One- and Two-Electron Integral Calculation - XUANYUAN Module

The XUANYUAN module primarily calculates one- and two-electron integrals and other necessary integrals, storing them to files.

Direct Parameter Type: Boolean

Specifies using integral-direct SCF calculations. This is now the default option and does not require user setting.

Integral-direct SCF does not store two-electron integrals. It pre-screens integrals using the Schwartz inequality based on their contribution to the Fock matrix. For systems with more than ~300 basis functions, it efficiently utilizes integral recomputation to avoid I/O operations and supports OpenMP multi-core parallelization. Most BDF modules requiring Fock-like matrices (J and K), such as SCF and TDDFT, implement integral-direct calculations.

Note

Integral-direct SCF also requires the Skeleton keyword in the compass module, which is now the default. To disable integral-direct SCF, use the Saorb keyword in the compass module.

Maxmem Parameter Type: String

Specifies the cache size for non-integral-direct SCF two-electron integral calculations. Larger caches reduce integral sorting frequency. Format: number + MW or GW. 1 Word = 2 Bytes, so 512MW = 1024 MB.

$xuanyuan
Maxmem
  512MW
$end

RSOMEGA / RS Parameter Type: Floating-point

Specifies the \(\omega\) parameter (sometimes denoted \(\mu\) in literature) for range-separated functionals (e.g., CAM-B3LYP). RS is a synonym for RSOMEGA. Required if using a range-separated DFT functional. Recommended values:

Standard \(\omega\) values for common range-separated functionals

Functional

\(\omega\)

CAM-B3LYP

0.33

LC-BLYP

0.33

wB97

0.40

wB97X

0.30

 
$xuanyuan
RSOMEGA
  0.33
$end

$scf
  dft
    cam-b3lyp
$end

Heff Parameter Type: Integer

  • Default: 0

  • Options: 0, 1, 2, 3/4, 5, 21, 22, 23

Specifies the scalar relativistic Hamiltonian:

  • 0: Non-relativistic (including cases using ECPs)

  • 1: sf-ZORA (not recommended for general users)

  • 2: sf-IORA (not recommended for general users)

  • 3, 4: sf-X2C (different implementations; generally use 3)

  • 5: sf-X2C + so-DKH3 (no spin-orbit part; requires Hsoc; accuracy under further testing) [12]

  • 21: sf-X2C (similar to 3/4, supports analytical derivatives & some one-electron properties) [27]

  • 22: sf-X2C-aXR (atomic X-matrix approximated sf-X2C; supports analytical derivatives & some properties) [27]

  • 23: sf-X2C-aU (atomic unitary transformation approximated sf-X2C; supports analytical derivatives & some properties) [27]

$xuanyuan
Heff
  3
$end

Hsoc Parameter Type: Integer

  • Options: 0, 1, 2, 3, 4, 5

Specifies the type of spin-orbit (SO) integrals:

  • 0: so-1e - Only one-electron SO integrals.

  • 1: so-1e + SOMF - Two-electron SO integrals via the effective Fock operator. Most accurate for all-electron calculations.

  • 2: so-1e + SOMF-1c - SOMF with one-center approximation. Recommended for large molecules with all-electron calculations.

  • 3: so-1e + SOMF-1c / no soo - Disables spin-other-orbit (SOO) contributions in option 2.

  • 4: so-1e + SOMF-1c / no soo + WSO_XC - Uses DFT to calculate SOO contributions.

  • 5: so-1e + somf-1c / no soo + WSO_XC-2x - Multiplies DFT part by -2 to model SOO (suggestion by Neese).

  • Adding 10 to any option uses the BP approximation operator.

  • For ECP basis sets (scalar ECP, SOECP, or mixed with all-electron non-relativistic), the only accepted value is 10 (default). This uses BP so-1e: SOECP integrals for SOECP atoms, effective nuclear charge for scalar ECP and non-relativistic all-electron atoms (limited element/basis support - see soint_util/zefflib.F90).

$xuanyuan
Hsoc
  1
$end

Clight Parameter Type: Integer

  • Default: 0

  • Options: 0, 1, 2, 100

Specifies the speed of light in atomic units, used for the calculation of the full-electron relativistic Hamiltonian.

  • 0: the default value for BDF.

  • 1: the default value for Gaussian 16.

  • 2: the default value for OpenMolcas.

  • 100: infinite speed of light, used for program debugging and reproducing non-relativistic results.

Nuclear Parameter Type: Integer

  • Default: 0

  • Options: 0, 1

Specifies the nuclear charge distribution model: * 0: Point charge model * 1: Gaussian charge model. For elements up to 110 (Ds), root-mean-square (RMS) nuclear radii are from Visscher and Dyall [71]. For elements Ds and beyond, RMS nuclear radii are estimated from the mass number A (in fermi):

\[\left<r^2\right> \approx 0.57 + 0.836 \, A^{1/3}\]

The mass number A is approximated from the nuclear charge Z using [72, 73]:

\[A \approx 0.004467 \, Z^2 + 2.163 \, Z - 1.168\]

NuclearRadii Input Block

Specifies nuclear radii. This block only takes effect if the finite nucleus model is enabled (nuclear=1). Unspecified atoms use default values. Input format follows the AtomMass block in the Compass module.