"""
Utility functions for antinature quantum chemistry calculations.
"""

import importlib
import warnings
from typing import Any, Dict, List, Optional, Tuple, Union

import numpy as np
import scipy.constants as constants

from .core.basis import MixedMatterBasis
from .core.correlation import AntinatureCorrelation
from .core.hamiltonian import AntinatureHamiltonian
from .core.integral_engine import AntinatureIntegralEngine

# Import project modules
from .core.molecular_data import MolecularData
from .core.scf import AntinatureSCF

# Constants for conversions
BOHR_TO_ANGSTROM = 0.529177249
HARTREE_TO_EV = 27.2114
FINE_STRUCTURE_CONSTANT = 7.2973525693e-3  # α
ELECTRON_MASS = 9.1093837015e-31  # kg
SPEED_OF_LIGHT = 299792458  # m/s
PLANCK_CONSTANT = 6.62607015e-34  # J·s
ELECTRON_RADIUS = 2.8179403227e-15  # m


def check_dependencies(dependencies: Dict[str, str]) -> Tuple[bool, List[str]]:
    """
    Check if all dependencies are installed with required versions.

    Parameters:
    -----------
    dependencies : Dict[str, str]
        Dictionary mapping package names to required version specs

    Returns:
    --------
    Tuple[bool, List[str]]
        (Success, List of missing/incompatible packages)

    Example:
    --------
    >>> check_dependencies({'numpy': '>=1.20.0', 'qiskit': '>=1.0.0'})
    """
    import pkg_resources

    missing = []

    for package, version_spec in dependencies.items():
        try:
            pkg_resources.require(f"{package}{version_spec}")
        except (pkg_resources.VersionConflict, pkg_resources.DistributionNotFound):
            missing.append(f"{package}{version_spec}")

    return len(missing) == 0, missing


def check_optional_dependencies() -> Dict[str, bool]:
    """
    Check which optional dependencies are available.

    Returns:
    --------
    Dict[str, bool]
        Dictionary indicating which optional features are available
    """
    dependencies = {
        'qiskit': False,  # For quantum simulation
        'pyscf': False,  # For advanced electronic structure
        'openfermion': False,  # For quantum chemistry mapping
    }

    # Check Qiskit
    try:
        import qiskit

        dependencies['qiskit'] = True
    except ImportError:
        pass

    # Check PySCF
    try:
        import pyscf

        dependencies['pyscf'] = True
    except ImportError:
        pass

    # Check OpenFermion
    try:
        import openfermion

        dependencies['openfermion'] = True
    except ImportError:
        pass

    return dependencies


def create_antinature_calculation(
    molecule_data: Union[Dict, MolecularData],
    basis_options: Optional[Dict] = None,
    calculation_options: Optional[Dict] = None,
) -> Dict:
    """
    Create a complete antinature calculation workflow.

    Parameters:
    -----------
    molecule_data : Dict or MolecularData
        Molecular structure information
    basis_options : Dict, optional
        Options for basis set generation
    calculation_options : Dict, optional
        Options for calculation parameters

    Returns:
    --------
    Dict
        Configuration for the calculation
    """
    # Initialize molecular data if needed
    if not isinstance(molecule_data, MolecularData):
        molecule_data = MolecularData(**molecule_data)

    # Set default options
    if basis_options is None:
        basis_options = {'quality': 'standard'}

    if calculation_options is None:
        calculation_options = {
            'include_annihilation': True,
            'include_relativistic': False,
            'scf_options': {
                'max_iterations': 100,
                'convergence_threshold': 1e-6,
                'use_diis': True,
            },
        }

    # Create basis
    basis = MixedMatterBasis()
    if (
        hasattr(basis, f"create_{molecule_data.name.lower()}_basis")
        and basis_options.get('quality') == molecule_data.name.lower()
    ):
        # Use specialized basis if available
        getattr(basis, f"create_{molecule_data.name.lower()}_basis")()
    else:
        # Use general basis otherwise
        quality = basis_options.get('quality', 'standard')
        basis.create_for_molecule(
            molecule_data.atoms, e_quality=quality, p_quality=quality
        )

    # Create integral engine
    integral_engine = AntinatureIntegralEngine()

    # Create Hamiltonian with the integral engine
    hamiltonian = AntinatureHamiltonian(
        molecular_data=molecule_data,
        basis_set=basis,
        integral_engine=integral_engine,
        include_annihilation=calculation_options.get('include_annihilation', True),
        include_relativistic=calculation_options.get('include_relativistic', False),
    )

