Rep:Mod:Gorrochategui97

Molecule #1: NH₃

The optimisation file is liked to here

Basic information

Bond length

1.01798 Å

Bond angle

105.745°

Calculation Method

RB3LYP

Basis set

6-31G(d,p)

Final energy

-56.55664124 a. u.

RMS gradient

0.00836082 a. u.

Point group

C_3v

Output

         Item               Value     Threshold  Converged?
 Maximum Force            0.000006     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000014     0.001800     YES
 RMS     Displacement     0.000009     0.001200     YES
-- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.018          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.018          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.018          -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              105.7446         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7446         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7446         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8637         -DE/DX =    0.0                 !

test molecule

Vibrations

- 6 modes according the 3N-6 rule.

- Modes 2 and 3 (1693.94) and 5 and 6 (3589.86) are degenerate.

- Modes 1, 2 and 3 show bending vibrations, while modes 4, 5 and 6 show stretching vibrations.

- Mode 4 is highly symmetric.

- Mode 1 is known as the umbrella mode.

- 5 bands will appear in the gaseous spectrum, as only mode 4 shows a symmetric stretch.

Charge analysis

Charge of N: -1.125.

Charge of H: 0.375.

N has a negative value due to being more electronegative, so it attracts the electrons of the H atoms.

Molecule #2: N₂

The optimisation file is linked to here

Basic information

Bond length

1.10550 Å

Bond angle

180°

Calculation Method

RB3LYP

Basis set

6-31G(d,p)

Final energy

-109.5235911 a. u.

RMS gradient

0.02473091 a. u.

Point group

D_h

Output

         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000000     0.001200     YES
 -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1055         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------

test molecule

Vibrations

Only one mode of vibration (stretching).

Charge analysis

Apolar bimolecular compound.

Molecule #3: H₂

The optimisation file is liked to here

Basic information

Bond length

0.74279 Å

Bond angle

180°

Calculation Method

RB3LYP

Basis set

6-31G(d,p)

Final energy

-1.17853936 a. u.

RMS gradient

0.00000017 a. u.

Point group

D_h

Output

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
 -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  0.7428        -DE/DX =    0.0                  !
 --------------------------------------------------------------------------------

test molecule

Vibrations

Only one mode of vibration (stretching).

Charge analysis

Apolar bimolecular compound.

Haber-Bosch reaction

N₂ + 3H₂ ---> 2NH₃

Energies

• E(NH₃) = -56.55664124 a. u.

• 2E(NH₃) = -113.1132825 a. u.

• E(N₂) = -109.5235911 a. u.

• E(H₂) = -1.17853936 a. u.

• 3E(H₂) = -3.53561808 a. u.

• ΔE = 2E(NH₃) - [E(N₂) + 3E(H₂)] = -0.05407332 a. u. = -141.9695017 kJ

Molecule #4: HCl

The optimisation file is liked to here

Basic information

Bond length

1.28599 Å

Bond angle

180°

Calculation Method

RB3LYP

Basis set

6-31G(d,p)

Final energy

-460.80077017 a. u.

RMS gradient

0.00135233 a. u.

Point group

C_v

Output

         Item               Value     Threshold  Converged?
 Maximum Force            0.000090     0.000450     YES
 RMS     Force            0.000090     0.000300     YES
 Maximum Displacement     0.000139     0.001800     YES
 RMS     Displacement     0.000197     0.001200     YES
-- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.286          -DE/DX =    0.0001                 !

test molecule

Vibrations

Only one mode of vibration (stretching).

Charge analysis

- Charge of Cl: -0.284.

- Charge of H: 0.284.

- Cl has a negative value due to being more electronegative, so it attracts the electron of the H atom.

Molecular orbitals

2s orbital of the chlorine atom (-9.47437 a. u.). It does not interact with the 1s orbital of hydrogen because it is too low in energy.

The image shows the bonding orbital (-0.47433 a. u.), made by the linear combination of the 1s orbital of hydrogen and the 3p_z of chlorine.

Presented here is a model of the 3px orbital of chlorine (-0.33163 a. u.). It does not overlap with any hydrogen orbital. Along with the 3px orbital, it is the HOMO of the molecule.

Presented here is a model of the 3py orbital of chlorine (-0.33163 a. u.). It does not overlap with any hydrogen orbital. Along with the 3px orbital, it is the HOMO of the molecule.

This is is the LUMO of the molecule, corresponding to the antibonding linear combination of the 1s orbital of hydrogen and the 3pz orbital of chloride (0.01366 a. u.).

Molecule #5: Cl₂

The optimisation file is liked to here

Basic information

The optimisation file is liked to here

Bond length

2.04174 Å

Bond angle

180°

Calculation Method

RB3LYP

Basis set

6-31G(d,p)

Final energy

-920.34987886 a. u.

RMS gradient

0.00002511 a. u.

Point group

D_h

Output

         Item               Value     Threshold  Converged?
 Maximum Force            0.000043     0.000450     YES
 RMS     Force            0.000043     0.000300     YES
 Maximum Displacement     0.000121     0.001800     YES
 RMS     Displacement     0.000172     0.001200     YES
-- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  2.0417          -DE/DX =    0.0                !

test molecule

Vibrations

Only one mode of vibration (stretching).

Charge analysis

Apolar bimolecular compound.