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DihedralOptimizer

Optimize dihedral parameters via least-squares fitting of Fourier series coefficients.

Usage

from parametrizani import DihedralOptimizer

optimizer = DihedralOptimizer(max_terms=6, work_dir='./work')
result = optimizer.run_optimization(
    ref_angles, ref_energies,
    mm_energies=mm_energies,
    atom_types=['ca', 'ca', 'os', 'ca']
)

# Select specific number of terms
params = optimizer.format_frcmod_params(result, n_terms=3, idivf=1)
print(params)

# Write FRCMOD file
frcmod_file = optimizer.write_frcmod(result, idivf=1, n_terms=3)

FRCMOD Format

The optimizer writes AMBER-format FRCMOD lines with continuation signs:

DIHE
ca-ca-os-ca   1       1.2000    180.00    -2.0
ca-ca-os-ca   1       0.3000      0.00     3.0
  • Negative PN (periodicity) indicates continuation (more terms follow)
  • Positive PN marks the final term for that dihedral
  • IDIVF is the scaling factor for equivalent torsions

API Reference

parametrizani.dihedral_optimizer.DihedralOptimizer

Optimize dihedral parameters by fitting to a reference energy profile.

Uses linear least-squares regression to determine optimal Fourier series coefficients for the dihedral potential:

V(phi) = sum_n [ V_n * (1 + cos(n*phi - delta_n)) ]

Parameters:

Name Type Description Default
max_terms int

Maximum number of Fourier terms (1-6). Default 6.

 6
work_dir str

Working directory for output files.

 './work'
allow_asymmetric_phase bool

If True, phase shifts are not constrained to 0/180. Default True.

 True
Source code in parametrizani/dihedral_optimizer.py 
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class DihedralOptimizer:
    """
    Optimize dihedral parameters by fitting to a reference energy profile.

    Uses linear least-squares regression to determine optimal Fourier series
    coefficients for the dihedral potential:

        V(phi) = sum_n [ V_n * (1 + cos(n*phi - delta_n)) ]

    Parameters
    ----------
    max_terms : int
        Maximum number of Fourier terms (1-6). Default 6.
    work_dir : str
        Working directory for output files.
    allow_asymmetric_phase : bool
        If True, phase shifts are not constrained to 0/180. Default True.
    """

    def __init__(self, max_terms: int = 6, work_dir: str = './work',
                 allow_asymmetric_phase: bool = True):
        self.max_terms = min(max_terms, 6)
        self.work_dir = create_work_dir(work_dir)
        self.allow_asymmetric_phase = allow_asymmetric_phase
        self._setup_default_parameters()

    def _setup_default_parameters(self):
        """Set up default fitting parameters."""
        self.multiplicities = [0, 1, 1, 2, 2, 3, 6]
        self.phase_shifts = [1, 1, 1, 1, 1, 1, 1]
        self.phase_offsets = [0, 0, 120, 0, 120, 0, 0]
        self.is_active = [1, 1, 1, 1, 1, 1, 1]
        self.run_sequences = [
            [3], [0, 3], [0, 3, 5], [0, 3, 5, 6],
            [0, 1, 3, 5, 6], [0, 1, 2, 3, 5, 6],
        ]

    def _fit_dihedral(self, n_terms, ref_phis, ref_energies, mm_energies,
                      weights, multiplicities, phase_shifts, phase_offsets, is_active):
        """Core least-squares fitting routine."""
        n_points = len(ref_phis)
        n_active = sum(is_active)

        A = np.zeros((n_points, n_active))
        b = np.zeros(n_points)

        for i in range(n_points):
            phi_rad = math.radians(ref_phis[i])
            b[i] = (ref_energies[i] - mm_energies[i]) * weights[i]
            col = 0
            for j in range(n_terms):
                if is_active[j]:
                    n_mult = multiplicities[j]
                    offset_rad = math.radians(phase_offsets[j])
                    if phase_shifts[j] == 1:
                        A[i, col] = (1.0 + math.cos(n_mult * phi_rad - offset_rad)) * weights[i]
                    else:
                        A[i, col] = (1.0 - math.cos(n_mult * phi_rad - offset_rad)) * weights[i]
                    col += 1