    # Build the Hamiltonian (this will compute all necessary integrals)
    hamiltonian_matrices = hamiltonian.build_hamiltonian()

    # Apply relativistic corrections if requested
    if calculation_options.get('include_relativistic', False):
        from .specialized.relativistic import RelativisticCorrection

        rel_correction = RelativisticCorrection(hamiltonian, basis, molecule_data)
        rel_correction.calculate_relativistic_integrals()
        hamiltonian = rel_correction.apply_corrections()

    # Run SCF calculation
    scf_solver = AntinatureSCF(
        hamiltonian=hamiltonian_matrices,
        basis_set=basis,
        molecular_data=molecule_data,
        **calculation_options.get('scf_options', {}),
    )

    scf_result = scf_solver.solve_scf()

    # Calculate annihilation rate if requested
    if (
        calculation_options.get('include_annihilation', False)
        and molecule_data.n_positrons > 0
    ):
        from .specialized.annihilation import AnnihilationOperator

        annihilation_op = AnnihilationOperator(basis, scf_result)
        annihilation_result = annihilation_op.calculate_annihilation_rate()
        scf_result.update(annihilation_result)

    return scf_result


def run_antinature_calculation(configuration: Dict) -> Dict:
    """
    Run a complete antinature calculation using the provided configuration.

    Parameters:
    -----------
    configuration : Dict
        Configuration from create_antinature_calculation

    Returns:
    --------
    Dict
        Results of the calculation
    """
    # Extract components
    scf_solver = configuration['scf_solver']

    # Run SCF calculation
    scf_results = scf_solver.solve_scf()

    # Optionally run post-SCF calculations
    post_scf_results = {}

    if configuration.get('run_mp2', False):
        correlation = AntinatureCorrelation(
            scf_result=scf_results,
            hamiltonian=configuration['hamiltonian_matrices'],
            basis=configuration['basis_set'],
        )
        post_scf_results['mp2_energy'] = correlation.mp2_energy()

    if configuration.get('calculate_annihilation', False) and 'correlation' in locals():
        post_scf_results['annihilation_rate'] = (
            correlation.calculate_annihilation_rate()
        )

    # Combine results
    results = {
        'scf': scf_results,
        'post_scf': post_scf_results,
        'molecular_data': configuration['molecular_data'],
        'basis_info': {
            'n_electron_basis': configuration['basis_set'].n_electron_basis,
            'n_positron_basis': configuration['basis_set'].n_positron_basis,
            'n_total_basis': configuration['basis_set'].n_total_basis,
        },
    }

    return results


def calculate_annihilation_rate(
    electron_density: np.ndarray,
    positron_density: np.ndarray,
    overlap_matrix: np.ndarray,
    basis_set: Union[MixedMatterBasis, Any],
    include_relativistic_effects: bool = False,
) -> float:
    """
    Calculate the electron-positron annihilation rate.

    Parameters:
    -----------
    electron_density : np.ndarray
        Electron density matrix
    positron_density : np.ndarray
        Positron density matrix
    overlap_matrix : np.ndarray
        Overlap matrix between electron and positron basis functions
    basis_set : MixedMatterBasis or other basis set object
        Basis set used for the calculation
    include_relativistic_effects : bool, optional
        Whether to include relativistic effects in the calculation

    Returns:
    --------
    float
        Annihilation rate in s^-1
    """
    # Basic implementation of annihilation rate
    # In real calculations, this would involve integrating the overlap
    # of electron and positron wavefunctions

    # Check inputs
    if electron_density is None or positron_density is None or overlap_matrix is None:
        warnings.warn(
            "Missing density matrices or overlap matrix, returning zero annihilation rate"
        )
        return 0.0

    # Calculate overlap integral between electron and positron densities
    # This is a simplified approximation
    if hasattr(basis_set, 'electron_basis') and hasattr(basis_set, 'positron_basis'):
        # For mixed basis sets
        n_e_basis = len(basis_set.electron_basis)
        n_p_basis = len(basis_set.positron_basis)
    else:
        # Try to infer dimensions
        n_e_basis = electron_density.shape[0]
        n_p_basis = positron_density.shape[0]

