Theoretical framework

General references to the calculation of properties of crystalline materials:

    C.Pisani
    Quantum-Mechanical Ab-initio calculation of the Properties of Crystalline Materials,
    Lect. N. Chem. 67, Spinger Verlag, Heidelberg, (1996)
    R. Dovesi, B. Civalleri, R. Orlando, C. Roetti, V. R. Saunders
    Ab initio quantum simulation in solid state chemistry,
    Rev. Comput. Chem. 21, 1-125 (2005)

The algorithms used in the development of CRYSTAL were presented in the following references:

    The Hartree-Fock method for periodic systems:
    C. Pisani and R. Dovesi
    Exact exchange Hartree-Fock calculations for periodic systems.
    I. Illustration of the method.
    Int. J. Quantum Chem.  17,  501-516 (1980)
    
    V.R. Saunders
    Ab initio Hartree-Fock calculations for periodic systems.
    Faraday Symp. Chem. S. 19, 79-84 (1984)
    
    C. Pisani, R. Dovesi and C. Roetti
    Hartree-Fock ab-initio of crystalline systems.
    Lect. N. Chem. 48, Spinger Verlag, Heidelberg, (1988)
    The Coulomb problem:
    R. Dovesi, C. Pisani, C. Roetti and V.R. Saunders
    Treatment of Coulomb interactions in Hartree-Fock calculations of periodic systems.
    Phys. Rev. B 28, 5781-5792 (1983) 
    V.R. Saunders, C. Freyria Fava, R. Dovesi, L. Salasco and C. Roetti
    On the electrostatic potential in crystalline systems where the charge
    density is expanded in Gaussian Functions.
    Mol. Phys. 77, 629-665 (1992)
    V.R. Saunders, C. Freyria Fava, R. Dovesi and C. Roetti
    On the electrostatic potential in linear periodic polymers.
    Comput. Phys. Commun. 84, 156-172 (1994)
    The exchange problem:
    M. Causà, R. Dovesi, R. Orlando, C. Pisani and V.R. Saunders
    Treatment of the exchange interactions in Hartree-Fock LCAO calculation
    of periodic systems.
    J. Phys. Chem. 92, 909-913 (1988)
    The symmetry:
    R. Dovesi
    On the role of symmetry in the ab initio Hartree-Fock linear
    combination of atomic orbitals treatment of periodic systems.
    Int. J. Quantum Chem. 29,  1755-1774 (1986)
    C.M. Zicovich-Wilson and R. Dovesi
    On the use of Symmetry Adapted Crystalline Orbitals in SCF-LCAO periodic calculations.
    I. The construction of the Symmetrized Orbitals. 
    Int. J. Quantum Chem. 67, 299-309 (1998)
    C.M. Zicovich-Wilson and R. Dovesi
    On the use of Symmetry Adapted Crystalline Orbitals in SCF-LCAO periodic calculations.
    II. Implementation of the Self-Consistent-Field scheme and examples.
    Int. J. Quantum Chem. 67, 309-320 (1998) 
    R. Dovesi, F. Pascale and C. M. Zicovich-Wilson
    The ab initio calculation of the vibrational spectrum of crystalline compounds;
    the role of symmetry and related computational aspects.
    In: Beyond Standard Quantum Chemistry: Applications from Gas to Condensed Phases,
    pp. 117-138;  R Hernández-Lamoneda (Editor)
    Transworld Research Network, Trivandrum, Kerala, India (2007);
    ISBN: 978-81-7895-293-2
    Nanotubes:
    Y. Noel, Ph. D'Arco, R. Demichelis, C.M. Zicovich-Wilson and R. Dovesi
    On the use of symmetry in the ab initio quantum mechanical simulation of
    nanotubes and related materials.
    J. Comput. Chem. 31, 855-862 (2010)
    DFT implementation:
    M. Causà, R. Dovesi, C. Pisani, R. Colle and A. Fortunelli
    Correlation correction to the Hartree-Fock total energy of solids.
    Phys. Rev. B 36, 891-897 (1987)
    M.D. Towler, M. Causà and A. Zupan
    Density Functional Theory in periodic systems using local Gaussian basis sets.
    Comp. Phys. Comm. 98, 181-205 (1996)
    Analytical gradients implementation:
    K. Doll, V.R. Saunders and N.M. Harrison
    Analytical Hartree-Fock gradients for periodic systems.
    Int. J. Quantum Chem.  82,  1-13 (2001)
    K. Doll, R. Dovesi and R. Orlando
    Analytical Hartree-Fock gradients with respect to the cell parameter
    for systems periodic in three dimensions.
    Theor. Chem. Acc. 112, 394-402 (2004)
    K. Doll, R. Dovesi and R. Orlando
    Analytical Hartree-Fock gradients with respect to the cell parameter:
    systems periodic in one and two dimensions.
    Theor. Chem. Acc. 115, 354-360 (2006)
    Geometry optimisation:
    B. Civalleri, Ph. D'Arco, R. Orlando, V.R. Saunders and R. Dovesi
    Hartree-Fock geometry optimisation of periodic systems with the CRYSTAL code.
    Chem. Phys. Lett.  348,  131-138 (2001)
    Transition state search:
    A. Rimola, C.M. Zicovich-Wilson, R. Dovesi and  P. Ugliengo
    The distinguished reaction coordinate method: search and characterization of
    transition state structures in crystalline systems using the periodic CRYSTAL program.
    J. Chem. Theory Comput. 6 (2010) 1341
    
    Localized Wannier functions:
    C.M. Zicovich-Wilson, R. Dovesi and V.R. Saunders
    A general method to obtain well localized Wannier functions for
    composite energy bands in LCAO periodic calculations.
    J. Chem. Phys. 115,  9708-9718 (2001)
    