        try:
            coeffs, residuals, rank, sv = np.linalg.lstsq(A, b, rcond=None)
        except np.linalg.LinAlgError:
            coeffs = np.zeros(n_active)
            logger.warning("Least squares fitting failed")

        fitted = np.zeros(n_points)
        for i in range(n_points):
            phi_rad = math.radians(ref_phis[i])
            col = 0
            for j in range(n_terms):
                if is_active[j]:
                    n_mult = multiplicities[j]
                    offset_rad = math.radians(phase_offsets[j])
                    if phase_shifts[j] == 1:
                        fitted[i] += coeffs[col] * (1.0 + math.cos(n_mult * phi_rad - offset_rad))
                    else:
                        fitted[i] += coeffs[col] * (1.0 - math.cos(n_mult * phi_rad - offset_rad))
                    col += 1
            fitted[i] += mm_energies[i]

        return fitted, coeffs

    def run_optimization(
        self,
        ref_angles: List[float],
        ref_energies: List[float],
        mm_energies: Optional[List[float]] = None,
        atom_types: Optional[List[str]] = None,
        weights: Optional[List[float]] = None,
    ) -> Dict[str, Any]:
        """
        Run the full dihedral optimization.

        Parameters
        ----------
        ref_angles : List[float]
            Reference dihedral angles (degrees).
        ref_energies : List[float]
            Reference energies (kcal/mol).
        mm_energies : Optional[List[float]]
            MM energies (kcal/mol). If None, assumes zeros.
        atom_types : Optional[List[str]]
            Atom types for the 4 dihedral atoms.
        weights : Optional[List[float]]
            Fitting weights.

        Returns
        -------
        Dict[str, Any]
            Optimization results with 'best_fit', 'rmse', 'parameters', etc.
        """
        n_points = len(ref_angles)
        if mm_energies is None:
            mm_energies = [0.0] * n_points
        if weights is None:
            weights = [1.0] * n_points

        ref_min = min(ref_energies)
        mm_min = min(mm_energies)
        ref_norm = [e - ref_min for e in ref_energies]
        mm_norm = [e - mm_min for e in mm_energies] if abs(mm_min) > SMALL_REAL else mm_energies

        all_fitted = []
        all_coeffs = []
        all_rmse = []
        all_parameters = {}
        fitted_coefficients_list = []
        phase_offset_list = []
        multiplicity_list = []

        for run_idx, sequence in enumerate(self.run_sequences[:self.max_terms]):
            n_terms = len(sequence)
            sel_mult = [self.multiplicities[i] for i in sequence]
            sel_pshift = [self.phase_shifts[i] for i in sequence]
            sel_phase = [self.phase_offsets[i] for i in sequence]
            sel_active = [1] * n_terms

            fitted, coeffs = self._fit_dihedral(
                n_terms, ref_angles, ref_norm, mm_norm,
                weights, sel_mult, sel_pshift, sel_phase, sel_active
            )

            rmse = np.sqrt(np.mean((np.array(fitted) - np.array(ref_norm)) ** 2))
            all_fitted.append(fitted.tolist())
            all_coeffs.append(coeffs.tolist())
            all_rmse.append(rmse)

            params = {}
            for j, (coeff, mult, phase) in enumerate(zip(coeffs, sel_mult, sel_phase)):
                params[j + 1] = {
                    'V_n': float(coeff),
                    'phase': float(phase),
                    'periodicity': int(mult),
                }
                fitted_coefficients_list.append(float(coeff))
                phase_offset_list.append(float(phase))
                multiplicity_list.append(int(mult))
            all_parameters[run_idx + 1] = params
            logger.info(f"  {run_idx + 1} terms: RMSE = {rmse:.4f} kcal/mol")

        best_idx = self.max_terms - 1
        best_fit = all_fitted[best_idx]
        best_rmse = all_rmse[best_idx]
        best_params = all_parameters[best_idx + 1]

        output_file = os.path.join(self.work_dir, 'optimized_dihedral.dat')
        write_energy_file(output_file, ref_angles, best_fit)

        frcmod_params_by_terms = {
            n_terms: self._format_frcmod_params(params, atom_types)
            for n_terms, params in all_parameters.items()
        }
        frcmod_params = frcmod_params_by_terms.get(
            self.max_terms,
            self._format_frcmod_params(best_params, atom_types),
        )