    # Ensure overlap matrix has right dimensions
    if overlap_matrix.shape != (n_e_basis, n_p_basis):
        if overlap_matrix.shape == (n_e_basis + n_p_basis, n_e_basis + n_p_basis):
            # Extract relevant part from block matrix
            overlap_subset = overlap_matrix[
                :n_e_basis, n_e_basis : n_e_basis + n_p_basis
            ]
        else:
            warnings.warn(
                f"Overlap matrix has incorrect shape: {overlap_matrix.shape}, expected: {(n_e_basis, n_p_basis)}"
            )
            overlap_subset = (
                np.ones((n_e_basis, n_p_basis)) * 0.5
            )  # Default approximation
    else:
        overlap_subset = overlap_matrix

    # Calculate annihilation rate using Dirac's formula with overlap
    # Γ = πr₀²c ∫|ψₑ(r)ψₚ(r)|² dr
    # where r₀ is the classical electron radius, c is the speed of light

    # Calculate wavefunction overlap integral
    overlap_integral = np.trace(
        np.dot(
            np.dot(electron_density, overlap_subset),
            np.dot(positron_density, overlap_subset.T),
        )
    )

    # Calculate annihilation rate
    # Convert from atomic units to SI for constants
    r0_squared = ELECTRON_RADIUS**2
    c = SPEED_OF_LIGHT

    # Base rate for 2-gamma annihilation
    rate = np.pi * r0_squared * c * overlap_integral

    # Apply relativistic correction if requested
    if include_relativistic_effects:
        # Add relativistic enhancement factor (~1.015 for ground state positronium)
        rel_factor = 1.0 + FINE_STRUCTURE_CONSTANT * np.pi / 2
        rate *= rel_factor

    # Convert to s^-1
    # The formula gives rate in atomic units, need to convert to s^-1
    # 1 a.u. of time = 2.4188843e-17 s
    atomic_time_to_seconds = 2.4188843e-17
    rate /= atomic_time_to_seconds

    return rate


def calculate_lifetime(annihilation_rate: float) -> float:
    """
    Calculate the positron lifetime from the annihilation rate.

    Parameters:
    -----------
    annihilation_rate : float
        Annihilation rate in s^-1

    Returns:
    --------
    float
        Lifetime in nanoseconds
    """
    if annihilation_rate <= 0:
        warnings.warn("Invalid annihilation rate, returning infinite lifetime")
        return float('inf')

    # Lifetime is the inverse of the annihilation rate
    lifetime_seconds = 1.0 / annihilation_rate

    # Convert to nanoseconds (1 ns = 1e-9 s)
    lifetime_ns = lifetime_seconds * 1e9

    return lifetime_ns


def calculate_density_grid(
    density_matrix: np.ndarray,
    basis_set: Any,
    grid_x: np.ndarray,
    grid_y: np.ndarray,
    grid_z: np.ndarray,
) -> np.ndarray:
    """
    Calculate the density on a 3D grid.

    Parameters:
    -----------
    density_matrix : np.ndarray
        Density matrix
    basis_set : Any
        Basis set object with eval_basis_functions method
    grid_x : np.ndarray
        Grid points in x direction
    grid_y : np.ndarray
        Grid points in y direction
    grid_z : np.ndarray
        Grid points in z direction

    Returns:
    --------
    np.ndarray
        3D array of density values with shape (len(grid_x), len(grid_y), len(grid_z))
    """
    # Initialize density grid
    density = np.zeros((len(grid_x), len(grid_y), len(grid_z)))

    # Check if input is valid
    if density_matrix is None or basis_set is None:
        warnings.warn("Missing density matrix or basis set, returning zero density")
        return density

    # Create meshgrid of points
    X, Y, Z = np.meshgrid(grid_x, grid_y, grid_z, indexing='ij')
    points = np.vstack([X.flatten(), Y.flatten(), Z.flatten()]).T

    # Evaluate basis functions on grid
    # Assuming basis_set has a method to evaluate basis functions on grid points
    if hasattr(basis_set, 'eval_basis_functions'):
        basis_values = basis_set.eval_basis_functions(points)
    else:
        # Simple approximation if no proper method exists
        # This is a placeholder and would need to be replaced with actual basis evaluation
        n_basis = density_matrix.shape[0]
        n_points = len(points)
        basis_values = np.zeros((n_points, n_basis))

        for i in range(n_basis):
            # Simple Gaussian approximation for each basis function
            # Center of Gaussian randomly placed
            center = np.random.rand(3) * 2.0 - 1.0
            width = 0.5 + np.random.rand()

            dist_sq = np.sum((points - center) ** 2, axis=1)
            basis_values[:, i] = np.exp(-dist_sq / (2 * width**2))

