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

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

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

# **T**

**Thermochemical resonance
energy **-** **see* Resonance
energy, various types of.*

**Thermodynamic stability **-**
**Those species are considered to be thermodynamically stable whose
free energies are sufficiently low compared to all reasonable decomposition
products so that detectable amounts of the former may exist in equilibrium.

**Three-center, four-electron
(3c-4e) bond** - see *Hypervalency*.

**Three-center, two-electron
(3c - 2e) bond **- A kind of* multicenter*
s-bond in which three atomic cores are
held together by two electrons. The 3c-2e bonds are particularly common
in the boron hydrides, carbocations (for example, the bond in the
CH_{2} fragment of the methanium cation, see *Hypercoordination*),
bridged metal alkyls and metal halides. The simplest example of the
3c-2e bond is in the H_{3}^{+} ion.

**Through-bond interaction
**-** **An intramolecular *orbital
interaction* of spatially separated *orbitals*,
where the orbitals interact through their mutual mixing with
s-orbitals of the intervening framework.

**Through-space interaction
**-** **The *orbital interaction*
that results from direct spatial overlap of two *orbitals*.

**Tight binding method **-** **Approximation
of *crystal orbitals* in solids
by a *Linear Combination of Atomic
Orbitals.* In general, tight binding is approximation in quantum
chemical methods by retaining *resonance
integrals* only for neighboring atoms.

**Topochemical principle **-
Reactions in the crystalline phase proceed under minimal atomic and
molecular displacement.

**Topological distance matrix **-**
**see *Topological index.*

**Topological electron distribution
theory** - The theory of molecular structure based on the analysis
of the topological properties of scalar fields of the *electron
density function* r(**r**) and
the *Laplacian of*
*the electron density*
[^{2}r(**r**)],
which are summarized in terms of their critical points, r_{c},
i.e. the points where r(**r**)
and (-^{2}r(**r**))
are equal to zero. The critical points are classified according to their
rank (number of non-zero eigenvalues) and signature (algebraic sum of
their signs) of the *Hessian matrix*
of r(**r**). Thus, a (3, -3) critical
point corresponds to a maximum of r(**r**)
related to an atomic nucleus, whereas a (3, -1) critical point (*bond
point*) is a saddle point that exists between every pair of neighboring
bonded atoms. BADER (1990); BADER,
POPELIER, and KEITH (1994).

See also *Atoms in molecules,
theory of* .

**Topological index **- A numerical
value associated with chemical constitution purporting for correlation
of chemical structure with various physical properties, chemical
reactivity or biological activity. The numerical basis for topological
indices is provided (depending on how a *molecular
graph *is converted into a numerical value) by either the
*adjacency matrix* or the*
topological distance matrix*.
In the latter the topological distance between two verices is the number
of edges in the shortest path between these.

**Topological resonance energy
(TRE) **-** **see* Resonance
energy, various types of.*

**Topomerization ***- *see*
Automerization.*

**Total energy of a molecular system -
**The sum of the total electronic energy, *E*_{ee} and
the energy of internuclear repulsion, *E*_{nr}. In the
*Hartree-Fock (SCF) method*,
the value of *E*_{ee} for a* closed-shell
molecular system* is given by

*E*_{ee} = 2
e_{i} +
(2*J*_{ij} - *K*_{ij})

where e_{i} stands for
orbital energies and *J*_{ij} and *K*_{ij}
stand for respectively *Coulomb*
and *exchange integrals*,
the summation being done over all occupied* molecular
orbitals. *The repulsion between the nuclei (A, B ...) is
defined by the expression:

*E*_{nr} =
*Z*_{A}*Z*_{B}/*R*_{AB}

**Transition state (TS)** (also*
*transition state structure, transition structure) - The structure
corresponding to the highest point on the *minimum
energy reaction path*, i.e. first order* saddle
point *on the *potential
energy surface*. In* transition
state spectroscopy*, the definition of the transition state
is broader. It embraces the entire process of bond breaking and
bond making and is used to denote the full family of configurations
through which the reacting particles evolve along the route from
reagents to products.

See also* Hessian matrix.*

**Transition State Theory (TST)**
**-** The theory which provides a conceptual framework for understanding
all chemical reactivity. It serves as a powerful computational tool
for translating molecular structures and energetics into prediction
of chemical reaction rates. EYRING (1935),
GARRET and TRUHLAR (1998).

**Transition state spectroscopy (TSS)
**- The femtosecond temporal resolution (10^{-14} - 10^{-13}
s = 10 - 100 fs) laser spectroscopy that enables one to detect the intermediate
configurations (*transition states*)
of a reacting system in real time and follow the nuclear motion and
energy redistribution. POLANYI and ZEWAIL
(1995).

**Transition vector **-** **The
eigenvector associated with the only negative eigenvalue of the *Hessian
matrix* representing the single direction in which the*
potential energy surface *is
a maximum. The transition vector is also a path of the* intrinsic
reaction coordinate* through the *saddle
point*.

**Transmission factor **- In the
equation of the theory of absolute reaction rates that relates the reaction
constant *k* with the height of the energy barrier
D*E*^{TS}, the value of the coefficient g
is equal to 1 when the conversion of reactants to products always
occurs upon attaining the height of energy barrier, and less than
1 when this condition is not met.

*k* = gt (*k*_{B}T/*h*)
(*Q*_{TS}/*Q*_{R}) exp(-D*E*^{TS}/*RT*)

where *k* is the rate constant for the reaction of conversion
of reactants R into products by proceeding through transition state
TS; *Q* are partition functions per unit volume, and
t is the quantum mechanical *tunnelling*
coefficient. In some descriptions k = gt
is referred to as the transmission factor.

**Tunnelling effect** - The passage
of a particle through a potential energy barrier the height of which
is larger than the energy of that particle. The effect is important
for some processes involving the transfer of electrons and light
atoms, particularly hydrogen atoms.