Table of contents
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
Keyword  Type  Description  Default 

ALG 
String  ERI contraction algorithm  DIRECT 
SCHWARTZ 
Double precision float  Criterion for ERI schwartz screening  10^{12} 
RI 
String  Method for the resolution of identity approximation (RI)  FALSE 
CDRI_THRESHOLD 
Double precision float  Criterion for inclusion in Cholesky decomposition based RI  10^{4} 
FINITE_NUCLEI 
String  Toggles use of Gaussian charge distribution instead of point charges to represent nuclei  DEFAULT 
ALG
Keyword
The 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
: InCore ERI contraction The integral contraction is performed incore using optimized level3 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.
SCHWARTZ
Keyword
The 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.
RI
Keyword
The 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\nuu)(tu)^{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.
 Use the additional basis specified in the

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.
 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
FINITE_NUCLEI
Keyword
The In some relativistic methods, (e.g. scalaronly 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 FINITE_NUCLEI
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
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

Häser, M., & Ahlrichs, R. (1989). Improvements on the direct SCF method. Journal of Computational Chemistry, 10(1), 104111.
↩ 
Kendall, R. A., & Früchtl, H. A. (1997). The impact of the resolution of the identity approximate integral method on modern ab initio algorithm development. Theoretical Chemistry Accounts, 97(14), 158163.
↩ 
Koch, H., Sánchez de Merás, A., & Pedersen, T. B. (2003). Reduced scaling in electronic structure calculations using Cholesky decompositions. The Journal of chemical physics, 118(21), 94819484.
↩ 
Visscher, L., & Dyall, K. G. (1997). Dirac–Fock atomic electronic structure calculations using different nuclear charge distributions. Atomic Data and Nuclear Data Tables, 67(2), 207224.
↩