View source for Physical organic chemistry

{{short description|Discipline of organic chemistry}}
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'''Physical organic chemistry''', a term coined by [[Louis Hammett]] in 1940, refers to a discipline of [[organic chemistry]] that focuses on the relationship between [[chemical structure]]s and [[chemical reaction|reactivity]], in particular, applying experimental tools of [[physical chemistry]] to the study of [[organic molecules]]. Specific focal points of study include the [[chemical kinetics|rates]] of [[organic reactions]], the relative [[chemical stability|chemical stabilities]] of the starting materials, [[reactive intermediate]]s, [[transition state]]s, and products of [[chemical reaction]]s, and non-covalent aspects of [[solvation]] and [[intermolecular interaction|molecular interactions]] that influence chemical reactivity. Such studies provide theoretical and practical frameworks to understand how changes in structure in solution or solid-state contexts impact [[reaction mechanism]] and [[Reaction rate|rate]] for each [[Organic chemistry|organic reaction]] of interest.

==Application==
Physical organic chemists use [[Theory|theoretical]] and experimental approaches work to understand these foundational problems in [[organic chemistry]], including classical and statistical [[chemical thermodynamics|thermodynamic]] calculations, [[Quantum chemistry|quantum mechanical theory]] and [[computational chemistry]], as well as experimental [[spectroscopy]] (e.g., [[nuclear magnetic resonance|NMR]]), [[Spectrometer|spectrometry]] (e.g., [[mass spectrometry|MS]]), and [[crystallography]] approaches. The field therefore has applications to a wide variety of more specialized fields, including [[electrochemistry|electro-]] and [[photochemistry]], [[polymer chemistry|polymer]] and [[supramolecular chemistry]], and [[bioorganic chemistry]], [[enzymology]], and [[chemical biology]], as well as to commercial enterprises involving [[process chemistry]], [[chemical engineering]], [[materials science]] and [[nanotechnology]], and [[pharmacology]] in [[drug discovery]] by design.

==Scope==
Physical organic chemistry is the study of the relationship between structure and reactivity of [[organic molecules]]. More specifically, physical organic chemistry applies the experimental tools of [[physical chemistry]] to the study of the structure of [[organic molecules]] and provides a theoretical framework that interprets how structure influences both [[Reaction mechanism|mechanisms]] and [[Reaction rate|rates]] of [[Organic chemistry|organic reactions]]. It can be thought of as a subfield that bridges [[organic chemistry]] with [[physical chemistry]].

Physical organic chemists use both experimental and theoretical disciplines such as [[spectroscopy]], [[Spectrometer|spectrometry]], [[crystallography]], [[computational chemistry]], and [[Quantum chemistry|quantum theory]] to study both the [[chemical kinetics|rates]] of [[organic reactions]] and the relative [[chemical stability]] of the starting materials, [[transition state]]s, and products.<ref name=Anslyn>{{cite book|last1=Dougherty|first1=Dennis A.|last2=Anslyn|first2=Eric V.|title=Modern Physical Organic Chemistry|year=2006|publisher=University Science Books|location=Sausalito, CA, USA|isbn=9781891389313}}{{page needed|date=June 2015}}</ref>{{page needed|date=June 2015}} Chemists in this field work to understand the physical underpinnings of modern [[organic chemistry]], and therefore physical organic chemistry has applications in specialized areas including [[polymer chemistry]], [[supramolecular chemistry]], [[electrochemistry]], and [[photochemistry]].<ref name=Anslyn/>{{page needed|date=June 2015}}

==History==
The term ''physical organic chemistry'' was itself coined by [[Louis Hammett]] in 1940 when he used the phrase as a title for his textbook.<ref>{{Cite journal |last1=Taft |first1=R W |last2=Deno |first2=N C |last3=Skell |first3=P S |date=October 1958 |title=Physical Organic Chemistry |url=https://www.annualreviews.org/doi/10.1146/annurev.pc.09.100158.001443 |journal=Annual Review of Physical Chemistry |language=en |volume=9 |issue=1 |pages=287–314 |doi=10.1146/annurev.pc.09.100158.001443 |bibcode=1958ARPC....9..287T |issn=0066-426X}}</ref>

==Chemical structure and thermodynamics==

===Thermochemistry===
{{Main|Thermochemistry|Chemical thermodynamics}}
Organic chemists use the tools of [[thermodynamics]] to study the [[chemical bond|bonding]], [[chemical stability|stability]], and energetics of chemical systems. This includes experiments to measure or determine the [[enthalpy]] (Δ''H''), [[entropy]] (Δ''S''), and [[Gibbs' free energy]] (Δ''G'') of a reaction, transformation, or isomerization. Chemists may use various chemical and mathematical analyses, such as a [[Van 't Hoff plot]], to calculate these values.

Empirical constants such as [[bond dissociation energy]], [[standard heat of formation]] (Δ<sub>f</sub>''H''°), and [[heat of combustion]] (Δ<sub>c</sub>''H''°) are used to predict the stability of molecules and the change in [[enthalpy]] (Δ''H'') through the course of the reactions. For complex molecules, a Δ<sub>f</sub>''H''° value may not be available but can be estimated using molecular fragments with known [[Enthalpy of formation|heats of formation]]. This type of analysis is often referred to as [[Benson group increment theory]], after chemist Sidney Benson who spent a career developing the concept.<ref name=Anslyn/>{{page needed|date=June 2015}} <ref>{{cite journal|last=Cohen|first=N.|author2=Benson, S. W.|title=Estimation of heats of formation of organic compounds by additivity methods|journal=Chemical Reviews|date=1 November 1993|volume=93|issue=7|pages=2419–2438|doi=10.1021/cr00023a005}}</ref><ref>{{cite journal|last=Benson|first=Sidney W.|author2=Cruickshank, F. R. |author3=Golden, D. M. |author4=Haugen, Gilbert R. |author5=O'Neal, H. E. |author6=Rodgers, A. S. |author7=Shaw, Robert |author8= Walsh, R. |title=Additivity rules for the estimation of thermochemical properties|journal=Chemical Reviews|date=1 June 1969|volume=69|issue=3|pages=279–324|doi=10.1021/cr60259a002}}</ref>

