The behavior of a system at a specified temperature can be
modeled by use of `KINETIC`. This
keyword allows extra kinetic energy to be added to the system. In order to
determine how much extra energy to add, an understanding of the issues involved
is essential.

The total energy of a system can be expressed as three sums:

(A) The heat of formation of the system, ΔH_{f0}.
This is an irreducible minimum, and represents the energy of the system at
equilibrium.

(B) The potential energy of the system. This is the heat
of formation of the system with its current geometry, ΔH_{f},
minus ΔH_{f0}. It represents the energy of
distortion from the equilibrium geometry.

(C) The kinetic energy of the system. This is the sum of the vibrational energies of motion of all the atoms in the system.

Energy term (A) is a constant, regardless of temperature. Energy
terms (B) plus (C) represent the internal energy (enthalpy), U, of the system.
At zero Kelvin, U is zero. At any other temperature, T, the enthalpy
represents the integral of the heat capacity from zero to T. In a DRC
calculation, any desired temperature can be specified by defining the
associated internal energy. The internal energy can be calculated using `
THERMO`, and specifying the temperature to be
used. In the output of a `THERMO` calculation, the enthalpy needed
is given at the intersection of `ENTHALPY` and `VIB`. In the
following example, this would be 578.5 cal/mol, or 0.578 kcal/mol.

TEMP. (K) PARTITION FUNCTION H.O.F. ENTHALPY HEAT CAPACITY ENTROPY KCAL/MOL CAL/MOLE CAL/K/MOL CAL/K/MOL 298.00 VIB. 0.2342D+01 578.4823 4.2357 3.6320 ROT. 0.3897D+04 888.2813 2.9808 19.4109 INT. 0.9125D+04 1466.7636 7.2165 23.0429 TRA. 0.1515D+27 1480.4688 4.9680 36.0322 TOT. 10.536 2947.2324 12.1845 59.0751

To set up a run at a given temperature, the ΔH_{f }
of the optimized system is needed. Calculate this first, then do a `THERMO`
calculation to get the enthalpy at the desired temperature. The next step
might be unexpected. Distort the geometry of the system slightly, and
re-calculate the heat of formation at the distorted geometry. Make sure
that it has increased by at least 0.2 kcal/mol, and preferably by a large
fraction of the enthalpy. A non-equilibrium starting geometry is needed in a DRC
calculation because otherwise the atoms would not be moving, and adding in
excess kinetic energy would not be possible (You can't make the atoms move
faster if they were not moving originally).

Work out how much extra kinetic energy would need to be added to equal the vibrational enthalpy at the desired temperature.

Let the calculated equilibrium heat of formation be -100.000
kcal/mol.

Let the desired internal vibrational energy be 0.578 kcal/mol.

Let the heat of formation of the distorted geometry be -99.500 kcal/mol.

Then the extra kinetic energy needed would be 0.078 kcal/mol.

Set up the DRC calculation using the distorted geometry and `KINETIC=0.078`.
Run this system. In the output, the starting heat of formation will be
that of the distorted system, and the kinetic energy will be zero or almost
zero. Over the next few femtoseconds, the heat of formation will become
more negative, and the kinetic energy will rise. When it exceeds 0.2
kcal/mol, the velocity vector for the system will be well defined, and the extra
kinetic energy will then be added. This will temporarily confuse the
predictor-corrector error reduction function, so errors in the calculation will
rise for a while, but once they become small the total energy of the system
(heat of formation of the current geometry plus kinetic energy) will be equal to ΔH_{f0}
plus the desired enthalpy.

A legitimate question is, why do it this way, why not add the velocity vector "by hand"? The problem is, the kinetic energy must not include rotational or translational terms. Translational contributions to the enthalpy are irrelevant for a single molecule, and the rotational contributions are conserved, so they, too, can be ignored (or can they?), all that matters is the dynamics of the non-translating, non-rotating system. Defining a velocity vector that achieves this is definitely non-trivial.