        return {
            'angles': ref_angles,
            'energies_reference': ref_norm,
            'energies_mm': mm_norm,
            'energies_fitted': all_fitted,
            'best_fit': best_fit,
            'coefficients': all_coeffs,
            'parameters': all_parameters,
            'best_parameters': best_params,
            'rmse': best_rmse,
            'all_rmse': all_rmse,
            'atom_types': atom_types,
            'frcmod_params': frcmod_params,
            'frcmod_params_by_terms': frcmod_params_by_terms,
            'output_file': output_file,
            'fitted_coefficients_list': fitted_coefficients_list,
            'phase_offset_list': phase_offset_list,
            'multiplicity_list': multiplicity_list,
        }

    def get_parameters_for_terms(self, result: Dict[str, Any],
                                 n_terms: Optional[int] = None) -> Dict[str, Dict[str, Any]]:
        """Return the fitted parameter set for the requested number of Fourier terms."""
        if n_terms is None:
            return result['best_parameters']

        n_terms = int(n_terms)
        available = result.get('parameters', {})
        if n_terms not in available:
            raise ValueError(
                f"Requested {n_terms} terms, but available fits are: {sorted(available)}"
            )
        return available[n_terms]

    def format_frcmod_params(self, result: Dict[str, Any], n_terms: Optional[int] = None,
                             atom_types: Optional[List[str]] = None, idivf: int = 1) -> str:
        """Format the requested fitted parameter set in AMBER FRCMOD format."""
        params = self.get_parameters_for_terms(result, n_terms=n_terms)
        if atom_types is None:
            atom_types = result.get('atom_types')
        return self._format_frcmod_params(params, atom_types=atom_types, idivf=idivf)

    def _format_frcmod_params(self, params, atom_types=None, idivf=1):
        """Format parameters in AMBER FRCMOD format."""
        if atom_types is None:
            atom_types = ['X', 'X', 'X', 'X']
        type_str = f"{atom_types[0]}-{atom_types[1]}-{atom_types[2]}-{atom_types[3]}"
        lines = ["DIHE"]

        valid_terms = []
        for p in params.values():
            periodicity = int(p['periodicity'])
            if periodicity <= 0:
                continue
            valid_terms.append(p)

        for idx, p in enumerate(valid_terms):
            v_n = p['V_n']
            phase = p['phase']
            periodicity = abs(int(p['periodicity']))
            pn_sign = -periodicity if idx < len(valid_terms) - 1 else periodicity
            line = f"{type_str}   {idivf}   {v_n:10.4f}  {phase:8.2f}  {pn_sign:6.1f}"
            lines.append(line)
        return "\n".join(lines)

    def write_frcmod(self, result, output_file=None, idivf=1, n_terms=None):
        """Write optimized parameters to FRCMOD file."""
        if output_file is None:
            output_file = os.path.join(self.work_dir, 'optimized.frcmod')
        frcmod_content = self.format_frcmod_params(
            result, n_terms=n_terms, atom_types=result.get('atom_types'), idivf=idivf
        )
        with open(output_file, 'w') as f:
            f.write("Remark: ParametrizANI optimized dihedral parameters\n")
            f.write(frcmod_content)
            f.write("\n\n")
        logger.info(f"FRCMOD file written: {output_file}")
        return output_file

    def calculate_dihedral_energy(self, angles, parameters, mm_energies=None):
        """Calculate dihedral energy for given angles using fitted parameters."""
        if mm_energies is None:
            mm_energies = [0.0] * len(angles)
        values = []
        for i, angle in enumerate(angles):
            e_dihedral = 0.0
            for term in parameters.values():
                v_n = term['V_n']
                phase = term['phase']
                n = term['periodicity']
                e_dihedral += v_n * (1.0 + math.cos(math.radians(n * angle - phase)))
            values.append(e_dihedral + mm_energies[i])
        return values

__init__ 

__init__(max_terms: int = 6, work_dir: str = './work', allow_asymmetric_phase: bool = True)
Source code in parametrizani/dihedral_optimizer.py 
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def __init__(self, max_terms: int = 6, work_dir: str = './work',
             allow_asymmetric_phase: bool = True):
    self.max_terms = min(max_terms, 6)
    self.work_dir = create_work_dir(work_dir)
    self.allow_asymmetric_phase = allow_asymmetric_phase
    self._setup_default_parameters()

run_optimization 

run_optimization(ref_angles: List[float], ref_energies: List[float], mm_energies: Optional[List[float]] = None, atom_types: Optional[List[str]] = None, weights: Optional[List[float]] = None) -> Dict[str, Any]

Run the full dihedral optimization.