The thermochemistry of reactive intermediates—[[carbocations]], [[carbanions]], and [[Radical (chemistry)|radicals]]—is also of interest to physical organic chemists. Group increment data are available for radical systems.<ref name=Anslyn/>{{page needed|date=June 2015}} Carbocation and carbanion stabilities can be assessed using hydride ion affinities and [[Acid dissociation constant|pK<sub>a</sub> values]], respectively.<ref name=Anslyn/>{{page needed|date=June 2015}}

===Conformational analysis===
One of the primary methods for evaluating chemical stability and energetics is [[Conformational isomerism|conformational analysis]]. Physical organic chemists use conformational analysis to evaluate the various types of [[Strain (chemistry)|strain]] present in a molecule to predict reaction products.<ref>{{cite book|last1=Carey|first1=Francis A.|title=Organic Chemistry|year=2008|publisher=McGraw-Hill|location=Boston, MA, USA|isbn=9780073047874|edition=7th}}{{page needed|date=June 2015}}</ref>{{page needed|date=June 2015}} Strain can be found in both acyclic and cyclic molecules, manifesting itself in diverse systems as [[Alkane stereochemistry|torsional strain]], [[allylic strain]], [[ring strain]], and [[Pentane interference|''syn''-pentane strain]].<ref name=Anslyn/>{{page needed|date=June 2015}} [[A-values]] provide a quantitative basis for predicting the [[Conformational analysis|conformation]] of a substituted [[cyclohexane]], an important class of cyclic organic compounds whose reactivity is strongly guided by conformational effects. The [[A value|A-value]] is the difference in the [[Gibbs' free energy]] between the axial and equatorial forms of substituted cyclohexane, and by adding together the [[A-values]] of various [[substituent]]s it is possible to quantitatively predict the preferred conformation of a cyclohexane derivative.

In addition to molecular stability, conformational analysis is used to predict reaction products. One commonly cited example of the use of [[conformational analysis]] is a bi-molecular [[elimination reaction]] (E2). This reaction proceeds most readily when the nucleophile attacks the species that is [[antiperiplanar]] to the leaving group. A [[molecular orbital]] analysis of this phenomenon suggest that this conformation provides the best overlap between the electrons in the R-H σ [[bonding orbital]] that is undergoing nucleophilic attack and the empty σ* [[antibonding]] orbital of the R-X bond that is being broken.<ref name=Isaacs95>{{cite book|last=Isaacs|first=Neil S.|title=Physical Organic Chemistry|year=1995|publisher=Longman Scientific & Technical|location=Harlow, ESS, ENG|isbn=978-0582218635|edition=2nd|url=https://archive.org/details/physicalorganicc00neil}}{{page needed|date=June 2015}}</ref>{{page needed|date=June 2015}} By exploiting this effect, [[conformational analysis]] can be used to design molecules that possess enhanced reactivity.

The physical processes which give rise to [[Alkane stereochemistry|bond rotation barriers]] are complex, and these barriers have been extensively studied through experimental and theoretical methods.<ref>{{cite journal|last=Mo|first=Yirong|author2=Gao, Jiali|title=Theoretical Analysis of the Rotational Barrier of Ethane|journal=Accounts of Chemical Research|date=1 February 2007|volume=40|issue=2|pages=113–119|doi=10.1021/ar068073w|pmid=17309192|s2cid=16332261}}</ref><ref>{{cite journal|last=Liu|first=Shubin|title=Origin and Nature of Bond Rotation Barriers: A Unified View|journal=The Journal of Physical Chemistry A|date=7 February 2013|volume=117|issue=5|pages=962–965|doi=10.1021/jp312521z|pmid=23327680|bibcode=2013JPCA..117..962L}}</ref><ref>{{cite journal|last=Liu|first=Shubin|author2=Govind, Niranjan|title=Toward Understanding the Nature of Internal Rotation Barriers with a New Energy Partition Scheme: Ethane and-Butane|journal=The Journal of Physical Chemistry A|date=1 July 2008|volume=112|issue=29|pages=6690–6699|doi=10.1021/jp800376a|pmid=18563887|bibcode=2008JPCA..112.6690L}}</ref>  A number of recent articles have investigated the predominance of the [[Steric effects|steric]], [[intermolecular force|electrostatic]], and [[Hyperconjugation|hyperconjugative]] contributions to rotational barriers in [[ethane#ethane barrier|ethane]], [[butane]], and more substituted molecules.<ref>{{cite journal|last=Yamamoto|first=Takuhei|author2=Chen, Pi-Yu |author3=Lin, Guangxin |author4=Błoch-Mechkour, Anna |author5=Jacobsen, Neil E. |author6=Bally, Thomas |author7= Glass, Richard S. |title=Synthesis and rotation barriers in 2, 6-Di-(-anisyl) anisole|journal=Journal of Physical Organic Chemistry|date=1 October 2012|volume=25|issue=10|pages=878–882|doi=10.1002/poc.2939|url=http://doc.rero.ch/record/29566/files/bal_srb.pdf}}</ref>

===Non-covalent interactions===
{{Main|Noncovalent bonding}}

[[File:Cryptand complex.svg|thumb|left|upright=1.15|[[Cryptand]] with a metal [[cation]] demonstrating [[host–guest chemistry]]. Cryptands are tricyclic compounds that tightly encapsulate the guest cation via [[Intermolecular force|electrostatic interactions]] (ion-dipole interaction).]]