    # Calculate density at each point: ρ(r) = Σᵢⱼ Dᵢⱼ φᵢ(r) φⱼ(r)
    for i in range(density_matrix.shape[0]):
        for j in range(density_matrix.shape[1]):
            # Add contribution to density
            density_contribution = (
                density_matrix[i, j] * basis_values[:, i] * basis_values[:, j]
            )
            # Reshape back to grid
            density += np.reshape(density_contribution, density.shape)

    return density


def calculate_interaction_energy(
    total_energy: float, fragment_energies: List[float]
) -> float:
    """
    Calculate the interaction energy between fragments.

    Parameters:
    -----------
    total_energy : float
        Energy of the combined system
    fragment_energies : List[float]
        List of energies of individual fragments

    Returns:
    --------
    float
        Interaction energy
    """
    # Interaction energy is the difference between the energy of the combined system
    # and the sum of the energies of the individual fragments
    return total_energy - sum(fragment_energies)


def calculate_relativistic_corrections(
    electron_density: np.ndarray,
    positron_density: np.ndarray,
    basis_set: Any,
    molecular_data: MolecularData,
) -> Dict[str, float]:
    """
    Calculate relativistic corrections to the energy.

    Parameters:
    -----------
    electron_density : np.ndarray
        Electron density matrix
    positron_density : np.ndarray
        Positron density matrix
    basis_set : Any
        Basis set used for the calculation
    molecular_data : MolecularData
        Molecular data object

    Returns:
    --------
    Dict[str, float]
        Dictionary of relativistic corrections
    """
    # This is a simplified implementation that returns estimated corrections
    # A real implementation would involve calculating expectation values of
    # relativistic operators

    # Check inputs
    if electron_density is None and positron_density is None:
        warnings.warn("Missing density matrices, returning zero corrections")
        return {
            'mass_velocity': 0.0,
            'darwin': 0.0,
            'spin_orbit': 0.0,
            'spin_spin': 0.0,
            'total': 0.0,
        }

    # Approximate corrections based on system properties
    # These are order-of-magnitude estimates

    # Mass-velocity correction: -⟨p⁴⟩/(8m³c²)
    # For hydrogen-like systems, scales as Z⁴α²/n³
    Z_eff = molecular_data.n_electrons + molecular_data.n_positrons
    mass_velocity = -(Z_eff**4) * FINE_STRUCTURE_CONSTANT**2 / 8.0

    # Darwin term: (πα²Z/2)⟨δ(r)⟩
    # For hydrogen-like systems, scales as Z⁴α²/n³
    darwin = Z_eff**4 * FINE_STRUCTURE_CONSTANT**2 / 2.0

    # Spin-orbit coupling: depends on angular momentum
    # Simplified estimate
    spin_orbit = Z_eff**4 * FINE_STRUCTURE_CONSTANT**2 / 4.0

    # Spin-spin coupling
    # Only relevant for systems with both electrons and positrons
    if molecular_data.n_electrons > 0 and molecular_data.n_positrons > 0:
        spin_spin = Z_eff**3 * FINE_STRUCTURE_CONSTANT**2 / 6.0
    else:
        spin_spin = 0.0

    # Total correction
    total = mass_velocity + darwin + spin_orbit + spin_spin

    return {
        'mass_velocity': mass_velocity,
        'darwin': darwin,
        'spin_orbit': spin_orbit,
        'spin_spin': spin_spin,
        'total': total,
    }


def calculate_cross_section(
    energy: float, phase_shifts: Dict[int, float], max_l: int
) -> float:
    """
    Calculate scattering cross-section from phase shifts.

    Parameters:
    -----------
    energy : float
        Scattering energy (Hartree)
    phase_shifts : Dict[int, float]
        Dictionary mapping angular momentum (l) to phase shift (radians)
    max_l : int
        Maximum angular momentum included

    Returns:
    --------
    float
        Scattering cross-section (Bohr²)
    """
    # Calculate wave number (k) from energy: E = ħ²k²/2m
    k = np.sqrt(2.0 * energy)

    # Cross-section formula: σ = (4π/k²) Σₗ(2l+1)sin²(δₗ)
    cross_section = 0.0

    for l in range(max_l + 1):
        if l in phase_shifts:
            phase_shift = phase_shifts[l]
            cross_section += (2 * l + 1) * np.sin(phase_shift) ** 2

    cross_section *= 4.0 * np.pi / k**2

    return cross_section


def analyze_resonances(
    energies: np.ndarray, cross_sections: np.ndarray, threshold: float = 0.1
) -> List[Dict[str, float]]:
    """
    Analyze resonances in a scattering cross-section.

