Forces and properties

Analytic nuclear gradients and the response-property layer. Properties run their own SCF from (mol, xc) and take a grid=becke(...) spec.

dftax.ks.forces.forces(mol: Molecule, xc: XCFunctional, result: KSResult | tuple | Array, *, grid: Becke | None = None, coulomb: ExactSpec | DFSpec | None = None, dispersion=None) -> Float[Array, 'n_atom 3']

Nuclear forces F = -dE/dR (Ha/Bohr), shape (n_atom, 3).

Parameters:

Name	Type	Description	Default
mol	Molecule	a native :class:~dftax.system.molecule.Molecule (the energy is rebuilt as a function of the nuclear coordinates, so the basis and grid must be reconstructible; PySCF Mole objects are not supported here).	required
xc	XCFunctional	the exchange-correlation functional.	required
result	KSResult | tuple | Array	the converged :class:~dftax.ks.scf.KSResult (from :func:~dftax.ks.scf.scf or :func:~dftax.ks.minimize.minimize), or the per-channel occupied coefficients directly. From a result the frozen density is taken from result.P (see :func:_occupied_coefficients), so the forces belong to exactly the density the solver returned.	required
grid	Becke | None	Becke-grid quality (a :func:~dftax.grid.becke spec; match the energy calculation; a chunk on the spec streams the XC grid here too). Explicit point grids cannot follow the nuclei, so only Becke specs are accepted.	None
coulomb	ExactSpec | DFSpec | None	a :func:~dftax.ks.terms.df spec (default, matching the KS default backend) or a plain materialized :func:~dftax.ks.terms.exact. df(chunk="auto") materializes the 3-center tensor when it fits the memory budget, packed over the kept shell pairs with exchange at the frozen occupied coefficients (:class:~dftax.ks.terms.PackedDFForcesCoulomb; smeared hybrids keep the square tensor), and otherwise streams the geometry gradient over shell-aligned auxiliary slabs (RI-J by plain autodiff, RI-K at the frozen occupied coefficients; see :func:dftax.ks.terms._streamed_df_rik_frozen); an int chunk forces streaming, chunk=None forces the materialized tensor. Range-separated hybrids stream both exchange channels (the LR 3-center rebuilt per slab). screen= (with an int chunk) streams too: the Schwarz shell-pair mask is resolved at the reference geometry and baked into the slab plans. The streamed path uses the cartesian auxiliary span, like the streamed SCF backend. Smeared (fractionally occupied) hybrid results need the materialized backend.	None

dftax.ks.properties.dipole(mol, xc: XCFunctional, *, origin=(0.0, 0.0, 0.0), debye: bool = False, grid: Becke | None = None, coulomb: ExactSpec | DFSpec | None = None, **scf_kw) -> Float[Array, 3]

Permanent electric dipole moment μ (atomic units, or Debye if debye).

μ = Σ_A Z_A (R_A − origin) − Tr(P · r) from the converged density. For a neutral molecule the result is independent of origin.

dftax.ks.properties.polarizability(mol, xc: XCFunctional, *, method: str = 'fd', field: float = 0.002, origin=(0.0, 0.0, 0.0), grid: Becke | None = None, coulomb: ExactSpec | DFSpec | None = None, **scf_kw) -> Float[Array, '3 3']

Static dipole polarizability tensor α_ij = ∂μ_i/∂E_j (atomic units).

method="fd" (default): central finite difference of the dipole under a uniform field of strength field (robust; one SCF per ±component). method="analytic": exact coupled-perturbed KS response via implicit differentiation of the SCF fixed point (:func:~dftax.ks.implicit.implicit_density), a single jax.jacobian through the converged density, no field stepping. Returned symmetrized.

dftax.ks.properties.hessian(mol, xc, *, method: str = 'fd', step: float = 0.001, origin=(0.0, 0.0, 0.0), grid: Becke | None = None, coulomb: ExactSpec | DFSpec | None = None, cg_iters: int = 64, **scf_kw) -> Float[Array, 'n n']

Nuclear Hessian ∂²E/∂R_A∂R_B (Ha/Bohr², shape (3N, 3N)).

method="fd" (default): central finite difference of the analytic Pulay-free forces (6N SCF solves). method="analytic": the exact orbital-rotation Schur complement H = E_RR − E_Rκ (E_κκ)⁻¹ E_κR at one tightly converged reference (3N CG response solves; RKS and UKS, materialized Coulomb backends; see :mod:dftax.ks.hessian). step applies to the FD path, cg_iters to the analytic response solves.

dftax.ks.properties.vibrations(mol, xc, *, hess=None, step: float = 0.001, grid: Becke | None = None, coulomb: ExactSpec | DFSpec | None = None, **scf_kw) -> Vibrations

Harmonic vibrational analysis (see :class:Vibrations).

dftax.ks.properties.ir_spectrum(mol, xc, *, step: float = 0.001, origin=(0.0, 0.0, 0.0), grid: Becke | None = None, coulomb: ExactSpec | DFSpec | None = None, **scf_kw) -> IRSpectrum

Harmonic IR spectrum from A_k ∝ |dμ/dQ_k|² (see :class:IRSpectrum).