Chemists use the study of intramolecular and intermolecular [[Non-covalent bonding|non-covalent bonding/interactions]] in molecules to evaluate reactivity. Such interactions include, but are not limited to, [[hydrogen bonding]], [[Intermolecular force|electrostatic interactions]] between charged molecules, [[dipole-dipole interactions]], [[Pi interaction|polar-π]] and [[Cation-pi interaction|cation-π]] interactions, [[Stacking (chemistry)|π-stacking]], [[Charge-transfer complex|donor-acceptor]] chemistry, and [[halogen bonding]]. In addition, the [[hydrophobic effect]]—the association of organic compounds in water—is an electrostatic, [[non-covalent interaction]] of interest to chemists. The precise physical origin of the hydrophobic effect originates from many [[Entropic force#Hydrophobic force|complex interactions]], but it is believed to be the most important component of [[molecular recognition|biomolecular recognition]] in water.<ref name=Anslyn/>{{page needed|date=June 2015}} For example, researchers elucidated the structural basis for folic acid recognition by folate acid receptor proteins.<ref>{{cite journal |last1=Chen |first1=Chen |last2=Ke |first2=Jiyuan |last3=Zhou |first3=X. Edward |last4=Yi |first4=Wei |last5=Brunzelle |first5=Joseph S. |last6=Li |first6=Jun |last7=Yong |first7=Eu-Leong |last8=Xu |first8=H. Eric |last9=Melcher |first9=Karsten |title=Structural basis for molecular recognition of folic acid by folate receptors |journal=Nature |date=14 July 2013 |volume=500 |issue=7463 |pages=486–489 |doi=10.1038/nature12327 |pmid=23851396 |pmc=5797940 |bibcode=2013Natur.500..486C }}</ref> The strong interaction between [[folic acid]] and [[folate receptor]] was attributed to both [[hydrogen bonds]] and [[hydrophobic interactions]]. The study of [[non-covalent interactions]] is also used to study binding and [[host–guest chemistry#Cooperativity|cooperativity]] in [[supramolecular]] assemblies and [[macrocyclic compounds]] such as [[crown ethers]] and [[cryptands]], which can act as hosts to guest molecules.

===Acid–base chemistry===
{{main|Acid–base reaction}}
[[File:PKa_phenol_vs_nitrophenol.svg|thumb|right|upright=1.35|The principles of [[Inductive effect|Induction]] and [[Resonance (chemistry)|resonance]] can be used to explain the different [[acid dissociation constant]] (or pK<sub>a</sub>) values for [[phenol]] ('''A''') and ''p''-nitrophenol ('''B'''). For '''B''', the [[electronegative]] [[nitro group]] stabilizes the conjugate base (phenoxide [[anion]]) via induction and through resonance by delocalizing the negative charge.]]

The properties of [[acid]]s and [[Base (chemistry)|bases]] are relevant to physical organic chemistry. Organic chemists are primarily concerned with [[Brønsted–Lowry]] acids/bases as proton donors/acceptors and [[Lewis acids and bases|Lewis acids/bases]] as electron acceptors/donors in organic reactions. Chemists use a series of factors developed from physical chemistry -- [[electronegativity]]/[[Inductive effect|Induction]], [[Bond-dissociation energy|bond strengths]], [[Chemical resonance|resonance]], [[Orbital hybridisation|hybridization]], [[aromaticity]], and [[solvation]]—to predict relative acidities and basicities.

The [[HSAB theory|hard/soft acid/base principle]] is utilized to predict molecular interactions and reaction direction. In general, interactions between molecules of the same type are preferred. That is, hard acids will associate with hard bases, and soft acids with soft bases. The concept of hard acids and bases is often exploited in the synthesis of inorganic [[coordination complex]]es.

==Kinetics==
{{main|Chemical kinetics}}
Physical organic chemists use the mathematical foundation of chemical kinetics to study the rates of reactions and reaction mechanisms. Unlike thermodynamics, which is concerned with the relative stabilities of the products and reactants (Δ''G''°) and their equilibrium concentrations, the study of kinetics focuses on the [[activation energy|free energy of activation]] (Δ''G''<sup>‡</sup>) -- the difference in free energy between the reactant structure and the transition state structure—of a reaction, and therefore allows a chemist to study the process of [[chemical equilibrium|equilibration]].<ref name=Anslyn/>{{page needed|date=June 2015}} Mathematically derived formalisms such as the [[Hammond's postulate|Hammond Postulate]], the [[Curtin-Hammett principle]], and the [[Microscopic reversibility|theory of microscopic reversibility]] are often applied to [[organic chemistry]]. Chemists have also used the principle of [[Thermodynamic versus kinetic reaction control|thermodynamic versus kinetic control]] to influence reaction products.

===Rate laws===
{{main|Rate equation}}
The study of [[chemical kinetics]] is used to determine the [[rate law]] for a reaction. The rate law provides a quantitative relationship between the rate of a [[chemical reaction]] and the [[concentrations]] or [[pressures]] of the chemical species present.<ref name=McQuarrie>{{cite book | last1=McQuarrie | first1=Donald A. | last2=Simon | first2= John D. | title=Physical Chemistry: A Molecular Approach | year=1997 | publisher=University Science Books | location=Sausalito, CA, USA |isbn=9780935702996 | edition=Rev. | url=https://books.google.com/books?isbn=0935702997 | access-date=21 June 2015}} Note, Amazon rather than Google allows access into this text.{{page needed|date=June 2015}}</ref>{{Page needed|date=June 2015}}  Rate laws must be determined by experimental measurement and generally cannot be elucidated from the [[chemical equation]]. The experimentally determined rate law refers to the stoichiometry of the [[Transition state|transition state structure]] relative to the ground state structure. Determination of the rate law was historically accomplished by monitoring the concentration of a reactant during a reaction through [[gravimetric analysis]], but today it is almost exclusively done through fast and unambiguous [[spectroscopic]] techniques. In most cases, the determination of rate equations is simplified by adding a large excess ("flooding") all but one of the reactants.