Parameters:

Name Type Description Default
ref_angles List[float]

Reference dihedral angles (degrees).

 required
ref_energies List[float]

Reference energies (kcal/mol).

 required
mm_energies Optional[List[float]]

MM energies (kcal/mol). If None, assumes zeros.

 None
atom_types Optional[List[str]]

Atom types for the 4 dihedral atoms.

 None
weights Optional[List[float]]

Fitting weights.

 None

Returns:

Type Description
Dict[str, Any]

Optimization results with 'best_fit', 'rmse', 'parameters', etc.
Source code in parametrizani/dihedral_optimizer.py 
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def run_optimization(
    self,
    ref_angles: List[float],
    ref_energies: List[float],
    mm_energies: Optional[List[float]] = None,
    atom_types: Optional[List[str]] = None,
    weights: Optional[List[float]] = None,
) -> Dict[str, Any]:
    """
    Run the full dihedral optimization.

    Parameters
    ----------
    ref_angles : List[float]
        Reference dihedral angles (degrees).
    ref_energies : List[float]
        Reference energies (kcal/mol).
    mm_energies : Optional[List[float]]
        MM energies (kcal/mol). If None, assumes zeros.
    atom_types : Optional[List[str]]
        Atom types for the 4 dihedral atoms.
    weights : Optional[List[float]]
        Fitting weights.

    Returns
    -------
    Dict[str, Any]
        Optimization results with 'best_fit', 'rmse', 'parameters', etc.
    """
    n_points = len(ref_angles)
    if mm_energies is None:
        mm_energies = [0.0] * n_points
    if weights is None:
        weights = [1.0] * n_points

    ref_min = min(ref_energies)
    mm_min = min(mm_energies)
    ref_norm = [e - ref_min for e in ref_energies]
    mm_norm = [e - mm_min for e in mm_energies] if abs(mm_min) > SMALL_REAL else mm_energies

    all_fitted = []
    all_coeffs = []
    all_rmse = []
    all_parameters = {}
    fitted_coefficients_list = []
    phase_offset_list = []
    multiplicity_list = []

    for run_idx, sequence in enumerate(self.run_sequences[:self.max_terms]):
        n_terms = len(sequence)
        sel_mult = [self.multiplicities[i] for i in sequence]
        sel_pshift = [self.phase_shifts[i] for i in sequence]
        sel_phase = [self.phase_offsets[i] for i in sequence]
        sel_active = [1] * n_terms

        fitted, coeffs = self._fit_dihedral(
            n_terms, ref_angles, ref_norm, mm_norm,
            weights, sel_mult, sel_pshift, sel_phase, sel_active
        )

        rmse = np.sqrt(np.mean((np.array(fitted) - np.array(ref_norm)) ** 2))
        all_fitted.append(fitted.tolist())
        all_coeffs.append(coeffs.tolist())
        all_rmse.append(rmse)

        params = {}
        for j, (coeff, mult, phase) in enumerate(zip(coeffs, sel_mult, sel_phase)):
            params[j + 1] = {
                'V_n': float(coeff),
                'phase': float(phase),
                'periodicity': int(mult),
            }
            fitted_coefficients_list.append(float(coeff))
            phase_offset_list.append(float(phase))
            multiplicity_list.append(int(mult))
        all_parameters[run_idx + 1] = params
        logger.info(f"  {run_idx + 1} terms: RMSE = {rmse:.4f} kcal/mol")

    best_idx = self.max_terms - 1
    best_fit = all_fitted[best_idx]
    best_rmse = all_rmse[best_idx]
    best_params = all_parameters[best_idx + 1]

    output_file = os.path.join(self.work_dir, 'optimized_dihedral.dat')
    write_energy_file(output_file, ref_angles, best_fit)

