Molecules 2014, 19(4), 5301-5312; https://doi.org/10.3390/molecules19045301 - 23 Apr 2014

Cited by 3 | Viewed by 6333

Abstract

We present ab-initio calculations of secondary isotope effects on NMR chemical shieldings. The change of the NMR chemical shift of a certain nucleus that is observed if another nucleus is replaced by a different isotope can be calculated by computing vibrational corrections on [...] Read more.

We present ab-initio calculations of secondary isotope effects on NMR chemical shieldings. The change of the NMR chemical shift of a certain nucleus that is observed if another nucleus is replaced by a different isotope can be calculated by computing vibrational corrections on the NMR parameters using electronic structure methods. We demonstrate that the accuracy of the computational results is sufficient to even distinguish different conformers. For this purpose, benchmark calculations for fluoro(2-2H)ethane in gauche and antiperiplanar conformation are carried out at the HF, MP2 and CCSD(T) level of theory using basis sets ranging from double- to quadruple-zeta quality. The methodology is applied to the secondary isotope shifts for 2-fluoronorbornane in order to resolve an ambiguity in the literature on the assignment of endo- and exo-2-fluoronorbornanes with deuterium substituents in endo-3 and exo-3 positions, also yielding insight into mechanistic details of the corresponding synthesis. Full article

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2013

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335 KiB

Open AccessReview

Advances in Kinetic Isotope Effect Measurement Techniques for Enzyme Mechanism Study

by Hong Gu and Shuming Zhang

Molecules 2013, 18(8), 9278-9292; https://doi.org/10.3390/molecules18089278 - 2 Aug 2013

Cited by 16 | Viewed by 7811

Abstract

Kinetic isotope effects (KIEs) are a very powerful tool for investigating enzyme mechanisms. Precision of measurement is the most important factor for KIE determinations, especially for small heavy atom KIEs. Internal competition is commonly used to measure small KIEs on V/K. Several methods, [...] Read more.

Kinetic isotope effects (KIEs) are a very powerful tool for investigating enzyme mechanisms. Precision of measurement is the most important factor for KIE determinations, especially for small heavy atom KIEs. Internal competition is commonly used to measure small KIEs on V/K. Several methods, including such as liquid scintillation counting, mass spectrometry, nuclear magnetic resonance spectroscopy and polarimetry have been used to determine KIEs. In this paper, which does not aspire to be an exhaustive review, we briefly review different experimental approaches for the measurement of KIEs on enzymatic reaction with an emphasis on newer techniques employing mass spectrometry and nuclear magnetic resonance spectrometry as well as some corresponding examples. Full article

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1113 KiB

Open AccessReview

The Application of Transient-State Kinetic Isotope Effects to the Resolution of Mechanisms of Enzyme-Catalyzed Reactions

by Harvey F. Fisher

Molecules 2013, 18(7), 8230-8242; https://doi.org/10.3390/molecules18078230 - 12 Jul 2013

Cited by 5 | Viewed by 5965

Abstract

Much of our understanding of the mechanisms of enzyme-catalyzed reactions is based on steady-state kinetic studies. Experimentally, this approach depends solely on the measurement of rates of free product appearance (d[P]/dt), a mechanistically and mathematically complex entity. Despite the ambiguity of [...] Read more.

Much of our understanding of the mechanisms of enzyme-catalyzed reactions is based on steady-state kinetic studies. Experimentally, this approach depends solely on the measurement of rates of free product appearance (d[P]/dt), a mechanistically and mathematically complex entity. Despite the ambiguity of this observed parameter, the method’s success is due in part to the elaborate rigorously derived algebraic theory on which it is based. Transient-state kinetics, on the other hand, despite its ability to observe the formation of intermediate steps in real time, has contributed relatively little to the subject due in, some measure, to the lack of such a solid mathematical basis. Here we discuss the current state of existing transient-state theory and the difficulties in its realistic application to experimental data. We describe a basic analytic theory of transient-state kinetic isotope effects in the form of three novel fundamental rules. These rules are adequate to define an extended mechanism, locating the isotope-sensitive step and identifying missing steps from experimental data. We demonstrate the application of these rules to resolved component time courses of the phenylalanine dehydrogenase reaction, extending the previously known reaction by one new prehydride transfer step and two new post hydride transfer steps. We conclude with an assessment of future directions in this area. Full article

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1117 KiB

Open AccessReview

Isotope Effects in ESR Spectroscopy

by Reinhard Stößer and Werner Herrmann

Molecules 2013, 18(6), 6679-6722; https://doi.org/10.3390/molecules18066679 - 7 Jun 2013

Cited by 14 | Viewed by 10368

Abstract

In order to present the relationship between ESR spectroscopy and isotope effects three levels are considered: (i) ESR spectroscopy is described on a general level up to the models for interpretation of the experimental spectra, which go beyond the usually used time and [...] Read more.