===Catalysis===
{{main|Catalysis}}
[[File:Catalytic reaction coordinate.jpg|thumb|right|upright=1.35|'''Reaction coordinate energy diagram for uncatalysed and catalysed reactions, the latter without and with change in mechanism.'''{{citation needed|date=June 2015}} ''Trace A.'' presents the uncatalysed reaction pathway (orange), with its free energy of activation. ''Trace B.'' presents a catalysed reaction pathway (blue), with its lowered relative free energy of activation. ''Trace C.'' presents a complex, altered reaction pathway (brown) for the same reaction proceeding by a different mechanism involving two kinetically discrete [[reactive intermediates|intermediates]].]]
The study of [[catalysis]] and catalytic reactions is very important to the field of physical organic chemistry. A [[catalyst]] participates in the chemical reaction but is not consumed in the process.<ref name=McQuarrie />{{page needed|date=June 2015}}  A catalyst lowers the [[activation energy]] barrier (Δ''G''<sup>‡</sup>), increasing the rate of a reaction by either stabilizing the transition state structure or destabilizing a key reaction intermediate, and as only a small amount of catalyst is required it can provide economic access to otherwise expensive or difficult to synthesize organic molecules. Catalysts may also influence a reaction rate by changing the [[Reaction mechanism|mechanism]] of the reaction.<ref name=Anslyn/>{{page needed|date=June 2015}}

===Kinetic isotope effect===
{{main|Kinetic isotope effect}}
Although a rate law provides the stoichiometry of the [[transition state]] structure, it does not provide any information about breaking or forming bonds.<ref name=Anslyn/>{{page needed|date=June 2015}} The substitution of an isotope near a reactive position often leads to a change in the rate of a reaction. Isotopic substitution changes the potential energy of reaction intermediates and transition states because heavier isotopes form stronger bonds with other atoms. Atomic mass affects the zero-point [[Molecular vibrations|vibrational state]] of the associated molecules, shorter and stronger bonds in molecules with heavier isotopes and longer, weaker bonds in molecules with light isotopes.<ref name=Isaacs95/>{{page needed|date=June 2015}}  Because vibrational motions will often change during a course of a reaction, due to the making and breaking of bonds, the frequencies will be affected, and the substitution of an isotope can provide insight into the reaction mechanism and rate law.

===Substituent effects===
The study of how substituents affect the reactivity of a molecule or the rate of reactions is of significant interest to chemists. Substituents can exert an effect through both [[steric]] and electronic interactions, the latter of which include [[resonance]] and [[inductive effects]]. The [[polarizability]] of molecule can also be affected. Most substituent effects are analyzed through [[Free-energy relationship|linear free energy relationships]] (LFERs). The most common of these is the [[Hammett equation|Hammett Plot Analysis]].<ref name=Anslyn/>{{page needed|date=June 2015}} This analysis compares the effect of various substituents on the ionization of [[benzoic acid]] with their impact on diverse chemical systems. The parameters of the Hammett plots are sigma (σ) and rho (ρ). The value of σ indicates the acidity of substituted benzoic acid relative to the unsubstituted form. A positive σ value indicates the compound is more acidic, while a negative value indicates that the substituted version is less acidic. The ρ value is a measure of the sensitivity of the reaction to the change in substituent, but only measures inductive effects. Therefore, two new scales were produced that evaluate the stabilization of localized charge through resonance. One is σ<sup>+</sup>, which concerns substituents that stabilize positive charges via resonance, and the other is σ<sup>−</sup> which is for groups that stabilize negative charges via resonance. [[Hammett equation|Hammett analysis]] can be used to help elucidate the possible mechanisms of a reaction. For example, if it is predicted that the [[transition state]] structure has a build-up of negative charge relative to the ground state structure, then [[polar effect|electron-donating groups]] would be expected to increase the rate of the reaction.<ref name=Anslyn/>{{page needed|date=June 2015}}

Other [[Linear free-energy relationship|LFER]] scales have been developed. [[Steric effects|Steric]] and polar effects are analyzed through [[Taft equation|Taft Parameters]]. Changing the solvent instead of the reactant can provide insight into changes in charge during the reaction. The [[Grunwald-Winstein equation|Grunwald-Winstein Plot]] provides quantitative insight into these effects.<ref name=Anslyn/>{{page needed|date=June 2015}} <ref>{{cite journal|last=Kevill|first=Dennis N.|author2=D'Souza, Malcolm J.|title=Concerning the development of scales of solvent ionizing power based on solvolyses of benzylic substrates|journal=Journal of Physical Organic Chemistry|date=1 June 1992|volume=5|issue=6|pages=287–294|doi=10.1002/poc.610050602}}</ref>

===Solvent effects===
{{main|Solvent effects}}
{{primary sources|section|date=June 2015}}
[[Solvents]] can have a powerful effect on [[solubility]], [[Chemical stability|stability]], and [[reaction rate]]. A change in solvent can also allow a chemist to influence the [[Thermodynamic versus kinetic reaction control|thermodynamic or kinetic control]] of the reaction. Reactions proceed at different rates in different solvents due to the change in charge distribution during a chemical transformation. Solvent effects may operate on the ground state and/or [[transition state]] structures.<ref name=Anslyn/>{{page needed|date=June 2015}}

An example of the effect of solvent on organic reactions is seen in the [[Solvent effects#Reaction examples|comparison of S<sub>N</sub>1 and S<sub>N</sub>2 reactions]].<ref>{{cite book|last1=Reichardt|first1=Christian|last2=Welton|first2=Thomas|title=Solvents and solvent effects in organic chemistry.|date=2011|publisher=Wiley-VCH|location=Weinheim, Germany|isbn=978-3-527-32473-6|edition=4th, updated and enl.}}</ref>{{explain|date=June 2015}}{{example needed|date=December 2017}}

[[Solvent]] can also have a significant effect on the [[thermodynamic equilibrium]] of a system, for instance as in the case of [[Solvent effects#Keto enol equilibria|keto-enol tautomerizations]]. In [[Protic solvent|non-polar aprotic]] solvents, the [[enol]] form is strongly favored due to the formation of an intramolecular [[hydrogen-bond]], while in [[Chemical polarity|polar]] [[aprotic]] solvents, such as [[methylene chloride]], the [[enol]] form is less favored due to the interaction between the polar solvent and the polar [[diketone]].{{example needed|date=December 2017}} In [[protic]] solvents, the equilibrium lies towards the keto form as the intramolecular [[hydrogen bond]] competes with hydrogen bonds originating from the solvent.<ref>{{cite journal|last=Mills|first=Sander G.|author2=Beak, Peter|title=Solvent effects on keto-enol equilibria: tests of quantitative models|journal=The Journal of Organic Chemistry|date=1 April 1985|volume=50|issue=8|pages=1216–1224|doi=10.1021/jo00208a014}}</ref>{{primary source inline|date=June 2015}}{{primary source inline|date=June 2015}} <ref>{{cite journal|last=Emsley|first=John|author2=Freeman, Neville J.|title=β-diketone interactions|journal=Journal of Molecular Structure|date=1 October 1987|volume=161|issue=1–2|pages=193–204|doi=10.1016/0022-2860(87)85074-3|bibcode=1987JMoSt.161..193E}}</ref>{{primary source inline|date=June 2015}}{{primary source inline|date=June 2015}} <ref>{{cite journal|last=Schlund|first=Sebastian |author2=Basílio Janke, Eline M. |author3=Weisz, Klaus |author4=Engels, Bernd |title=Predicting the tautomeric equilibrium of acetylacetone in solution. I. The right answer for the wrong reason?|journal=Journal of Computational Chemistry|volume=31 |issue=4 |pages=665–70 |date=1 January 2009|doi=10.1002/jcc.21354|pmid=19557765 |s2cid=6003410 }}</ref>{{primary source inline|date=June 2015}}{{primary source inline|date=June 2015}}