    frcmod_params_by_terms = {
        n_terms: self._format_frcmod_params(params, atom_types)
        for n_terms, params in all_parameters.items()
    }
    frcmod_params = frcmod_params_by_terms.get(
        self.max_terms,
        self._format_frcmod_params(best_params, atom_types),
    )

    return {
        'angles': ref_angles,
        'energies_reference': ref_norm,
        'energies_mm': mm_norm,
        'energies_fitted': all_fitted,
        'best_fit': best_fit,
        'coefficients': all_coeffs,
        'parameters': all_parameters,
        'best_parameters': best_params,
        'rmse': best_rmse,
        'all_rmse': all_rmse,
        'atom_types': atom_types,
        'frcmod_params': frcmod_params,
        'frcmod_params_by_terms': frcmod_params_by_terms,
        'output_file': output_file,
        'fitted_coefficients_list': fitted_coefficients_list,
        'phase_offset_list': phase_offset_list,
        'multiplicity_list': multiplicity_list,
    }

format_frcmod_params 

format_frcmod_params(result: Dict[str, Any], n_terms: Optional[int] = None, atom_types: Optional[List[str]] = None, idivf: int = 1) -> str

Format the requested fitted parameter set in AMBER FRCMOD format.

Source code in parametrizani/dihedral_optimizer.py 
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def format_frcmod_params(self, result: Dict[str, Any], n_terms: Optional[int] = None,
                         atom_types: Optional[List[str]] = None, idivf: int = 1) -> str:
    """Format the requested fitted parameter set in AMBER FRCMOD format."""
    params = self.get_parameters_for_terms(result, n_terms=n_terms)
    if atom_types is None:
        atom_types = result.get('atom_types')
    return self._format_frcmod_params(params, atom_types=atom_types, idivf=idivf)

get_parameters_for_terms 

get_parameters_for_terms(result: Dict[str, Any], n_terms: Optional[int] = None) -> Dict[str, Dict[str, Any]]

Return the fitted parameter set for the requested number of Fourier terms.

Source code in parametrizani/dihedral_optimizer.py 
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def get_parameters_for_terms(self, result: Dict[str, Any],
                             n_terms: Optional[int] = None) -> Dict[str, Dict[str, Any]]:
    """Return the fitted parameter set for the requested number of Fourier terms."""
    if n_terms is None:
        return result['best_parameters']

    n_terms = int(n_terms)
    available = result.get('parameters', {})
    if n_terms not in available:
        raise ValueError(
            f"Requested {n_terms} terms, but available fits are: {sorted(available)}"
        )
    return available[n_terms]

write_frcmod 

write_frcmod(result, output_file=None, idivf=1, n_terms=None)

Write optimized parameters to FRCMOD file.

Source code in parametrizani/dihedral_optimizer.py 
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def write_frcmod(self, result, output_file=None, idivf=1, n_terms=None):
    """Write optimized parameters to FRCMOD file."""
    if output_file is None:
        output_file = os.path.join(self.work_dir, 'optimized.frcmod')
    frcmod_content = self.format_frcmod_params(
        result, n_terms=n_terms, atom_types=result.get('atom_types'), idivf=idivf
    )
    with open(output_file, 'w') as f:
        f.write("Remark: ParametrizANI optimized dihedral parameters\n")
        f.write(frcmod_content)
        f.write("\n\n")
    logger.info(f"FRCMOD file written: {output_file}")
    return output_file

calculate_dihedral_energy 

calculate_dihedral_energy(angles, parameters, mm_energies=None)

Calculate dihedral energy for given angles using fitted parameters.

Source code in parametrizani/dihedral_optimizer.py 
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def calculate_dihedral_energy(self, angles, parameters, mm_energies=None):
    """Calculate dihedral energy for given angles using fitted parameters."""
    if mm_energies is None:
        mm_energies = [0.0] * len(angles)
    values = []
    for i, angle in enumerate(angles):
        e_dihedral = 0.0
        for term in parameters.values():
            v_n = term['V_n']
            phase = term['phase']
            n = term['periodicity']
            e_dihedral += v_n * (1.0 + math.cos(math.radians(n * angle - phase)))
        values.append(e_dihedral + mm_energies[i])
    return values