In order to present the relationship between ESR spectroscopy and isotope effects three levels are considered: (i) ESR spectroscopy is described on a general level up to the models for interpretation of the experimental spectra, which go beyond the usually used time and mass independent spin-Hamilton operator, (ii) the main characteristics of the generalized isotope effects are worked out, and finally (iii) the basic, mainly quantum mechanical effects are used to describe the coupling of electron spins with the degrees of freedom, which are accessible under the selected conditions, of the respective paramagnetic object under investigation. The ESR parameters and the respective models are formalized so far, that they include the time and mass depending influences and reflect the specific isotope effects. Relations will be established between the effects in ESR spectra to spin relaxation, to spin exchange, to the magnetic isotope effect, to the Jahn-Teller effects, as well as to the influence of zero-point vibrations. Examples will be presented which demonstrate the influence of isotopes as well as the kind of accessible information. It will be differentiated with respect to isotope effects in paramagnetic centres itself and in the respective matrices up to the technique of ESR imaging. It is shown that the use of isotope effects is indispensable in ESR spectroscopy. Full article

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904 KiB

Open AccessReview

Isotope Effects as Probes for Enzyme Catalyzed Hydrogen-Transfer Reactions

by Daniel Roston, Zahidul Islam and Amnon Kohen

Molecules 2013, 18(5), 5543-5567; https://doi.org/10.3390/molecules18055543 - 14 May 2013

Cited by 45 | Viewed by 10283

Abstract

Kinetic Isotope effects (KIEs) have long served as a probe for the mechanisms of both enzymatic and solution reactions. Here, we discuss various models for the physical sources of KIEs, how experimentalists can use those models to interpret their data, and how the [...] Read more.

Kinetic Isotope effects (KIEs) have long served as a probe for the mechanisms of both enzymatic and solution reactions. Here, we discuss various models for the physical sources of KIEs, how experimentalists can use those models to interpret their data, and how the focus of traditional models has grown to a model that includes motion of the enzyme and quantum mechanical nuclear tunneling. We then present two case studies of enzymes, thymidylate synthase and alcohol dehydrogenase, and discuss how KIEs have shed light on the C-H bond cleavages those enzymes catalyze. We will show how the combination of both experimental and computational studies has changed our notion of how these enzymes exert their catalytic powers. Full article

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373 KiB

Open AccessArticle

Theoretical Study of H/D Isotope Effects on Nuclear Magnetic Shieldings Using an ab initio Multi-Component Molecular Orbital Method

by Taro Udagawa, Takayoshi Ishimoto and Masanori Tachikawa

Molecules 2013, 18(5), 5209-5220; https://doi.org/10.3390/molecules18055209 - 7 May 2013

Cited by 17 | Viewed by 5570

Abstract

We have theoretically analyzed the nuclear quantum effect on the nuclear magnetic shieldings for the intramolecular hydrogen-bonded systems of σ-hydroxy acyl aromatic species using the gauge-including atomic orbital technique combined with our multi-component density functional theory. The effect of H/D quantum nature for [...] Read more.

We have theoretically analyzed the nuclear quantum effect on the nuclear magnetic shieldings for the intramolecular hydrogen-bonded systems of σ-hydroxy acyl aromatic species using the gauge-including atomic orbital technique combined with our multi-component density functional theory. The effect of H/D quantum nature for geometry and nuclear magnetic shielding changes are analyzed. Our study clearly demonstrated that the geometrical changes of hydrogen-bonds induced by H/D isotope effect (called geometrical isotope effect: GIE) is the dominant factor of deuterium isotope effect on ¹³C chemical shift. Full article

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281 KiB

Open AccessArticle

Spectroscopic Studies of Amino Acid Ionic Liquid-Supported Schiff Bases

by Paula Ossowicz, Ewa Janus, Grzegorz Schroeder and Zbigniew Rozwadowski

Molecules 2013, 18(5), 4986-5004; https://doi.org/10.3390/molecules18054986 - 29 Apr 2013

Cited by 32 | Viewed by 7294

Abstract

Amino acid ionic liquid-supported Schiff bases, derivatives of salicylaldehyde and various amino acids (L-threonine, L-valine, L-leucine, L-isoleucine and L-histidine) have been investigated by means of various spectroscopic techniques (NMR, UV-Vis, IR, MS) and deuterium isotope effects on ¹³C-NMR chemical shifts. The results [...] Read more.