[[File:Epimerization.jpg|thumb|right|upright=2| '''[[Solvent effects]] and the [[epimerization]] of a [[Chiral (chemistry)|chiral]] [[Grignard reagent]].'''<ref name=GaoJACS13/>{{primary source inline|date=June 2015}} The ''cis'' form of the reagent is stabilized, and so more strongly favored, in the reaction solvent [[THF]], over [[diethyl ether]]; a larger equilibrium constant is observed in [[THF]].]]
A modern example of the study of [[solvent effects]] on [[chemical equilibrium]] can be seen in a study of the [[epimerization]] of [[Chirality (chemistry)|chiral]] cyclopropylnitrile [[Grignard reagents]].<ref name=GaoJACS13>{{cite journal|last=Gao|first=Ming |author2=Patwardhan, Neeraj N. |author3=Carlier, Paul R.|title=Stereochemical Inversion of a Cyano-Stabilized Grignard Reagent: Remarkable Effects of the Ethereal Solvent Structure and Concentration|journal=[[Journal of the American Chemical Society|J. Am. Chem. Soc.]]|volume=135|issue=38|pages=14390–14400|doi=10.1021/ja407348s|pmid=23978216 |year=2013 }}</ref>{{primary source inline|date=June 2015}}{{primary source inline|date=June 2015}} This study reports that the [[equilibrium constant]] for the [[Cis-trans isomerism|''cis'' to ''trans'' isomerization]]  of the [[Grignard reagent]] is much greater—the preference for the ''cis'' form is enhanced—in [[THF]] as a reaction solvent, over [[diethyl ether]]. However, the faster rate of ''[[Cis-trans isomerism|cis-trans isomerization]]'' in [[THF]] results in a loss of [[stereochemical]] purity. This is a case where understanding the effect of solvent on the stability of the [[molecular configuration]] of a reagent is important with regard to the selectivity observed in an [[asymmetric synthesis]].

==Quantum chemistry==
{{main|Quantum chemistry}}
Many aspects of the structure-reactivity relationship in organic chemistry can be rationalized through [[resonance (chemistry)|resonance]], electron pushing, [[inductive effects|induction]], the [[octet rule|eight electron rule]], and s-p [[orbital hybridization|hybridization]], but these are only helpful formalisms and do not represent physical reality. Due to these limitations, a true understanding of physical organic chemistry requires a more rigorous approach grounded in [[particle physics]]. [[Quantum chemistry]] provides a rigorous theoretical framework capable of predicting the properties of molecules through calculation of a molecule's electronic structure, and it has become a readily available tool in physical organic chemists in the form of popular software packages.{{citation needed|date=June 2015}}  The power of quantum chemistry is built on the wave model of the [[atom]], in which the [[atomic nucleus|nucleus]] is a very small, positively charged sphere surrounded by a diffuse [[electron]] cloud. Particles are defined by their associated [[wavefunction]], an equation which contains all information associated with that particle.<ref name=McQuarrie/>{{Page needed|date=June 2015}} All information about the system is contained in the wavefunction. This information is extracted from the [[wavefunction]] through the use of mathematical operators.
{{Equation box 1
|indent=:
|title='''Time-independent Schrödinger equation''' (''general'')
|equation=<math>E\Psi=\hat H \Psi</math>
|cellpadding
|border
|border colour = #50C878
|background colour = #ECFCF4}}
The energy associated with a particular [[wavefunction]], perhaps the most important information contained in a wavefunction, can be extracted by solving the [[Schrödinger equation]] (above, Ψ is the wavefunction, E is the energy, and Ĥ is the Hamiltonian operator)<ref name=McQuarrie />{{page needed|date=June 2015}} in which an appropriate [[Hamiltonian operator]] is applied. In the various forms of the Schrödinger equation, the overall size of a particle's probability distribution increases with decreasing particle mass. For this reason, nuclei are of negligible size in relation to much lighter [[electrons]] and are treated as point charges in practical applications of quantum chemistry.

Due to complex interactions which arise from electron-electron repulsion, algebraic solutions of the Schrödinger equation are only possible for systems with one electron such as the [[hydrogen]] atom, H<sub>2</sub><sup>+</sup>, H<sub>3</sub><sup>2+</sup>, etc.; however, from these simple models arise all the familiar [[atomic orbitals|atomic]] (s,p,d,f) and bonding (σ,π) orbitals. In systems with multiple electrons, an overall multielectron wavefunction describes all of their properties at once. Such wavefunctions are generated through the linear addition of single electron wavefunctions to generate an initial guess, which is repeatedly modified until its associated energy is minimized. Thousands of guesses are often required until a satisfactory solution is found, so such calculations are performed by powerful computers. Importantly, the solutions for atoms with multiple electrons give properties such as diameter and [[electronegativity]] which closely mirror experimental data and the patterns found in the [[periodic table]]. The solutions for molecules, such as [[methane]], provide exact representations of their [[electronic structure]] which are unobtainable by experimental methods.{{citation needed|date=June 2015}} Instead of four discrete σ-bonds from carbon to each hydrogen atom, theory predicts a set of four bonding molecular orbitals which are delocalized across the entire molecule. Similarly, the true electronic structure of [[1,3-butadiene]] shows delocalized [[pi bond|π-bonding]] [[molecular orbitals]] stretching through the entire molecule rather than two isolated double bonds as predicted by a simple [[Lewis structure]].{{citation needed|date=June 2015}}

