D Hindered Rotation, "Unsymmetrical" (hrd)

1-D Hindered Rotation, "Unsymmetrical" (hrd)

This type is intended for unsymmetrical rotors (e.g. the CH 2 Cl rotor) and flexible internal rotors. For this type, one must provide the torsional potential energy and reduced moment of inertia (or rotational constant) as functions of the dihedral angle χ (radians). For a discussion, see the Technical Notes.

Note that computer program lamm, described in Chapter 8 is designed to assist in computing moments of inertia as a function of dihedral angle. Thus lamm is more appropriate than MomInert for flexible internal rotations.

For convenience, three forms of the torsional potential energy are accepted (all coefficients in units of cm -1 ):

V () n ! = 1 ) " cos n

Type Vhrd1

( # V ( !+$ V ) )

n =1

Type Vhrd2

V () ! =V 0 + V $ n cos n ( " V ( !+# V ) )

n =1

Vhrd3

V () ! =V 0 V c Type s + $ n cos n ( " V ( !+# V ) ) + V sin n

$ n ( " V ( !+# V ) )

n =1

where χ is the dihedral angle (radians), σ v is the symmetry number for the potential energy, φ V is

a phase angle for the potential (radians). Also for convenience, either the rotational constant or the moment of inertia, which are

functions of the dihedral angle, can be entered (all coefficients in units of cm -1 ). It is VERY

IMPORTANT that the angles are defined in the same way both for the potential and for the mass factor.

Type -1 Bhrd1 (all coefficients in units of cm )

B () ! =B 0 + B $ cos n n ( " B ( !+# B ) )

n =1

Type 2 Ihrd1 (all coefficients in units of amu•Å )

I () ! =I 0 + I $ n cos n ( " I ( !+# I ) )

n =1

where χ is the dihedral angle (radians), σ B and σ I are symmetry numbers and φ B and φ I are phase angles (radians). Repeat: It is VERY IMPORTANT that the same phase angle be used both for

the potential and for the mass factor: φ V =φ B or φ I .

Hindered Gorin Model (gor) and Fitting to Experimental Rate Constants (fit)

Thermo includes the capability to automatically find the hindrance parameters for the Hindered Gorin transition state. 36-43 One can choose one or both of the following types

( IDOF) of degrees of freedom.

1) IDOF = gor selected for one vibrational stretching mode. For a selected potential energy function, Thermo finds the center of mass distance r max corresponding to maximum of

V effective at temperature T, where the rotational energy in the 2-D pseudo-diatomic rotation is assumed to be RT. From the value of r max , Thermo computes the 2-D moment of inertia.

2) IDOF = fit selected for two (linear molecule) or three (non-linear) rotational dimensions. Thermo finds the hindrance parameters γ ( gamma) and η (eta) that produce a good fit at each temperature to experimental rate constants (one for each temperature) that are entered.

If both IDOF = gor and IDOF = fit are selected, Thermo finds the maximum of

V effective and uses it to find the hindrance parameters ( gamma and eta) that produce a good fit to experimental rate constants (one for each of the Nt temperatures) that are entered.

The selectable potential energy functions are: MORSE (Morse Oscillator)

V Morse () r =D e { 1 ! exp ! #$ " Morse ( r !r e ) %& } !D e

µ ! Morse =2 "# e

2D e