GitLab

Table of contents

• Table of contents
• Details
• Keywords
  • The ALG Keyword
  • The TPITRANSALG Keyword
  • The SCHWARTZ Keyword
  • The RI Keyword
  • The FINITENUCLEI Keyword
  • The LIBCINT Keyword
  • Four-component integral keywords
• Example
  • Auxiliary basis RI with all ERIs stored
  • Cholesky decomposition RI with ERIs formed on the fly
• References

Details

The INTS section handles the specification of parameters relevant to the evaluation / contraction of the operator integrals. The INTS section is optional, and the default parameters are often sufficient. The defaults are often overly conservative for some applications, and the performance of e.g. the direct electron repulsion integral (ERI) contraction can be drastically altered by a proper toggling of these parameters.

Keywords

The ALG Keyword

ChronusQ currently supports two types of ERI contraction algorithms:

• DIRECT: Direct ERI contraction
  • This is the default in ChronusQ due to the negligible memory requirement and efficiency through screening. However, if the memory required to store the ERI tensor in core is readily available, the INCORE integral contraction will often be much more efficient
• INCORE: In-Core ERI contraction
  • The integral contraction is performed in-core using optimized level-3 BLAS operations. The option is wildly memory intensive, but if the memory can be afforded, the option is highly efficient. If this option is chosen and there is not enough memory specified, the job will end and the amount of memory required for the ERI storage will be written to the log file.

The TPITRANSALG Keyword

• N6: can be INCORE or DIRECT.
  • The first half transformation uses same functions to build Fock matrix in SingleSlater. In the case with DIRECT algorithm, Schwartz screening will be applied with transformation.
• N5: currently only INCORE is implemented.

The SCHWARTZ Keyword

An upper bound to the magnitude of elements within the ERI tensor is given by:¹

|(\mu\nu|\lambda\kappa)| \leq \sqrt{(\mu\nu|\mu\nu)}\sqrt{(\lambda\kappa|\lambda\kappa)}

This can be used to prescreen the evaluation of (\mu\nu|\kappa\lambda) if the left hand side of the equation is below a certain value. The SCHWARTZ keyword gives the user control over this cutoff value.

The RI Keyword

Because the ERI tensor is rank 4, adding more basis functions will cause the number of significant ERIs to scale as \mathcal{O}(n^4) where n is the number of basis functions. For large systems or large basis sets, this may be computationally intractable. In these cases, one may use an auxiliary basis fit to reproduce the four index ERIs from three and two index integrals, reducing the scaling to \mathcal{O}(n^3):^2,3

(\mu\nu|\lambda\kappa) = \sum_{tu} (\mu\nu|u)(t|u)^{-1}(u|\lambda\kappa)

Where t and u are auxiliary basis functions. There are two main ways to generate this auxiliary basis. The first method is to use a predetermined auxiliary basis.² The second method is to generate this basis on the fly with a Cholesky decomposition.³ Both approaches are available in ChronusQ, toggled by the RI keyword. The options are:

• FALSE (Default)
  • Do not do any RI approximation method
• AUXBASIS
  • Use the additional basis specified in the DFBasis section.
• CHOLESKY
  • Form an auxiliary basis on the fly from a Cholesky decomposition. The criterion for vectors that are kept by this method is given by the CDRI_THRESHOLD keyword.

The FINITENUCLEI Keyword

In some relativistic methods, (e.g. scalar-only relativistic corrections or the exact two component method) using point nuclei can introduce singularities in the working equations. In these cases, it is recommended to use finite, sharply peaked charge distributions. ChronusQ will use a Gaussian to approximate the charge distribution for atom X according to the following formula:⁴

\rho_X = Z_X \left ( \frac{\zeta}{\pi} \right)^{\frac{3}{2}}  e^{ - \zeta R^2 } 

Where the exponent is given by

\zeta = \frac{3}{2} ( 0.52917721092\mathrm{e}^{-5} \times [ 0.8636 A_X^{\frac{1}{3}} + 0.57 ] )^{-2}

and A_X is the atomic mass of atom X.

The options for FINITENUCLEI are

• DEFAULT (Default)
  • Chooses either point or finite nuclear charge distributions based on the Hamiltionian
• TRUE
  • Turns on finite nuclei
• FALSE
  • Turns off finite nuclei

The LIBCINT Keyword

Libcint library has native support to general contraction basis sets. It is also able to compute integrals necessary in four-component calculations.

The options for LIBCINT are

• FALSE (Default)
  • Use libint library
• TRUE
  • Use libcint library

Four-component integral keywords

BARECOULOMB, DIRACCOULOMB, SSSS, GAUNT, GAUGE and BREIT. See description in the Keywords section.

Example

Auxiliary basis RI with all ERIs stored

[INTS]
alg = incore
ri = auxbasis

Cholesky decomposition RI with ERIs formed on the fly

[INTS]
alg = direct
ri = cholesky

References