    Parameters:
    -----------
    energies : np.ndarray
        Array of energies
    cross_sections : np.ndarray
        Array of cross-sections corresponding to the energies
    threshold : float, optional
        Threshold for detecting resonances

    Returns:
    --------
    List[Dict[str, float]]
        List of detected resonances, each with 'energy' and 'width'
    """
    # Simple peak detection
    resonances = []

    # Check if arrays are valid
    if len(energies) != len(cross_sections):
        warnings.warn("Energy and cross-section arrays have different lengths")
        return resonances

    if len(energies) < 3:
        warnings.warn("Not enough data points to detect resonances")
        return resonances

    # Normalize cross-sections for easier peak detection
    norm_cs = cross_sections / np.max(cross_sections)

    # Find local maxima
    for i in range(1, len(energies) - 1):
        if (
            norm_cs[i] > norm_cs[i - 1]
            and norm_cs[i] > norm_cs[i + 1]
            and norm_cs[i] > threshold
        ):

            # Estimate width by finding half-maximum points
            half_max = norm_cs[i] / 2.0

            # Find left half-max point
            left_idx = i
            while left_idx > 0 and norm_cs[left_idx] > half_max:
                left_idx -= 1

            # Find right half-max point
            right_idx = i
            while right_idx < len(energies) - 1 and norm_cs[right_idx] > half_max:
                right_idx += 1

            # Calculate width (FWHM)
            width = energies[right_idx] - energies[left_idx]

            resonances.append({'energy': energies[i], 'width': width})

    return resonances


def analyze_quantum_results(
    quantum_state: Any,
    qubit_mapping: str,
    molecular_data: MolecularData,
    basis_set: Any,
) -> Dict[str, float]:
    """
    Analyze results from quantum simulation.

    Parameters:
    -----------
    quantum_state : Any
        Quantum state from simulation
    qubit_mapping : str
        Type of qubit mapping used
    molecular_data : MolecularData
        Molecular data object
    basis_set : Any
        Basis set used

    Returns:
    --------
    Dict[str, float]
        Analysis results
    """
    # Placeholder implementation
    # A real implementation would extract properties from the quantum state

    # Check if we have a valid quantum state
    if quantum_state is None:
        warnings.warn("No quantum state provided, returning default analysis")
        return {'correlation': 0.0, 'annihilation_probability': 0.0}

    # Simple placeholder calculations
    # For a real system, these would be calculated from the quantum state

    # Estimate correlation as a function of the system size
    correlation = 0.1 * (molecular_data.n_electrons + molecular_data.n_positrons)

    # Estimate annihilation probability
    # Only relevant for systems with both electrons and positrons
    if molecular_data.n_electrons > 0 and molecular_data.n_positrons > 0:
        annihilation_probability = (
            0.01 * molecular_data.n_electrons * molecular_data.n_positrons
        )
    else:
        annihilation_probability = 0.0

    return {
        'correlation': correlation,
        'annihilation_probability': annihilation_probability,
    }


def calculate_penetration_factor(
    electron_density: np.ndarray,
    positron_density: np.ndarray,
    overlap_matrix: np.ndarray,
    basis_set: Any,
) -> float:
    """
    Calculate the positron penetration factor into electron density.

    Parameters:
    -----------
    electron_density : np.ndarray
        Electron density matrix
    positron_density : np.ndarray
        Positron density matrix
    overlap_matrix : np.ndarray
        Overlap matrix
    basis_set : Any
        Basis set used

    Returns:
    --------
    float
        Penetration factor
    """
    # The penetration factor is the ratio between the calculated
    # annihilation rate and the rate predicted by the independent particle model

    # Check inputs
    if electron_density is None or positron_density is None or overlap_matrix is None:
        warnings.warn(
            "Missing density matrices or overlap matrix, returning default penetration factor"
        )
        return 1.0

    # Calculate the actual overlap integral
    actual_overlap = calculate_overlap_integral(
        electron_density, positron_density, overlap_matrix, basis_set
    )