    C.M. Zicovich-Wilson and R. Dovesi
    Localized functions in crystalline systems and their  variational manifolds.
    In: Beyond Standard Quantum Chemistry: Applications from Gas to Condensed Phases,
    pp. 140-169; R Hernández-Lamoneda (Editor)
    Transworld Research Network, Trivandrum, Kerala, India (2007);
    ISBN: 978-81-7895-293-2
    Vibration frequencies at Gamma:
    F. Pascale, C.M. Zicovich-Wilson, F. Lopez Gejo, B. Civalleri, R. Orlando and  R. Dovesi
    The calculation of vibrational frequencies of crystalline compounds
    and its implementation in the CRYSTAL code.
    J. Comput. Chem. 25, 888-897 (2004) 
    C.M. Zicovich-Wilson, F. Pascale, C. Roetti, V.R. Saunders, R. Orlando and R. Dovesi
    Calculation of vibration frequencies of alpha-quartz: the effect of Hamiltonian
    and basis set.
    J. Comput. Chem. 25, 1873-1881 (2004) 
    C.M. Zicovich-Wilson, F. J. Torres, F. Pascale, L. Valenzano, R. Orlando and R. Dovesi
     Ab initio simulation of the IR spectra of pyrope, grossular and andradite.
    J. Comput. Chem. 29, 2268-2278 (2008)
    Calculation of elastic constants:
    W.F. Perger, J. Cryswell, B. Civalleri and R. Dovesi
    Ab initio calculation of elastic constants of cristalline systems with the CRYSTAL code.
    Comput. Phys. Commun. 180, 1753-1759 (2009)
    Calculation of dielectric constants:
    C. Darrigan, M. Rérat, G. Mallia and R. Dovesi
    Implementation of the finite field perturbation method in the CRYSTAL
    program for calculating the dielectric constant of periodic systems.
    J. Comput. Chem. 24, 1305-1312 (2003) 
    M. Ferrero, M. Rérat, R. Orlando, R. Dovesi
    Coupled perturbed Hartree-Fock for periodic systems:
    the role of symmetry and related computational aspects.
    J. Chem. Phys. 128, 014110  (2008)
    M. Ferrero, M. Rérat, P. Orlando, R. Dovesi
    The calculation of static polarizabilities of periodic compounds.
    The implementation in the CRYSTAL code for 1D, 2D and 3D systems.
    J. Comput. Chem. 29, 1450-1459 (2008)
    Piezoelectricity and spontaneous polarization:
    S. Dall'Olio and R. Dovesi
    Spontaneous polarization as a Berry phase of the Hartree-Fock wavefunction:
    the case of KNbO3.
    Phys. Rev. B 56, 10105-10114 (1997)
    M. Sgroi, C. Pisani and M. Busso
    Ab initio density functional simulation of structural and electronic properties
    of MgO ultrathin adlayers on the (001) Ag surface.
    Thin Solid Films 400, 64-70 (2001)
    Y. Noel, M. Llunell,  R. Orlando, Ph. D'Arco and R. Dovesi
    Performance of various Hamiltonians in the study of the piezoelectric properties
    of crystalline compounds. The case of BeO and ZnO.
    Phys. Rev. B  66, 214107 (2002)
    Solid solutions:
    A. Meyer, Ph. D'Arco, R. Orlando and R. Dovesi
    Andradite-uvarovite solid solutions. An ab initio all-electron quantum mechanical
    simulation with the CRYSTAL code.
    J. Phys. Chem. C 113, 14507-14511 (2009)
    London-type empirical correction for dispersion interactions (Grimme scheme)
    B. Civalleri, C.M. Zicovich-Wilson, L. Valenzano and P. Ugliengo
    B3LYP augmented with an empirical dispersion term (B3LYP-D*) as
    applied to molecular crystals.
    CrystEngComm 10, 405 (2008); 1693(E)
    Magnetic properties:
    M.D. Towler, N.L. Allan, N.M. Harrison, V.R. Saunders, W.C. Mackrodt and E. Aprà
    An ab initio Hartree-Fock study of MnO and NiO.
    Phys. Rev. B 50, 5041-5054 (1994)
    M.D. Towler, R. Dovesi and V. R. Saunders
    Magnetic interactions and the co-operative Jahn-Teller effect in KCuF3.
    Phys. Rev. B 52, 10150-10159 (1995)
    R. Dovesi, F. Freyria Fava, C. Roetti and V.R. Saunders
    Structural, electronic and magnetic properties of KMF3  (M = Mn, Fe, Co, Ni).
    Faraday Discuss. 106, 173-187 (1997)
    EPR constants:
    A. Lichanot, C. Larrieu, R. Orlando and R. Dovesi
    Lithium trapped-hole centre in magnesium oxide.
    An ab-initio supercell study.
    J. Phys. Chem. Solids 59, 7-12 (1998)
    A. Lichanot, C. Larrieu, C. Zicovich-Wilson, C. Roetti, R. Orlando and R. Dovesi
    Trapped-hole centres containing lithium and sodium in MgO, CaO and SrO.
    An ab initio supercell study.
    J. Phys. Chem. Solids 59, 1119-1124 (1998).
    A. Lichanot, Ph. Baranek, M. Merawa, R. Orlando and R. Dovesi
    VOH and VOD centers in alkaline-earth oxides: an ab initio supercell study.
    Phys. Rev. B 62, 12812-12819 (2000)
     G. Mallia, R. Orlando, C. Roetti, P. Ugliengo and R. Dovesi
    The F-center in LiF: a quantum mechanical ab initio investigation of the hyperfine interaction
    between the unpaired electron at the vacancy and its first seven neighbors.
    Phys. Rev. B 63, 235102 (2001)