Amino acid ionic liquid-supported Schiff bases, derivatives of salicylaldehyde and various amino acids (L-threonine, L-valine, L-leucine, L-isoleucine and L-histidine) have been investigated by means of various spectroscopic techniques (NMR, UV-Vis, IR, MS) and deuterium isotope effects on ¹³C-NMR chemical shifts. The results have shown that in all studied amino acid ionic liquid-supported Schiff bases (except the L-histidine derivative) a proton transfer equilibrium exists and the presence of the COO⁻ group stabilizes the proton transferred NH-form. Full article

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266 KiB

Open AccessArticle

Zero-Point Corrections for Isotropic Coupling Constants for Cyclohexadienyl Radical, C₆H₇ and C₆H₆Mu: Beyond the Bond Length Change Approximation

by Bruce S. Hudson and Suzanne K. Chafetz

Molecules 2013, 18(5), 4906-4916; https://doi.org/10.3390/molecules18054906 - 25 Apr 2013

Cited by 8 | Viewed by 6272

Abstract

Zero-point vibrational level averaging for electron spin resonance (ESR) and muon spin resonance (µSR) hyperfine coupling constants (HFCCs) are computed for H and Mu isotopomers of the cyclohexadienyl radical. A local mode approximation previously developed for computation of the effect of replacement of [...] Read more.

Zero-point vibrational level averaging for electron spin resonance (ESR) and muon spin resonance (µSR) hyperfine coupling constants (HFCCs) are computed for H and Mu isotopomers of the cyclohexadienyl radical. A local mode approximation previously developed for computation of the effect of replacement of H by D on ¹³C-NMR chemical shifts is used. DFT methods are used to compute the change in energy and HFCCs when the geometry is changed from the equilibrium values for the stretch and both bend degrees of freedom. This variation is then averaged over the probability distribution for each degree of freedom. The method is tested using data for the methylene group of C₆H₇, cyclohexadienyl radical and its Mu analog. Good agreement is found for the difference between the HFCCs for Mu and H of CHMu and that for H of CHMu and CH₂ of the parent radical methylene group. All three of these HFCCs are the same in the absence of the zero point average, a one-parameter fit of the static HFCC, a(0), can be computed. That value, 45.2 Gauss, is compared to the results of several fixed geometry electronic structure computations. The HFCC values for the ortho, meta and para H atoms are then discussed. Full article

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458 KiB

Open AccessArticle

Theoretical Analysis on the Kinetic Isotope Effects of Bimolecular Nucleophilic Substitution (S_N2) Reactions and Their Temperature Dependence

by Wan-Chen Tsai and Wei-Ping Hu

Molecules 2013, 18(4), 4816-4843; https://doi.org/10.3390/molecules18044816 - 23 Apr 2013

Cited by 9 | Viewed by 7951

Abstract

Factors affecting the kinetic isotope effects (KIEs) of the gas-phase S_N2 reactions and their temperature dependence have been analyzed using the ion-molecule collision theory and the transition state theory (TST). The quantum-mechanical tunneling effects were also considered using the canonical variational [...] Read more.

Factors affecting the kinetic isotope effects (KIEs) of the gas-phase S_N2 reactions and their temperature dependence have been analyzed using the ion-molecule collision theory and the transition state theory (TST). The quantum-mechanical tunneling effects were also considered using the canonical variational theory with small curvature tunneling (CVT/SCT). We have benchmarked a few ab initio and density functional theory (DFT) methods for their performance in predicting the deuterium KIEs against eleven experimental values. The results showed that the MP2/aug-cc-pVDZ method gave the most accurate prediction overall. The slight inverse deuterium KIEs usually observed for the gas-phase S_N2 reactions at room temperature were due to the balance of the normal rotational contribution and the significant inverse vibrational contribution. Since the vibrational contribution is a sensitive function of temperature while the rotation contribution is temperature independent, the KIEs are thus also temperature dependent. For S_N2 reactions with appreciable barrier heights, the tunneling effects were predicted to contribute significantly both to the rate constants and to the carbon-13, and carbon-14 KIEs, which suggested important carbon atom tunneling at and below room temperature. Full article

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564 KiB

Open AccessArticle

¹H-MAS-NMR Chemical Shifts in Hydrogen-Bonded Complexes of Chlorophenols (Pentachlorophenol, 2,4,6-Trichlorophenol, 2,6-Dichlorophenol, 3,5-Dichlorophenol, and p-Chlorophenol) and Amine, and H/D Isotope Effects on ¹H-MAS-NMR Spectra

by Hisashi Honda

Molecules 2013, 18(4), 4786-4802; https://doi.org/10.3390/molecules18044786 - 22 Apr 2013

