In this project, H2O and HCN molecules were optimized starting with different initial structures, in order to explore the effect of initial structure guess on optimization process and final optimized geometry.

Methods
The geometry optimization was performed in Material Studio with CASTEP Calculation Package [1]. The functional of Perdew Burke, and Ernzerhoff was employed [2]. Since H2O and HCN are two dimensional molecules, two degrees of freedom, including bond length and angle need to be considered for optimization.

Determine Lattice Parameter
To mimic a gas phase molecule, a supercell representing empty space needs to be built. Fig. 1a shows the energy change with lattice parameter and Fig. 1b shows the computational time change with lattice parameter. Considering computational cost and accuracy, lattice parameter of 10 Å was chosen for further study, as energy change between 10 Å and 9 Å is only 0.001 eV, and energy change between 10 Å and 12 Å is also 0.001 eV.


Fig 1 a, Energy change with lattice parameter; 1 b, computational time with lattice parameter

Determine Energy Cutoff
Similar to lattice parameter determination, energy cut-off determination was based on computational cost and accuracy, which were shown in Fig 2. Energy cut-off of 750 eV was chosen for further studies as energy tolerance is less than 0.005 eV.


Fig 2 a, Energy change with energy cut-off; 1 b, computational time with energy cut-off

H2O structure
Influence of initial bond length on optimization
In this section, we will explore how initial O-H bond length affect optimization by fixing H-O-H bond angle 110.37 degree and changing H-O bond length.

Fig 3. Initial structure of H2O molecule
We can see from Table 1, the optimized O-H bond length is 0.97 Å. As initial guess molecule geometry getting closer to the optimized molecular geometry, the computational time and number of iteration will decrease. There is no big difference on final energies and optimized H-O-H bond angle for different initial structures.

Influence of initial bond angle on optimization
In this section, we will explore how initial H-O-H bond angle affect optimization by fixing H-O bond 0.97 Å, as shown in Fig 4.

Fig 4. Fixed H-O bond length and changing H-O-H bond angle
From Table 2, we can see the optimized O-H bond length is 0.97 Å and H-O-H bond angle is 104.23. As initial guess molecule geometry getting closer to the optimized molecular geometry, the computational time and number of iteration will decrease. There is no big difference on final energies and optimized O-H bond length for different initial structures.

HCN structure
Influence of initial H-C bond length on optimization
In this section, we will explore how initial C-H bond length affect optimization by fixing C-N bond length of 1.51 Å and H-C-N bond angle of 180, as shown in Fig 5.

Fig 5. Fixed C-N bond length and H-C-N bond angle
We can see from Table 3, the optimized C-H bond length is 1.075 Å and H-C-N bond angle is about 179.9 degree. As initial guess molecule geometry getting closer to the optimized molecular geometry, the computational time and number of iteration will decrease. There is no big difference on final energies and optimized C-N bond length for different initial structures.

Influence of initial H-C-N bond angle on optimization
In this section, we will explore how initial H-C-N bond angle affect optimization by fixing C-N bond length of 1.159 Å.
It is worth to note that in Table 4, the first 4 rows we were attaching H to N in order to make the corresponding angle. It turned out that such initial structure will generate C-N-H molecule after optimization, as shown in Fig 6. From the first 4 rows, we can conclude as initial geometry getting closer to optimized structure, the optimization time and number of iteration will decrease. But for the last row data, we attached H to C atom and H-C-N angle is very close to optimized structure, we found energy of H-C-N molecule is lower than C-N-H molecule.


Fig 6. optimized C-N-H molecule from Table 5 first 4 rows data.

Conclusion
A good estimate of atomic geometry will greatly increase DFT calculation speed.

Reference
[1] “First principle methods using CASTEP” Zeitschrift fuer Kristallographie 220(5-6) pp. 567-570 (2005)
[2] Perdew, J. P; Burke, K; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865-3868