**Glossary of terms used in theoretical
organic chemistry **

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[C] [D] [E]
[F] [G] [H]
[I] [J-K] [L]
[M]

[N] [O] [P]
[Q-R] [S] [T]
[U-V] [W-Z]

# **Q-R**

**Quantitative structure-activity
relationships (QSAR) **- Mathematical models designed for the
correlation of various types of biological activity, chemical reactivity,
equilibria, physical and physicochemical properties with electronic,
steric, hydrophobic and other factors of a molecular structure of
a given series of compounds such as substituent constants,
*topological indices* as well as with solvent and other physicochemical
parameters. IUPAC PHOTOCHEMICAL GLOSSARY
(1988). HANSCH (1993).

**Quantum mechanical resonance energy
(QMRE)** - see* Resonance energy, various
types of*.

**Radiationless transition
- **A transition between two states of a system without photon emission
or absorption.

**Radical** - A *molecular
entity* possessing an *atomic*
or *molecular orbital *occupied
by one electron. A radical (*free
radical*) has a net electronic spin experimentally observable
in paramagnetic behaviour. Paramagnetic metal ions are not normally
regarded as radicals. IUPAC PHYSICAL
ORGANIC CHEMISTRY GLOSSARY (1994).

**Reaction coordinate **- A structural
parameter or a certain function of several of these, the variation of
which along the* reaction path
*defines the *energy profile*
of a given reaction. In mathematical terms, the arc length along
the *minimum energy reaction path.*

**Reaction field*** *-* *The
response field from the induced* polarization
*charges of an outer medium which creates an extra potential
at the immersed molecule. The reaction field interacts with the solute
molecular system giving rise to a solvent effect (see also* solvation
energy*).

**Reaction graph **-** **Topological
representation of either all possible reactions that occur (or can occur)
in a given chemical system or a subset of these reactions, for which
each vertex stands for a component of the system (molecule or ion) and
each edge connecting two given vertices stands for the reaction path.
Most usable are the reaction graphs for intramolecular rearrangements,
with vertices standing for isomers and edges standing for their
isomerization paths. BALABAN (1994).

**Reaction path **- The gradient line
(or classic trajectory) in the configurational space interconnecting
the reactant and product energy minima on the *potential
energy surface*. BASILEVSKY and SHAMOV
(1981); EYRING and POLANYI (1931); MINYAEV
(1994); TRUHLAR, STECKLER, and GORDON
(1987).

See also *Intrinsic reaction coordinate,
Minimum energy reaction path.*

**Reaction path Hamiltonian
(RPH) **-** **A *Hamiltonian*
that deals with the dynamics occurring in a small amplitude many-dimensional
harmonic valley centered on the *reaction
path* as determined by the *intrinsic
reaction coordinate*. By calculating curvature properties of
the reaction path and coupling between the small amplitude degrees
of freedom, insight into the mechanism of energy disposal along
the reaction path is conveniently gained. MILLER,
HANDY, and ADAMS (1980).

**Reaction profile **-** **see**
***Energy profile*

**Relative hardness **- The difference
between the values of the absolute hardnesses (h)
of a given molecule and the corresponding reference structure (h_{a}):
h_{r} = h -
h_{a} . The values of relative hardnesses
correlate well with the* resonance energies*
of cyclic compounds and may be used as an index of *aromaticity*.

**Relativistic effects** - Corrections
to exact nonrelativistic energy from the fact that inner shell electrons
in heavy atoms move with velocities comparable in order of magnitude
to the velocity of light.The most important relativistic effect
is *spin-orbit coupling.
*See also* spin-spin coupling.
*PYKKÖ (1986)

**Renner effect **- The dynamic instability
of linear molecular species in the *degenerate
electronic states*. The Renner effect is a particular case
of the *Jahn-Teller effect.*

**Reorganization energy **-
The energy (term l in the *Marcus
equation*) required for all structural adjustments (in the
reactants and in the surrounding solvent molecules) which are needed
in order to arrange the reactants in the reactive configuration.
IUPAC: PHYSICAL ORGANIC CHEMISTRY
GLOSSARY (1994).