dftax.ks.properties.raman_spectrum(mol, xc, *, step: float = 0.01, field: float = 0.002, origin=(0.0, 0.0, 0.0), grid: Becke | None = None, coulomb: ExactSpec | DFSpec | None = None, **scf_kw) -> RamanSpectrum

Harmonic Raman activities (Å⁴/amu, up to the usual constant) from the polarizability derivatives dα/dQ. Expensive: a polarizability (field FD) at every ±Cartesian displacement (O(N) Hessians' worth of work).

dftax.ks.properties.alchemical_deriv(mol, xc: XCFunctional, *, grid: Becke | None = None, coulomb: ExactSpec | DFSpec | None = None, **scf_kw) -> Float[Array, n_atom]

Alchemical gradient ∂E/∂Z_A at fixed electron count (Ha per unit charge).

Hellmann-Feynman: the converged density (every spin channel, held fixed via its solve-based projector) and the energy is differentiated w.r.t. the nuclear charges, which enter only the nuclear-attraction and nuclear-repulsion terms.

coulomb=None resolves to :func:~dftax.ks.terms.exact here (not the DF default) for backward compatibility, but df(...) works: the auxiliary basis is resolved eagerly against the molecule (its centers are geometry-fixed here; only the charges vary), so the raw-:class:System charge closure and the outer solve share the same fitted backend.

dftax.ks.properties.Vibrations

Harmonic analysis: frequencies (cm⁻¹, negative = imaginary), mass-weighted modes (columns), Cartesian displacement modes (columns).

__annotations__ class-attribute

dict() -> new empty dictionary dict(mapping) -> new dictionary initialized from a mapping object's (key, value) pairs dict(iterable) -> new dictionary initialized as if via: d = {} for k, v in iterable: d[k] = v dict(**kwargs) -> new dictionary initialized with the name=value pairs in the keyword argument list. For example: dict(one=1, two=2)

__doc__ class-attribute

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to 'utf-8'. errors defaults to 'strict'.

__firstlineno__ class-attribute

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating-point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer iteral.

int('0b100', base=0) 4

__match_args__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

__module__ class-attribute

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to 'utf-8'. errors defaults to 'strict'.

__orig_bases__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

__slots__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

__static_attributes__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

cart_modes class-attribute

Alias for field number 2

frequencies class-attribute

Alias for field number 0

modes class-attribute

Alias for field number 1

dftax.ks.properties.IRSpectrum

Harmonic IR spectrum: frequencies (cm⁻¹) and intensities (km/mol).

__annotations__ class-attribute

dict() -> new empty dictionary dict(mapping) -> new dictionary initialized from a mapping object's (key, value) pairs dict(iterable) -> new dictionary initialized as if via: d = {} for k, v in iterable: d[k] = v dict(**kwargs) -> new dictionary initialized with the name=value pairs in the keyword argument list. For example: dict(one=1, two=2)

__doc__ class-attribute

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to 'utf-8'. errors defaults to 'strict'.

__firstlineno__ class-attribute

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating-point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer iteral.

int('0b100', base=0) 4

__match_args__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

__module__ class-attribute

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to 'utf-8'. errors defaults to 'strict'.

__orig_bases__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

__slots__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

__static_attributes__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

frequencies class-attribute

Alias for field number 0

intensities class-attribute

Alias for field number 1

dftax.ks.properties.RamanSpectrum

Harmonic Raman spectrum: frequencies (cm⁻¹) and activities (Å⁴/amu).

__annotations__ class-attribute

dict() -> new empty dictionary dict(mapping) -> new dictionary initialized from a mapping object's (key, value) pairs dict(iterable) -> new dictionary initialized as if via: d = {} for k, v in iterable: d[k] = v dict(**kwargs) -> new dictionary initialized with the name=value pairs in the keyword argument list. For example: dict(one=1, two=2)

__doc__ class-attribute

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to 'utf-8'. errors defaults to 'strict'.

__firstlineno__ class-attribute

int([x]) -> integer int(x, base=10) -> integer

Convert a number or string to an integer, or return 0 if no arguments are given. If x is a number, return x.int(). For floating-point numbers, this truncates towards zero.

If x is not a number or if base is given, then x must be a string, bytes, or bytearray instance representing an integer literal in the given base. The literal can be preceded by '+' or '-' and be surrounded by whitespace. The base defaults to 10. Valid bases are 0 and 2-36. Base 0 means to interpret the base from the string as an integer iteral.

int('0b100', base=0) 4

__match_args__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

__module__ class-attribute

str(object='') -> str str(bytes_or_buffer[, encoding[, errors]]) -> str

Create a new string object from the given object. If encoding or errors is specified, then the object must expose a data buffer that will be decoded using the given encoding and error handler. Otherwise, returns the result of object.str() (if defined) or repr(object). encoding defaults to 'utf-8'. errors defaults to 'strict'.

__orig_bases__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

__slots__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

__static_attributes__ class-attribute

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable's items.

If the argument is a tuple, the return value is the same object.

activities class-attribute

Alias for field number 1

frequencies class-attribute

Alias for field number 0