Molecular orbitals of water

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Molecular structure

The initital view in the JSmol-frame above shows the bond lengths and angles of the water molecule as obtained from a geometry optimization (see Computational details below). The structure is V-shaped with a bond angle of 103.7°. In addition one can see that the electron density is delocalized over the whole molecule. The calculated dipole moment of the molecule is 2.7 Debye and directed along the negative z-axis.

Molecular orbitals

The shape and energy of the MO:s have been calculated (see details below) and can be viewed by selecting a radio button above. The MO:s have been ordered and numbered according to their energy. At the bottom are the low-energy orbitals which are occupied by two electrons each in the ground state of the molecule. These MO:s are generally bonding or non-bonding (with respect to the oxygen-hydrogen bonds). At the top are listed some unoccupied high-energy orbitals. These are mostly anti-bonding (or non-bonding).

The orbital with lowest energy (MO 0) is essentially an oxygen 1s orbital at very low energy (-511 eV). The next one (MO 1, -24.7 eV) is a bonding MO involving O-2s and H-1s atomic orbitals. MO 2 (-12.6 eV) and MO 3 (-8.31 eV) involve O-2py and O-pz orbitals, respectively, and are also contributing to the σ-bonds with the hydrogen atoms. MO 4 (-6.43 eV) is the highest occupied molecular orbital (HOMO) and is essentially a (non-bonding) O-px atomic orbital.

Above the HOMO is the LUMO (lowest unoccupied molecular orbital, MO 5, 1.15 eV) which doesn't contain any electrons in the ground state, as is the case for the orbitals at higher energies. MO 5 is a mixture of O-2s, O-2pz and H-1s atomic orbitals and is anti-bonding with respect to the O-H axes.

See [Falstad, 2014] for a Java applet that illustrates bonding and antibonding MO:s.

Computational details

The results described here have been computed by Örjan Hansson with density functional theory (DFT) using the quantum-chemical program package ORCA (version 3.0.3) [Neese, 2012].

Initital coordinates were taken from textbook data and the geometry was optimized with ORCA in three steps: First, vibrational frequencies were calculated with a semiempiric method (NDDO/ZNDDO_1). Secondly, the resulting Hessian was used in an initital optimization with DFT using UKS wave functions and the BP86 functional with grid 2 and the RI approximation. The basis used was Def2_SVP (with Def2_SV_J for RI). Thirdly, this was followed by a refined optimization with DFT using UKS wave functions and the BP86 functional with grid 4 and the RI approximation. The basis used was Def2_TZVP (with Def2_TZV_J for RI). A relativistic DKH2 treatment was included in the third step as well as a COSMO model of water solvent.

Molecular orbitals and dipole moment were then calculated as for the third step above using the optimized geometry but with simpler basis functions (SV and SV_J for RI), resulting in only 13 molecular orbitals.

Surfaces depicting electron densities and molecular orbitals were saved to files on a Gaussian CUBE format. These files were then converted to the JVXL format using Jmol, resulting in a reduction of file sizes from approximately 3 MB to 7 kB and a drastically faster loading of the figure above.

The computations were done on a PC with a 2.2 GHz Intel Core i7 64 bit processor, 16 GB RAM and a Windows 10 operative system. Each of the four steps in the calculation described above required at most of the order of 10 seconds.

References

• Falstad, P. (2014) Molecular Orbital Viewer v1.5a
• Neese, F. (2012) The ORCA program system, Wiley Interdiscip. Rev.: Comput. Mol. Sci., 2, 73-78.