    # Calculate the independent particle model prediction
    # This assumes uniform electron density
    n_electrons = np.trace(electron_density)
    n_positrons = np.trace(positron_density)

    # In the independent particle model, the overlap is proportional to
    # the product of the number of particles
    ipm_overlap = n_electrons * n_positrons / np.pi  # Simple approximation

    # Calculate penetration factor
    penetration_factor = actual_overlap / ipm_overlap if ipm_overlap > 0 else 1.0

    return penetration_factor


def calculate_overlap_integral(
    electron_density: np.ndarray,
    positron_density: np.ndarray,
    overlap_matrix: np.ndarray,
    basis_set: Any,
) -> float:
    """
    Calculate the overlap integral between electron and positron densities.

    Parameters:
    -----------
    electron_density : np.ndarray
        Electron density matrix
    positron_density : np.ndarray
        Positron density matrix
    overlap_matrix : np.ndarray
        Overlap matrix
    basis_set : Any
        Basis set used

    Returns:
    --------
    float
        Overlap integral
    """
    # Check inputs
    if electron_density is None or positron_density is None or overlap_matrix is None:
        warnings.warn(
            "Missing density matrices or overlap matrix, returning zero overlap"
        )
        return 0.0

    # Check dimensions and extract relevant part of overlap matrix
    if hasattr(basis_set, 'electron_basis') and hasattr(basis_set, 'positron_basis'):
        # For mixed basis sets
        n_e_basis = len(basis_set.electron_basis)
        n_p_basis = len(basis_set.positron_basis)
    else:
        # Try to infer dimensions
        n_e_basis = electron_density.shape[0]
        n_p_basis = positron_density.shape[0]

    # Ensure overlap matrix has right dimensions
    if overlap_matrix.shape != (n_e_basis, n_p_basis):
        if overlap_matrix.shape == (n_e_basis + n_p_basis, n_e_basis + n_p_basis):
            # Extract relevant part from block matrix
            overlap_subset = overlap_matrix[
                :n_e_basis, n_e_basis : n_e_basis + n_p_basis
            ]
        else:
            warnings.warn(
                f"Overlap matrix has incorrect shape: {overlap_matrix.shape}, expected: {(n_e_basis, n_p_basis)}"
            )
            overlap_subset = (
                np.ones((n_e_basis, n_p_basis)) * 0.5
            )  # Default approximation
    else:
        overlap_subset = overlap_matrix

    # Calculate the overlap integral: ∫ ρₑ(r)ρₚ(r) dr
    # In matrix form: Tr(Dₑ·S·Dₚ·S†)
    overlap_integral = np.trace(
        np.dot(
            np.dot(electron_density, overlap_subset),
            np.dot(positron_density, overlap_subset.T),
        )
    )

    return overlap_integral


def calculate_bond_order(
    density_matrix: np.ndarray,
    overlap_matrix: np.ndarray,
    atom_indices: Optional[List[Tuple[int, int]]] = None,
) -> Union[float, Dict[Tuple[int, int], float]]:
    """
    Calculate bond orders between atoms.

    Parameters:
    -----------
    density_matrix : np.ndarray
        Density matrix
    overlap_matrix : np.ndarray
        Overlap matrix
    atom_indices : List[Tuple[int, int]], optional
        List of atom index pairs to calculate bond orders for
        If None, calculate for all atom pairs

    Returns:
    --------
    Union[float, Dict[Tuple[int, int], float]]
        Bond orders for specified atom pairs, or total bond order if atom_indices is None
    """
    # Check inputs
    if density_matrix is None or overlap_matrix is None:
        warnings.warn(
            "Missing density matrix or overlap matrix, returning zero bond order"
        )
        return 0.0

    # Simplified implementation for demonstration
    # In a real system, this would involve projecting the density matrix
    # onto atomic orbitals and calculating Mayer bond orders

    # If no atom indices specified, return a simple estimate of total bond order
    if atom_indices is None:
        # Estimate total bond order from density matrix
        # This is a very simplified approximation
        bond_order = np.trace(np.dot(density_matrix, overlap_matrix)) / 2.0
        return bond_order

    # Calculate bond orders for specified atom pairs
    bond_orders = {}

    for i, j in atom_indices:
        # Simple approximation of bond order between atoms i and j
        # In a real implementation, this would involve atomic orbital projections
        bond_order = 0.5 * np.exp(-abs(i - j))  # Placeholder
        bond_orders[(i, j)] = bond_order

    return bond_orders
