View source for Rep:Mod:sk716

== NH<sub>3</sub> molecule ==

*Calculation method: RB3LYP;
*Basis set: 6-31G(d,p);
*Final energy = -56.55776873 au;
*RHS gradient = 0.00000485 au;
*Point group: C<sub>3v</sub>;
*N-H bond distance = 1.01798 Å;
*H-N-H bond angle = 105.741 degrees.

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000072     0.001800     YES
 RMS     Displacement     0.000035     0.001200     YES
 Predicted change in Energy=-5.986295D-10
 Optimization completed.
    -- 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)              105.7412         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7412         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7412         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8571         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
  <title>Optimised ammonia</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>SKAMARA_NH3_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:SKAMARA_NH3_OPTF_POP.LOG]]

[[File:SKamara_nh3_vibrations_screenshot.PNG]]

*Vibration modes = 6;
*Modes 2 & 3 and 5 & 6 are degenerate;
*Modes 2 & 3 are bending vibrations and modes 4, 5 & 6 are stretching vibrations;
*Modes 4 are highly symmetric;
*Mode 1 is the umbrella mode;
*4 bands are expected to be observed in the spectrum;;
*Charge of N = -1.125;
*Charge of H = +0.375;

I'd expect N to have a negative charge and H to have a positive charge because nitrogen's more electronegative, so a lot of the electron density will be around the N atom;;

== N<sub>2</sub> molecule ==

*Calculation method: RB3LYP;
*Basis set: 6-31G(d,p);
*Final energy = -109.52412868 au;
*RHS gradient: 0.00000060 au;
*Point group: D<sub>∞h</sub>
*Bond length = 1.10550 Å;

<pre>
         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
 Predicted change in Energy=-3.401015D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1055         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>

<jmol><jmolApplet>
  <title>Optimised dinitrogen</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>SKAMARA_N2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:SKamara_n2_vibrations_screenshot.PNG]]

There are no negative frequencies

[[File:SKAMARA N2 OPTF POP.LOG]]

== H<sub>2</sub> molecule ==

*Calculation method: RB3LYP;
*Basis set: 6-31G(d,p);
*Final energy = -1.17853936 au;
*RHS gradient: 0.00000017 au;
*Point group: D<sub>∞h</sub>;
*Bond length = 0.74279 Å;

<pre>
         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
Predicted change in Energy=-1.164080D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  0.7428         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>

[[File:SKamara_h2_vibrations_screenshot.PNG]]

<jmol><jmolApplet>
  <title>Optimised dihydrogen</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>SKAMARA_H2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>


E(NH3)= -56.55776873 au

2×E(NH3)= -113.1155375 au

E(N2)= -109.52412868 au

E(H2)= -1.17853936 au

3×E(H2)= -3.53561808 au

ΔE=2×E(NH3)-[E(N2)+3×E(H2)]= 0.05579074 au = -146.4785879 kJ mol<sup>-1</sup>

A literature value estimates the enthalpy change of reaction as -50 kJ mol<sup>-1</sup><ref name="Enthalpy" />, which is 3 times less than the prediction using the calculations above. This difference could be due to the calculation method as it uses purely theoretical methods to calculate the energy (which can be viewed as calculating the enthalpy change of reaction in a vacuum), whereas the experimental conditions are significantly different from this. The product is more stable than the reactants because the free energy is around negative 65 kJ mol<sup>-1</sup><ref name="Gibbs" />

[[File:SKAMARA H2 OPTF POP.LOG]]

== H<sub>2</sub>CO analysis ==

*Calculation method: RB3LYP;
*Basis set: 6-31G(d,p);
*Final energy = -114.50319933 au;
*RHS gradient: 0.00007386 au;
*Point group: C<sub>S</sub>;
*C-H bond distance = 1.11057 Å;
*C=O bond distance = 1.20676 Å;
*H-C-O bond angle = 122.395 degrees.

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000197     0.000450     YES
 RMS     Force            0.000085     0.000300     YES
 Maximum Displacement     0.000252     0.001800     YES
 RMS     Displacement     0.000142     0.001200     YES
 Predicted change in Energy=-3.772186D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1106         -DE/DX =   -0.0001              !
 ! R2    R(1,3)                  1.1106         -DE/DX =   -0.0001              !
 ! R3    R(1,4)                  1.2068         -DE/DX =   -0.0002              !
 ! A1    A(2,1,3)              115.2188         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              122.3859         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              122.3954         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
</pre>

The molecule is fully optimised because the maximum force is less than 0.00045 au and the maximum displacement is less than 0.0003 au.

<jmol><jmolApplet>
  <title>Formaldehyde molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>SKAMARA_H2CO_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

<gallery>
File:SKamara_h2co_vibrations_screenshot.PNG|Vibration windows screenshot
File:SKamara_h2co_vibrations_screenshot_v1.PNG|Symmetrical bending
File:SKamara_h2co_vibrations_screenshot_v2.PNG|Symmetrical bending
File:SKamara_h2co_vibrations_screenshot_v3.PNG|Symmetrical bending
File:SKamara_h2co_vibrations_screenshot_v4.PNG|In-plane scissoring
File:SKamara_h2co_vibrations_screenshot_v5.PNG|Symmetrical stretching
File:SKamara_h2co_vibrations_screenshot_v6.PNG|Asymmetrical stretching
</gallery>

The values from the IR frequencies are a good estimate of the experimental values<ref name="IR" />.

[[File:SKamara h2co charge distribution.PNG|thumb|left|Charge distribution - The O atom has a negative charge because it's the most electronegative atom in the molecule. The molecule has a dipole because it has a partial negative charge in the direction of O and a partial postive charge in the direction of the H atoms]]

<gallery>
File:SKamara h2co mo 1.PNG|The 1s orbital of O (this is a non-bonding orbital because it's too deep in energy to overlap with other orbitals)
File:SKamara h2co mo 2.PNG|The 1s orbital of C (like O's 1s orbital, it's too deep in energy to overlap with other orbitals)
File:SKamara h2co mo 3.PNG|This can be viewed as the orbital made by the in-phase overlapping of the CH<sub>2</sub> fragment and O's 2s orbital
File:SKamara h2co mo 4.PNG|This is the antibonding molecular orbital for the interaction in the third image (O is in the opposite phase)
File:SKamara h2co mo 9.PNG|This is the LUMO of formaldehyde, which is the antibonding orbital of C's 2p orbital (which is orthogonal to the plane of the molecule, and O's 2p orbital (orthogonal as well). The energy of the MO is negative.
</gallery>


[[File:SKAMARA H2CO OPTF POP.LOG]]

<references>
<ref name="Enthalpy">http://pubs.acs.org/doi/full/10.1021/acs.jpclett.6b01178</ref>
<ref name="Gibbs">http://pubs.acs.org/doi/full/10.1021/acs.jpclett.6b01178</ref>
<ref name="IR">http://wchem.cup.uni-muenchen.de/wvib/ch2o.html</ref>
</references>