**Resonance effect** - see *Mesomeric
effect*.

**Resonance energy (RE), various types
of **-** **Part of the *total energy*
due to electron *delocalization*.
To find the value of the resonance energy (RE), the difference must
be calculated between a quantity characterizing experimentally determined
energy of a given molecule (such as *heat
of atomization* or* heat
of formation*) and the same characteristic obtained with the
aid of an additive scheme, e.g. sum of the *bond
energies* (*thermochemical
resonance energy*). When the
*total energy* or the heat of formation (atomization) is calculated
with use of quantum mechanical methods, the RE value is referred
to as the *quantum* *mechanical
resonance energy* (QMRE). Various schemes for the determination
of QMRE are distinguished by the choice of the reference structure
which should have non-interacting p-bonds.
In the framework of the *valence
bond theory*, the reference structure is represented by a single
(usually the most stable) *resonance structure*. *Hückel
resonance energy*, HRE, is equivalent to the *delocalization
energy*, DE. For a conjugated hydrocarbon

HRE = DE = -[*E*_{p} - *n*_{C=C}(2a
+ 2b)]

where *n* is the number of p-bonds
and *E*_{p} is the total p-electron
energy.

*Dewar resonance energy*,
DRE, is the quantity which allows one to account for the effects
of cyclic electron delocalization and thus serves as a measure of the
aromatic stabilization (see *aromaticity*)
of a cyclic molecular entity. The model reference structure is not
a system of isolated p-bonds (as is the case
for HRE), but a hypothetical cyclic polyene with the number of the
p- and s-bonds
equal to that in a given molecule. The condition of the additivity
of bond energies for cyclic polyenes is adopted.

DRE = D*H*_{a} - *H*_{a}^{add}

where D*H*a is the calculated heat
of atomization of a given conjugated molecule and D*H*_{a}^{add}
is the heat of atomization for the reference structure.

*Topological resonance
energy*, TRE - The TRE scheme rests on the formalism of *graph
theory*. A *characteristic
polynomial* is constructed for the reference structure with only
the acyclic Sachs graphs for the given molecule taken into account.
An advantage of the TRE scheme is in the fact that it can be easily
extended to radicals and ions and applied to * excited
states.*

For the purposes of comparison of the resonance energies of molecules
of different sizes, the normalized quantity *resonance
energy per electron*, REPE, has been introduced. DEWAR
(1969); MINKIN, GLUKHOVTSEV, and SIMKIN
(1994).

** Resonance energy per electron
(REPE)** - *see Resonance energy, various
types of.*

**Resonance hybrid **-** **A localized
valence bond representation of a molecule. This describes pictorially
an electronic *wavefunction*
that makes some contribution to the state wavefunction of the system.
Resonance hybrids are needed to describe the state of a system when
that system is not adequately described by a single Lewis structure.

**Resonance integral **-** **In
the *LCAO MO approximation*,
the energy of the overlap electron density between the* atomic
orbitals* c_{m} and c_{n}
due to attraction by the core (see *Core*
*approximation*). In
*semiempirical quantum*
*mechanical methods*
resonance integrals are adjustable parametric functions or parameters
designed to achieve better agreement with experimental data.

**Restricted Hartree-Fock (RHF) method** - see *Hartree-Fock
method*.

**Ribbon delocalization **-
Electron* delocalization* realized
in both acyclic and cyclic p-conjugated,**
1**, and s-bonded, **2**, ribbon-like
systems.

For cyclic systems, a variety of linkage fashions between several
ribbons (pericyclic, spirocyclic, longicyclic and laticyclic) is
possible.

**Rice, Ramsperger, Kassel and Marcus
(RRKM) theory** - A theory of unimolecular and recombination reactions
based on the application of *transition
state* theory to a microcanonical ensemble of excited reactant
molecules.

**Rydberg orbital -** For an atom,
an *orbital* whose principal quantum
number is greater than that of any occupied orbital of the *ground
state*. For a molecular entity, a *molecular
orbital* which correlates with a Rydberg *atomic
orbital* in an atomic fragment produced by dissociation.

**Rydberg state** - An *electronic
state* that arises by the excitation of a valence electron to
a diffuse atomic-like orbital. For instance, the lowest lying Rydberg
state (n, 3S) of NH_{3} can be described as resulting from
the excitation of a nonbonding orbital to a 3S *Rydberg
orbital*. EVLETH and KASSAB (1988).