Slater orbitals for alkali earth metals and noble gases

[riclambo]

Hello Forum,
Does anyone know where I can find the slater bases for the alkali metal 'np' orbitals and the noble gas '(n+1)p' orbitals, either altogether or individually? I'm a physicist and wanted to know what the standard (or even non-standard) reference is? I know that the occupied 'ns' orbitals for the alkali Earth and the occupied 'np' orbitals for the noble gases are reasonably easy to find. But what about these unoccupied orbitals necessary for transition calculations.

Any help would be greatly appreciated.

Regards,
Ricardo

 

[alxm]

Are you asking about orbitals or basis sets?

"Slater-type orbitals", or Slater-type basis functions in more modern and accurate terminology, refers to a basis set composed of exponential functions and spherical harmonics. Slater-type functions haven't seen much use for the better part of the last 40 years. Pople's minimal STO-nG basis set, which approximates STO-type functions with gaussians is around, but is considered too crude for general use these days. AFAIK it was never parameterized for anything higher than Argon.

Asking about 'unoccupied orbitals' doesn't make sense if you mean basis sets. But it doesn't make sense to ask about orbitals without specifying what kind of orbitals you mean, and in what basis. Hartree-Fock orbitals? Kohn-Sham orbitals? Natural orbitals? Are you sure you know what you're looking for?

 

[riclambo]

Thanks for the quick reply Alxm. I will try to formulate my question more clearly, though please bear with me as this is not my field.

I want to calculate the p_sigma and p_pi overlap integrals for various alkali metal/rare gas combinations. I know that the Slater basis functions for the 'np' rare gas Hartree-Fock orbitals exist (At. Data Nucl. Data Tables, 53, 113, 1993). But I would like to use the (n+1)p rare gas orbitals. Similarly, I know that exponents and coefficients for the valence ns orbitals of the alkali metals are available, but I would like to use the wave functions for the ground state unoccupied metal valence np orbitals.

Since the Slater-type functions haven't been used for about 40 years and minimal STO-ng basis sets have not been used to parametrize anything higher than Argon, what can I use? I intended to use the Hartree-Fock orbitals, but I will happy to use any other orbitals and parametrizations that will give me a reasonable and easily obtainable answer for the overlap integrals.

I hope this is more clear. Once more, any help would be appreciated.

Regards,
Ricardo

 

[riclambo]

Are you asking about orbitals or basis sets?

"Slater-type orbitals", or Slater-type basis functions in more modern and accurate terminology, refers to a basis set composed of exponential functions and spherical harmonics. Slater-type functions haven't seen much use for the better part of the last 40 years. Pople's minimal STO-nG basis set, which approximates STO-type functions with gaussians is around, but is considered too crude for general use these days. AFAIK it was never parameterized for anything higher than Argon.

Asking about 'unoccupied orbitals' doesn't make sense if you mean basis sets. But it doesn't make sense to ask about orbitals without specifying what kind of orbitals you mean, and in what basis. Hartree-Fock orbitals? Kohn-Sham orbitals? Natural orbitals? Are you sure you know what you're looking for?

Thanks. I will take a look at my notes and try to restate the problem.

 

[DrDu]

Slater-type functions haven't seen much use for the better part of the last 40 years.

That's an overgeneralization. AFAIK they are used in semiempirical models like INDO-S which are still quite useful for computations e.g. of excitation spectra of biomolecules in combination with molecular mechanics.

 

[cgk]

I want to calculate the p_sigma and p_pi overlap integrals for various alkali metal/rare gas combinations. I know that the Slater basis functions for the 'np' rare gas Hartree-Fock orbitals exist (At. Data Nucl. Data Tables, 53, 113, 1993). But I would like to use the (n+1)p rare gas orbitals. Similarly, I know that exponents and coefficients for the valence ns orbitals of the alkali metals are available, but I would like to use the wave functions for the ground state unoccupied metal valence np orbitals.

Then what you should do is to start up your favorite quantum chemisty program and tell it to calculate these integrals for you, using realistic Gaussian basis sets[1]. If you don't have one in your institute, you could look into high performance computing centers affiliated with your university. (Calculating overlap integals is of course nothing requring HPC, but these often have such software modules installed)

Using single Slater functions to represent the orbitals is most likely not a good idea if you are looking for more than qualitative numbers, even if it is just about overlap. If you insist on radial Slater functions, you could try fitting them to contracted Gaussian ANO functions. Also, even overlap integrals over Slater functions are non-trivial, and you might not be able to calculate them without effort.

[1] For example, atomic natural orbital basis sets like ANO-RCC for your purpose, which is a generally contracted basis set best handled with Molpro or Molcas. These also have contracted basis functions for representing virtual orbitals.

 

[DrDu]

I don't understand most of the answers given. The approximation of slater orbitals by a sum of gaussians converges only poorly; it is especially difficult to reproduce the "cusp".
The only reason why gaussians are the standard choice is because there exist analytical expressions for multicenter integrals.

 

[cgk]

I don't understand most of the answers given. The approximation of slater orbitals by a sum of gaussians converges only poorly; it is especially difficult to reproduce the "cusp".
The only reason why gaussians are the standard choice is because there exist analytical expressions for multicenter integrals.

The Gaussian vs Slater issue has been discussed in this thread: https://www.physicsforums.com/showthread.php?t=440376
Note the the convergence to atomic orbitals, is actually fast, not slow, and that the cusp issue is irrelevant for almost all purposes (unlike the exponential decay issue, which can bite you in a few situations).

The main point about the Gaussians is that with contracted Gaussian functions you can approximate the actual Hartree-Fock orbitals (or Kohn-Sham orbital or natural orbitals) directly with the basis functions[1]. If you take a single Slater function instead of a contracted Gaussian this will never happen. Slater orbitals are only much better than Gaussians for H and He, because in these two cases the "real" AOs actually *are* Slater functions, while for all other elements they are not. For these other elements you'd need contracted Slater functions, too, to represent the orbitals. And if that happens there is no point in using Slaters in the first place and you can simply use Gaussians directly.

[1] And these basis functions are pre-made, you don't need to construct them yourself

 

[alxm]

That's an overgeneralization. AFAIK they are used in semiempirical models like INDO-S which are still quite useful for computations e.g. of excitation spectra of biomolecules in combination with molecular mechanics.

Well, I didn't say they weren't used at all; there are also some DFT methods which make use of them.
But it's a small drop in the bucket compared to gaussian basis sets. (Also, remember it's 2011 now; so INDO-S is almost 40 years old!)

I don't really know how popular semiempirical methods are in that context since I don't do them myself.
But know Walter Thiel is mostly using (DFT) QM/MM for that kind of stuff these days, which I think says something.

 

[DrDu]

cjk, alxm, you have quite strong arguments on your side. I realize that I am now already for quite some years out of that field.