Cited by 7 | Viewed by 7805

Abstract

Chemical shifts (CS) of the ¹H nucleus in N···H···O type hydrogen bonds (H-bond) were observed in some complexes between chlorophenols [pentachlorophenol (PCP), 2,4,6-tricholorophenol (TCP), 2,6-dichlorophenol (26DCP), 3,5-dichlorophenol (35DCP), and p-chlorophenol (pCP)] and nitrogen-base (N-Base) by solid-state high-resolution ¹H-NMR [...] Read more.

Chemical shifts (CS) of the ¹H nucleus in N···H···O type hydrogen bonds (H-bond) were observed in some complexes between chlorophenols [pentachlorophenol (PCP), 2,4,6-tricholorophenol (TCP), 2,6-dichlorophenol (26DCP), 3,5-dichlorophenol (35DCP), and p-chlorophenol (pCP)] and nitrogen-base (N-Base) by solid-state high-resolution ¹H-NMR with the magic-angle-spinning (MAS) method. Employing N-Bases with a wide range of pK_a values (0.65–10.75), ¹H-MAS-NMR CS values of bridging H atoms in H-bonds were obtained as a function of the N-Base’s pK_a. The result showed that the CS values were increased with increasing pK_a values in a range of DpK_a < 0 [DpK_a = pK_a(N-Base) - pK_a(chlorophenols)] and decreased when DpK_a > 2: The maximum CS values was recorded in the PCP (pK_a = 5.26)–4-methylpyridine (6.03), TCP (6.59)–imidazole (6.99), 26DCP (7.02)–2-amino-4-methylpyridine (7.38), 35DCP (8.04)–4-dimethylaminopyridine (9.61), and pCP (9.47)–4-dimethylaminopyridine (9.61) complexes. The largest CS value of 18.6 ppm was recorded in TCP–imidazole crystals. In addition, H/D isotope effects on ¹H-MAS-NMR spectra were observed in PCP–2-amino-3-methylpyridine. Based on the results of CS simulation using a B3LYP/6-311+G** function, it can be explained that a little changes of the N–H length in H-bond contribute to the H/D isotope shift of the ¹H-MAS-NMR peaks. Full article

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304 KiB

Open AccessArticle

Deuterium Isotope Effects on ¹³C-NMR Chemical Shifts of 10-Hydroxybenzo[h]quinolines

by Poul Erik Hansen, Fadhil S. Kamounah and Daniel T. Gryko

Molecules 2013, 18(4), 4544-4560; https://doi.org/10.3390/molecules18044544 - 17 Apr 2013

Cited by 16 | Viewed by 7100

Abstract

Deuterium isotope effects on ¹³C-NMR chemical shifts are investigated in a series of 10-hydroxybenzo[h]quinolines (HBQ’s) The OH proton is deuteriated. The isotope effects on ¹³C chemical shifts in these hydrogen bonded systems are rather unusual. The formal four-bond effects [...] Read more.

Deuterium isotope effects on ¹³C-NMR chemical shifts are investigated in a series of 10-hydroxybenzo[h]quinolines (HBQ’s) The OH proton is deuteriated. The isotope effects on ¹³C chemical shifts in these hydrogen bonded systems are rather unusual. The formal four-bond effects are found to be negative, indicating transmission via the hydrogen bond. In addition unusual long-range effects are seen. Structures, NMR chemical shifts and changes in nuclear shieldings upon deuteriation are calculated using DFT methods. Two-bond deuterium isotope effects on ¹³C chemical shifts are correlated with calculated OH stretching frequencies. Isotope effects on chemical shifts are calculated for systems with OH exchanged by OD. Hydrogen bond potentials are discussed. New and more soluble nitro derivatives are synthesized. Full article

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562 KiB

Open AccessReview

H/D Isotope Effects in Hydrogen Bonded Systems

by Lucjan Sobczyk, Monika Obrzud and Aleksander Filarowski

Molecules 2013, 18(4), 4467-4476; https://doi.org/10.3390/molecules18044467 - 16 Apr 2013

Cited by 54 | Viewed by 8310

Abstract

An extremely strong H/D isotope effect observed in hydrogen bonded A-H^…B systems is connected with a reach diversity of the potential shape for the proton/deuteron motion. It is connected with the anharmonicity of the proton/deuteron vibrations and of the tunneling effect, [...] Read more.

