¿Why i have 24 atomic orbitals for Cu(I) atom?

Ricardo Moreno-Inzunza @Ricardo-Moreno-Inzunza

21 March 2025 1 3K Report

Hi.

I'm working with Cu(I) complexes with electronic structure calculations, specifically with DFT calculations in Gaussian 16 Software. I'm performed pop=full analysis and i note that the copper atom have 24 orbitals:

1S(Cu1) 2S(Cu1) 3S(Cu1) 4S(Cu1) 5S(Cu1) 6PX(Cu1) 6PY(Cu1) 6PZ(Cu1) 7PX(Cu1) 7PY(Cu1) 7PZ(Cu1) 8PX(Cu1) 8PY(Cu1) 8PZ(Cu1) 9D0(Cu1) 9D+1(Cu1) 9D-1(Cu1) 9D+2(Cu1) 9D-2(Cu1) 10D0(Cu1) 10D+1(Cu1) 10D-1(Cu1) 10D+2(Cu1) 10D-2(Cu1)

Additionally, i had a single point calculation for more details of the atomic orbitals of the copper ion and the results indicate that the HOMO state it is conformed by 95.92% for the 9D+2 level.

My input archive is:

#p pop=full iop(3/33=1) m06/dgdzvp geom=check guess=read scrf=(solvent=ethanol)

I am very confused because the electronic configuration of Cu(I) is 1s2 2s2 2p6 3s2 3p6 3d10 and in my results the level 9 is participating in the HOMO.

Could someone explain to me the reason for all this?

Jürgen Weippert

The orbitals in a basis set are not the exact atomic orbitals of the corresponding atom (these are analytically unavailable, anyway). Two important aspects you should be aware of:

If you solve the Schrödinger equation for the H atom, you will get Slater type functions (exponential radial decay, e-r). These are difficult to handle because integrals cannot be evaluated analytically. For that reason, Gaussian type orbitals (GTO) are used as approximations. That means that the especially the cusps of the wavefunctions around the nucleus aren't modelled properly. So, if you run your GTO-built basis set through the Schrödinger equation or an approximation of it, it will mix the available functions in order to compensate for that which will inevitably also involve the higher orbitals.

For the valence electrons, it is common to use more basis function per orbital which is indicated by the n-tuple valence. Additionally, polarization functions which may e.g. involve spherical harmonics which you would expect only in higher shells are commonly added. So, a basis set like def2-TZVP has triple zeta valence and additional polarization.

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