A complete electronic structure offers great predictive power for organic transformations and dynamics, especially in cases concerning [[aromaticity|aromatic molecules]], extended [[pi bond|π systems]], [[organometallic chemistry|bonds between metal ions and organic molecules]], molecules containing nonstandard [[heteroatoms]] like [[organoselenium chemistry|selenium]] and [[organoboron chemistry|boron]], and the [[conformational isomerism|conformational dynamics]] of large molecules such as [[proteins]] wherein the many approximations in chemical formalisms make structure and reactivity prediction impossible. An example of how electronic structure determination is a useful tool for the physical organic chemist is the metal-catalyzed dearomatization of [[benzene]]. [[(Benzene)chromium tricarbonyl|Chromium tricarbonyl]] is highly [[electrophilic]] due to the withdrawal of electron density from filled [[chromium]] d-orbitals into [[antibonding]] [[carbon monoxide|CO]] orbitals, and is able to [[covalent bond|covalently bond]] to the face of a benzene molecule through delocalized [[molecular orbitals]]. The CO [[ligands]] [[inductive effect|inductively]] draw electron density from benzene through the [[chromium]] atom, and dramatically activate benzene to [[nucleophilic]] attack. Nucleophiles are then able to react to make hexacyclodienes, which can be used in further transformations such as [[Diels-Alder Reaction|Diels Alder cycloadditions]].<ref>{{cite journal |last1=Semmelhack |first1=M. F. |last2=Hall |first2=H. T. |last3=Yoshifuji |first3=M. |title=.eta.5-Cyclohexadienyltricarbonylchromium(0) intermediates in the reaction of carbanions with .eta.6-arenetricarbonylchromium(0) |journal=Journal of the American Chemical Society |date=September 1976 |volume=98 |issue=20 |pages=6387–6389 |doi=10.1021/ja00436a056 }}</ref>

[[File:Chromium Promoted Dearomatization of Benzene.tif|thumb|center|upright=2.25|Chromium's unoccupied d-orbitals mediate electron withdrawal from benzene, greatly enhancing its electrophilicity.]]

Quantum chemistry can also provide insight into the mechanism of an organic transformation without the collection of any experimental data. Because wavefunctions provide the total energy of a given molecular state, guessed molecular geometries can be optimized to give relaxed molecular structures very similar to those found through experimental methods.<ref>{{cite book|last=Schaefer III|first=Henry F. | title=Quantum Chemistry: The Development of ''ab initio'' Methods in Molecular Electronic Structure Theory | year=2004 | publisher=R.R. Donnelly (Courier, Dover) | location=Chicago, IL, USA | isbn=978-0486432465 | url=https://books.google.com/books?isbn=0486432467 | access-date= 21 June 2015}}{{page needed|date=June 2015}}</ref>{{page needed|date=June 2015}} [[Reaction coordinate]]s can then be simulated, and [[transition state]] structures solved. Solving a complete energy surface for a given reaction is therefore possible, and such calculations have been applied to many problems in organic chemistry where kinetic data is unavailable or difficult to acquire.<ref name=Anslyn/>{{page needed|date=June 2015}}

==Spectroscopy, spectrometry, and crystallography==
Physical organic chemistry often entails the identification of molecular structure, dynamics, and the concentration of reactants in the course of a reaction. The interaction of molecules with light can afford a wealth of data about such properties through nondestructive [[spectroscopy|spectroscopic experiments]], with [[light]] absorbed when the energy of a photon matches the difference in energy between two [[energy level|states]] in a molecule and emitted when an excited state in a molecule collapses to a lower energy state. Spectroscopic techniques are broadly classified by the type of excitation being probed, such as [[Infrared spectroscopy|vibrational]], [[rotational spectroscopy|rotational]], [[Ultraviolet–visible spectroscopy|electronic]], [[nuclear magnetic resonance]] (NMR), and [[electron paramagnetic resonance]] spectroscopy. In addition to spectroscopic data, structure determination is often aided by complementary data collected from [[crystallography|X-Ray diffraction]] and [[mass spectrometry|mass spectrometric]] experiments.<ref name=drago>{{cite book|last=Drago|first=Russell S.|title=Physical Methods for Chemists|year=1992|publisher=Saunders|location=Ft. Worth, TX, USA|isbn= 9780030970375|edition=2nd|url=https://books.google.com/books?isbn=0030970377|access-date=22 June 2014}}{{page needed|date=June 2015}}</ref>{{page needed|date=June 2015}}

===NMR and EPR spectroscopy===
{{main|Nuclear magnetic resonance|Electron paramagnetic resonance}}
[[Image:NMR splitting.gif|thumb|upright=1.3|Splitting of nuclei spin states in an external magnetic field]]
One of the most powerful tools in physical organic chemistry is [[NMR spectroscopy]]. An external [[magnetic field]] applied to a [[paramagnetism|paramagnetic]] nucleus generates two discrete states, with positive and negative [[Spin (physics)|spin]] values diverging in [[energy]]; the difference in energy can then be probed by determining the frequency of light needed to excite a change in spin state for a given magnetic field. Nuclei that are not indistinguishable in a given molecule absorb at different frequencies, and the integrated peak area in an NMR spectrum is proportional to the number of nuclei responding to that frequency.<ref name = keeler-2>{{cite web | publisher = [[University of California, Irvine]] | work = Understanding NMR Spectroscopy | author = James Keeler | url = http://www-keeler.ch.cam.ac.uk/lectures/Irvine/chapter2.pdf | title = NMR and energy levels (Ch.2) | access-date = 2013-10-26}}</ref> It is possible to quantify the relative concentration of different organic molecules simply by [[Integral|integration]] peaks in the spectrum, and many kinetic experiments can be easily and quickly performed by following the progress of a reaction within one NMR sample. [[Proton NMR]] is often used by the synthetic organic chemist because protons associated with certain [[functional groups]] give characteristic absorption energies, but NMR spectroscopy can also be performed on [[isotopes]] of [[nitrogen]], [[carbon]], [[fluorine]], [[phosphorus]], [[boron]], and a [[nuclear magnetic resonance#isotopes|host of other elements]]. In addition to simple absorption experiments, it is also possible to determine the rate of fast atom exchange reactions through suppression exchange measurements, interatomic distances through multidimensional [[nuclear overhauser effect|nuclear Overhauser effect]] experiments, and through-bond spin-spin coupling through [[Two-dimensional nuclear magnetic resonance spectroscopy|homonuclear correlation spectroscopy]].<ref>{{cite book|last=Keeler|first=James|title=Understanding NMR spectroscopy|year=2010|publisher=Wiley|location=Chichester|isbn=978-0-470-74608-0|edition=2nd}}</ref> In addition to the spin excitation properties of nuclei, it is also possible to study the properties of organic [[radical (chemistry)|radicals]] through the same fundamental technique. Unpaired electrons also have a net [[electron magnetic moment|spin]], and an external magnetic field allows for the extraction of similar information through [[electron paramagnetic resonance]] (EPR) spectroscopy.<ref name=Anslyn/>{{page needed|date=June 2015}}