An extremely strong H/D isotope effect observed in hydrogen bonded A-H^…B systems is connected with a reach diversity of the potential shape for the proton/deuteron motion. It is connected with the anharmonicity of the proton/deuteron vibrations and of the tunneling effect, particularly in cases of short bridges with low barrier for protonic and deuteronic jumping. Six extreme shapes of the proton motion are presented starting from the state without possibility of the proton transfer up to the state with a full ionization. The manifestations of the H/D isotope effect are best reflected in the infra-red absorption spectra. A most characteristic is the run of the relationship between the isotopic ratio n_H/n_D and position of the absorption band shown by using the example of NHN hydrogen bonds. One can distinguish a critical range of correlation when the isotopic ratio reaches the value of ca. 1 and then increases up to unusual values higher than . The critical range of the isotope effect is also visible in NQR and NMR spectra. In the critical region one observes a stepwise change of the NQR frequency reaching 1.1 MHz. In the case of NMR, the maximal isotope effect is reflected on the curve presenting the dependence of Δd (¹H,²H) on d (¹H). This effect corresponds to the range of maximum on the correlation curve between dH and ΔpK_a that is observed in various systems. There is a lack in the literature of quantitative information about the influence of isotopic substitution on the dielectric properties of hydrogen bond except the isotope effect on the ferroelectric phase transition in some hydrogen bonded crystals. Full article

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546 KiB

Open AccessArticle

Probing Ionic Liquid Aqueous Solutions Using Temperature of Maximum Density Isotope Effects

by Mohammad Tariq, José M. S. S. Esperança, Luís P. N. Rebelo and José N. Canongia Lopes

Molecules 2013, 18(4), 3703-3711; https://doi.org/10.3390/molecules18043703 - 25 Mar 2013

Cited by 4 | Viewed by 5311

Abstract

This work is a new development of an extensive research program that is investigating for the first time shifts in the temperature of maximum density (TMD) of aqueous solutions caused by ionic liquid solutes. In the present case we have compared the shifts [...] Read more.

This work is a new development of an extensive research program that is investigating for the first time shifts in the temperature of maximum density (TMD) of aqueous solutions caused by ionic liquid solutes. In the present case we have compared the shifts caused by three ionic liquid solutes with a common cation—1-ethyl-3-methylimidazolium coupled with acetate, ethylsulfate and tetracyanoborate anions—in normal and deuterated water solutions. The observed differences are discussed in terms of the nature of the corresponding anion-water interactions. Full article

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530 KiB

Open AccessArticle

Enthalpy/Entropy Contributions to Conformational KIEs: Theoretical Predictions and Comparison with Experiment

by Aaron Fong, Matthew P. Meyer and Daniel J. O'Leary

Molecules 2013, 18(2), 2281-2296; https://doi.org/10.3390/molecules18022281 - 18 Feb 2013

Cited by 8 | Viewed by 6417

Abstract

Previous theoretical studies of Mislow’s doubly-bridged biphenyl ketone 1 and dihydrodimethylphenanthrene 2 have determined significant entropic contributions to their normal (1) and inverse (2) conformational kinetic isotope effects (CKIEs). To broaden our investigation, we have used density functional methods [...] Read more.

Previous theoretical studies of Mislow’s doubly-bridged biphenyl ketone 1 and dihydrodimethylphenanthrene 2 have determined significant entropic contributions to their normal (1) and inverse (2) conformational kinetic isotope effects (CKIEs). To broaden our investigation, we have used density functional methods to characterize the potential energy surfaces and vibrational frequencies for ground and transition structures of additional systems with measured CKIEs, including [2.2]-metaparacyclophane-d (3), 1,1'-binaphthyl (4), 2,2'-dibromo-[1,1'-biphenyl]-4,4'-dicarboxylic acid (5), and the 2-(N,N,N-trimethyl)-2'-(N,N-dimethyl)-diaminobiphenyl cation (6). We have also computed CKIEs in a number of systems whose experimental CKIEs are unknown. These include analogs of 1 in which the C=O groups have been replaced with CH₂ (7), O (8), and S (9) atoms and ring-expanded variants of 2 containing CH₂ (10), O (11), S (12), or C=O (13) groups. Vibrational entropy contributes to the CKIEs in all of these systems with the exception of cyclophane 3, whose isotope effect is predicted to be purely enthalpic in origin and whose Bigeleisen-Mayer ZPE term is equivalent to ΔΔ H^‡. There is variable correspondence between these terms in the other molecules studied, thus identifying additional examples of systems in which the Bigeleisen-Mayer formalism does not correlate with ΔH/ΔS dissections. Full article

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