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Enhanced PromptCovalent bond, molecular structure, carbon atom, shared electrons, electron cloud, chemical stability, strong intermolecular forces, solid-state material properties, thermal conductivity, electrical conductivity, ductility, malleability, crystalline lattice structure, rigid framework, three-dimensional arrangement, atoms arranged in a repeating pattern, strong covalent bonds holding the structure together, thermal expansion coefficient, specific heat capacity, melting point, boiling point, density, hardness, Young's modulus, shear modulus, Poisson's ratio, crystal symmetry, Bravais lattices, Miller indices, atomic packing efficiency, coordination number, bonding orbitals, hybridization, orbital overlap, electronegativity difference, polarizability, charge distribution, electrostatic potential, quantum mechanics, wave-particle duality, Schrödinger equation, Born-Oppenheimer approximation, Hartree-Fock method, density functional theory, computational chemistry, molecular dynamics simulations, ab initio calculations, basis sets, pseudopotentials, relativistic corrections, non-relativistic approximations, post-Hartree-Fock methods, many-body perturbation theory, configuration interaction, coupled-cluster theory, perturbative expansions, variational principles, Rayleigh-Ritz variational principle, Hellmann-Feynman theorem, Kohn-Sham equations, Hohenberg-Kohn theorems, Thomas-Fermi screening, exchange-correlation functionals, generalized gradient approximations, meta-GGA functionals, hybrid functionals, range-separated hybrids, exact-exchange models, local density approximations, linear scaling methods, resolution-of-the-identity, Cholesky decomposition, tensor train decompositions, spectral decomposition, Lanczos algorithm, Arnoldi iteration, subspace iteration, Davidson diagonalization, iterative eigensolvers, direct inversion in the iterative subspace, preconditioned conjugate gradients, quasi-Newton methods, Broyden-Fletcher-Goldfarb-Shanno algorithm, limited-memory BFGS, quasi-Newton updates, Jacobian matrix, Hessian matrix, Fisher information matrix, covariance matrix, correlation matrix, variance-covariance matrix, probability distributions, Bayesian inference, maximum likelihood estimation, least-squares minimization, regularization techniques, Lasso regression, ridge regression, elastic net regression, group Lasso, sparse regression, sparse PCA, sparse singular value decomposition, compressive sensing, total variation minimization, convex optimization, non-convex optimization, stochastic gradient descent, Adam optimizer, RMSProp, Adagrad, Adadelta, Nadam, AMSGrad, look-ahead Lanczos, look-ahead conjugate gradient, Chebyshev polynomials, polynomial interpolation, Fourier analysis, fast Fourier transform, discrete cosine transform, Haar wavelet transform, wavelet shrinkage, soft thresholding, hard thresholding, Stein's unbiased risk estimator, cross-validation, k-fold cross-validation, leave-one-out cross-validation, bootstrap resampling, permutation testing, Monte Carlo integration, importance sampling, Markov chain Monte Carlo, Metropolis-Hastings algorithm, Gibbs sampling, Langevin dynamics, Hamiltonian Monte Carlo, simulated annealing, genetic algorithms, particle swarm optimization, differential evolution, cuckoo search, firefly algorithm, bat algorithm, whale optimization algorithm, harmony search, imperialist competitive algorithm, charged system simulation, molecular mechanics, empirical force fields, classical MD simulations, Newton's equations of motion, velocity-verlet integrator, leapfrog integrator, Verlet algorithm, Gear's predictor-corrector method, Runge-Kutta methods, symplectic integrators, parallel tempering, umbrella sampling, free-energy perturbation, thermodynamic integration, Bennett acceptance ratio, replica exchange, multiple histogram reweighting, transition path sampling, forward flux sampling, steered molecular dynamics, constant pH molecular dynamics, constant temperature molecular dynamics, constant pressure molecular dynamics, isothermal-isobaric ensemble, canonical ensemble,