===Vibrational spectroscopy===
{{main|Infrared spectroscopy}}
[[Image:HarmOsziFunktionen.png|upright=1.6|thumb|The first eight states in a quantum harmonic oscillator. The horizontal axis shows the position ''x'', and the vertical axis shows the energy. Note the even spacing of the energy levels: all excitations between adjacent states require the same energy, and therefore absorb the same wavelength of light]]
[[Infrared spectroscopy|Vibrational spectroscopy]], or infrared (IR) spectroscopy, allows for the identification of [[functional groups]] and, due to its low expense and robustness, is often used in teaching labs and the real-time monitoring of reaction progress in difficult to reach environments (high pressure, high temperature, gas phase, [[phase boundaries]]). [[Molecular vibrations]] are quantized in an analogous manner to electronic wavefunctions, with integer increases in frequency leading to higher [[energy level|energy states]]. The difference in energy between vibrational states is nearly constant, often falling in the energy range corresponding to infrared photons, because at normal temperatures molecular vibrations closely resemble [[harmonic oscillators]]. It allows for the crude identification of [[functional groups]] in [[organic molecules]], but spectra are complicated by vibrational coupling between nearby functional groups in complex molecules. Therefore, its utility in structure determination is usually limited to simple molecules. Further complicating matters is that some vibrations do not induce a change in the [[dipole#molecular dipoles|molecular dipole moment]] and will not be observable with standard IR absorption spectroscopy. These can instead be probed through [[Raman spectroscopy]], but this technique requires a more elaborate apparatus and is less commonly performed. However, as Raman spectroscopy relies on light scattering it can be performed on microscopic samples such as the surface of a [[heterogeneous catalyst]], a [[phase boundary]], or on a one microliter (μL) subsample within a larger liquid volume.<ref name=drago />{{page needed|date=June 2015}} The applications of [[vibrational spectroscopy]] are often used by astronomers to study the composition of [[molecular cloud|molecular gas clouds]], [[extrasolar planet|extrasolar planetary atmospheres]], and [[planet|planetary surfaces]].

===Electronic excitation spectroscopy===
{{main|Ultraviolet-visible spectroscopy}}
[[Ultraviolet–visible spectroscopy|Electronic excitation spectroscopy]], or ultraviolet-visible (UV-vis) spectroscopy, is performed in the [[visible spectrum|visible]] and [[ultraviolet]] regions of the [[electromagnetic spectrum]] and is useful for probing the difference in energy between the highest energy occupied (HOMO) and lowest energy unoccupied (LUMO) [[molecular orbital]]s. This information is useful to physical organic chemists in the design of organic [[photochemistry|photochemical]] systems and [[dye]]s, as absorption of different wavelengths of [[visible light]] give [[organic molecules]] color. A detailed understanding of an electronic structure is therefore helpful in explaining electronic excitations, and through careful control of molecular structure it is possible to tune the HOMO-LUMO gap to give desired colors and excited state properties.<ref name="Visible and Ultraviolet Spectroscopy">{{cite web|last=Reusch|first=William|url=http://www2.chemistry.msu.edu/faculty/reusch/VirtTxtJml/Spectrpy/UV-Vis/spectrum.htm|title=Visible and Ultraviolet Spectroscopy|work=Michigan State University Website|publisher=Michigan State University|access-date=26 October 2013}}</ref>

====Mass spectrometry====
{{main|Mass spectrometry}}
[[Mass spectrometry]] is a technique which allows for the measurement of [[molecular mass]] and offers complementary data to [[spectroscopic]] techniques for structural identification. In a typical experiment a gas phase sample of an [[organic material]] is [[ionized]] and the resulting [[ion|ionic species]] are accelerated by an applied [[electric field]] into a [[magnetic field]]. The deflection imparted by the magnetic field, often combined with the time it takes for the molecule to reach a detector, is then used to calculate the [[molecular mass|mass]] of the molecule. Often in the course of sample [[ionization]] large molecules break apart, and the resulting data show a parent mass and a number of smaller fragment masses; such fragmentation can give rich insight into the sequence of proteins and nucleic acid polymers. In addition to the mass of a molecule and its fragments, the distribution of [[isotope|isotopic variant]] masses can also be determined and the qualitative presence of certain elements identified due to their characteristic natural [[isotope analysis|isotope distribution]]. The ratio of fragment mass population to the parent ion population can be compared against a library of empirical fragmentation data and matched to a known molecular structure.<ref>{{cite book|editor1=Alan J. Handley |editor2=Edward R. Adlard|title=Gas chromatographic techniques and applications|year=2000|publisher=CRC Press |location=Boca Raton, FL|isbn=978-0-8493-0514-6|page=168}}</ref> Combined [[Gas chromatography–mass spectrometry|gas chromatography and mass spectrometry]] is used to qualitatively identify molecules and quantitatively measure concentration with great precision and accuracy, and is widely used to test for small quantities of biomolecules and illicit narcotics in blood samples. For synthetic organic chemists it is a useful tool for the characterization of new compounds and reaction products.

