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Calling Sequence
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AOIntegrals(molecule, options)
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Parameters
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molecule
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list of lists; each list has 4 elements, the string of an atom's symbol and atom's x, y, and z coordinates
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options
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(optional) equation(s) of the form option = value where option is one of integral_type, basis, spin, charge, symmetry, unit, max_memory
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Description
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The AOIntegrals command generates electronic integrals in an atomic-orbital basis set.
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The following types of integrals, specified by the integral_type keyword, are available:
- "overlap" (default): overlap matrix (S)
- "kinetic": kinetic energy matrix (T)
- "nuclear": nuclear attraction matrix (V)
- "dipole": dipole moment integrals (x, y, z)
- "eri": Electron repulsion integrals (U)
- "quadrupole": Nuclear quadrupole moment integrals (xx, yy, zz, xy, xz, yz)
- "giao": gauge-including atomic orbital (GIAO) integrals for NMR shielding (3 components)
- "efg": electric-field gradient integrals (xx, yy, zz, xy, xz, yz)
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The nuclear attraction integrals, kinetic energy integrals, and overlap integrals are one-electron integrals, and hence, each is returned as an r×r Matrix where r is the number of orbitals.
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The electron repulsion integrals are returned as an r×r×r×r Array where r is the number of orbitals.
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Integrals with multiple components (e.g., dipole, quadrupole, giao, efg) are returned are 3-index Arrays with the first index being the component.
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On the Windows operating system the AOIntegrals command requires the installation of Microsoft's Windows Subsystem for Linux (WSL). For Windows 10 (version 2004 and higher) and Windows 11 you can install the WSL by opening the Command Prompt in administrator mode and entering the command: wsl --install -d Ubuntu For additional details, please refer to: https://learn.microsoft.com/en-us/windows/wsl/install
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Options
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basis = string -- name of the basis set. See Basis for a list of available basis sets. Default is "sto-3g".
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spin = nonnegint -- twice the total spin S (= 2S). Default is 0.
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charge = nonnegint -- net charge of the molecule. Default is 0.
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symmetry = string/boolean -- is the Schoenflies symbol of the abelian point-group symmetry which can be one of the following: D2h, C2h, C2v, D2, Cs, Ci, C2, C1. true finds the appropriate symmetry while false (default) does not use symmetry.
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ghost = list of lists -- each list has the string of an atom's symbol and the atom's x, y, and z coordinates. See Ghost Atoms.
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unit = string -- "Angstrom" or "Bohr". Default is "Angstrom".
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max_memory = posint -- allowed memory in MB. Default is 4000.
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