====Crystallography====
{{main|Crystallography}}
[[Image:Buckycatcher JACS 2007 V129 p3843.jpg|thumb|Single crystal structure of a [[fullerene]] caught in molecular tweezers.]]
Unlike spectroscopic methods, [[X-ray crystallography]] always allows for unambiguous structure determination and provides precise bond angles and lengths totally unavailable through spectroscopy. It is often used in physical organic chemistry to provide an absolute [[molecular geometry|molecular configuration]] and is an important tool in improving the synthesis of a pure [[enantiomeric]] substance. It is also the only way to identify the position and bonding of elements that lack an [[NMR spectroscopy|NMR]] active [[atomic nucleus|nucleus]] such as [[oxygen]]. Indeed, before x-ray structural determination methods were made available in the early 20th century all organic structures were entirely conjectural: [[Tetrahedral molecular geometry|tetrahedral]] [[carbon]], for example, was only confirmed by the [[crystal structure]] of [[diamond]],<ref>{{cite journal |last1=Bragg |first1=W. H. |last2=Bragg |first2=W. L. |title=The Structure of the Diamond |journal=Nature |date=July 1913 |volume=91 |issue=2283 |pages=557 |doi=10.1038/091557a0 |bibcode=1913Natur..91..557B |s2cid=3987932 |url=https://zenodo.org/record/1429564 |doi-access=free }}</ref> and the delocalized structure of benzene was confirmed by the [[crystal structure]] of [[hexamethylbenzene]].<ref>{{cite journal |last1=Lonsdale |first1=K. |title=The Structure of the Benzene Ring |journal=Nature |date=November 1928 |volume=122 |issue=3082 |pages=810 |doi=10.1038/122810c0 |bibcode=1928Natur.122..810L |s2cid=4105837 |doi-access=free }}</ref> While [[crystallography]] provides organic chemists with highly satisfying data, it is not an everyday technique in organic chemistry because a perfect [[single crystal]] of a target compound must be grown. Only complex molecules, for which NMR data cannot be unambiguously interpreted, require this technique. In the example below, the structure of the host–guest complex would have been quite difficult to solve without a single crystal structure: there are no protons on the [[fullerene]], and with no covalent bonds between the two halves of the organic complex spectroscopy alone was unable to prove the hypothesized structure.{{citation needed|date=February 2020}}

==See also==
* ''[[Journal of Physical Organic Chemistry]]''
* [https://www.gaussian.com/ Gaussian, an example of a commercially available quantum mechanical software package used. particularly, in academic settings]

==References==
{{Reflist}}

==Further reading==

===General===
* Peter Atkins & Julio de Paula, 2006, "Physical chemistry," 8th Edn., New York, NY, USA:Macmillan, {{ISBN|0716787598}}, accessed 21 June 2015. [E.g., see p.&nbsp;422 for a group theoretical/symmetry description of [[atomic orbital]]s contributing to bonding in methane, CH<sub>4</sub>, and pp.&nbsp;390f for estimation of π-electron binding energy for [[1,3-butadiene]] by the Hückel method.]
* Thomas H. Lowry & Kathleen Schueller Richardson, 1987, ''Mechanism and Theory in Organic Chemistry,'' 3rd Edn., New York, NY, USA:Harper & Row, {{ISBN|0060440848}}, accessed 20 June 2015. [The authoritative textbook on the subject, containing a number of appendices that provide technical details on molecular orbital theory, kinetic isotope effects, transition state theory, and radical chemistry.]
* Eric V. Anslyn & Dennis A. Dougherty, 2006, ''Modern Physical Organic Chemistry'', Sausalito, Calif.: University Science Books, {{ISBN|1891389319}}. [A modernized and streamlined treatment with an emphasis on applications and cross-disciplinary connections.]
* Michael B. Smith & Jerry March, 2007, "March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure," 6th Ed., New York, NY, USA:Wiley & Sons, {{ISBN|0470084944}}, accessed 19 June 2015.
* Francis A. Carey & Richard J. Sundberg, 2006, "Advanced Organic Chemistry: Part A: Structure and Mechanisms," 4th Edn., New York, NY, USA:Springer Science & Business Media, {{ISBN|0306468565}}, accessed 19 June 2015.
* Hammett, Louis P. (1940) ''[https://archive.org/details/in.ernet.dli.2015.168388 Physical Organic Chemistry]'', New York, NY, USA: McGraw Hill, accessed 20 June 2015.

===History===
* {{cite journal|last=Hammond|first=George S.|title=Physical organic chemistry after 50 years: It has changed, but is it still there?|journal=[[Pure and Applied Chemistry|Pure Appl. Chem.]]|year=1997|volume=69|issue=9|pages=1919–22|doi=10.1351/pac199769091919|s2cid=53723796|url=http://pac.iupac.org/publications/pac/pdf/1997/pdf/6909x1919.pdf|access-date=20 June 2015}} [An outstanding starting point on the history of the field, from a critically important contributor, referencing and discussing the early Hammett text, etc.]

===Thermochemistry===
*  [[L. K. Doraiswamy]], 2005, "Estimation of properties of organic compounds (Ch. 3)," pp.&nbsp;36–51, 118-124 (refs.), in ''Organic Synthesis Engineering,'' Oxford, Oxon, ENG:Oxford University Press, {{ISBN|0198025696}}, accessed 22 June 2015. (This book chapter surveys a very wide range of physical properties and their estimation, including the narrow list of thermochemical properties appearing in the June 2015 WP article, placing the Benson et al. method alongside many other methods. L. K. Doraiswamy is ''Anson Marston Distinguished Professor of Engineering'' at [[Iowa State University]].)
* {{cite book |doi=10.1021/bk-1998-0677.ch001 |chapter=Computational Thermochemistry |series=ACS Symposium Series |year=1998 |last1=Irikura |first1=Karl K. |last2=Frurip |first2=David J. |volume=677 |pages=2–18 |editor1-last=Irikura |editor1-first=Karl K. |editor2-last=Frurip |editor2-first=David J. |title=Computational Thermochemistry: Prediction and Estimation of Molecular Thermodynamics |publisher=American Chemical Society |isbn=978-0-8412-3533-5 }}

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[[Category:Physical organic chemistry| ]]
[[Category:Organic chemistry]]