B. Wilson, J. , J. C. Decius, and P. C. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra, Journal of The Electrochemical Society, vol.102, issue.9, 1980.
DOI : 10.1149/1.2430134

R. Bunker and P. Jensen, Fundamentals of molecular symmetry, Series in Chemical Physics, 2005.

K. Marquardt and . Sagui, A complete list of symmetry adapted expressions to the fourth power for compact bending potentials in molecules with and symmetry from a general symbolic algebra program, Molecular Physics, vol.105, issue.9, p.1157, 2007.
DOI : 10.1016/0022-2852(76)90353-2

URL : https://hal.archives-ouvertes.fr/hal-00513085

. Hamermesh, Group Theory and its Applications to Physical Problems, American Journal of Physics, vol.30, issue.10, 1962.
DOI : 10.1119/1.1941790

R. Taylor, Lecture notes in quantum chemistry. european summer school in quantum chemistry, Molecular symmetry and quantum chemistry, pp.89-176, 1992.

P. Champion, G. Pierre, F. Michelot, and J. Moret-bailly, Composantes cubiques normales des tenseurs spheriques, Canadian Journal of Physics, vol.55, issue.6, p.512, 1977.
DOI : 10.1139/p77-070

L. Moret-bailly, J. Gautier, and . Montagutelli, Clebsch-Gordan coefficients adapted to cubic symmetry, Journal of Molecular Spectroscopy, vol.15, issue.3, p.355, 1965.
DOI : 10.1016/0022-2852(65)90151-7

V. Nikitin, M. Rey, and V. G. Tyuterev, Rotational and vibrational energy levels of methane calculated from a new potential energy surface, Chemical Physics Letters, vol.501, issue.4-6, p.179, 2011.
DOI : 10.1016/j.cplett.2010.11.008

F. Cassam-chena¨?chena¨? and . Patras, Symmetry-adapted polynomial basis for global potential energy surfaces-applications to XY4 molecules, Journal of Mathematical Chemistry, vol.118, issue.4, p.938, 2008.
DOI : 10.1007/s10910-008-9354-y

J. C. Varandas and J. N. Murrell, Choosing points in potential energy surfaces for fitting polynomial functions: application of permutational symmetry, Chemical Physics Letters, vol.84, issue.3, p.440, 1981.
DOI : 10.1016/0009-2614(81)80381-8

A. Schmelzer and J. N. Murrell, The general analytic expression forS4-symmetry-invariant potential functions of tetra-atomic homonuclear molecules, International Journal of Quantum Chemistry, vol.1897, issue.2, p.287, 1985.
DOI : 10.1002/qua.560280210

A. Collins and D. F. Parsons, Implications of rotation???inversion???permutation invariance for analytic molecular potential energy surfaces, The Journal of Chemical Physics, vol.99, issue.9, p.6756, 1993.
DOI : 10.1063/1.465819

J. Ischtwan and S. D. Peyerimhoff, General algebraic expressions of totally symmetric potential functions for AXn (n = 3,4) molecules, International Journal of Quantum Chemistry, vol.96, issue.5, p.471, 1993.
DOI : 10.1002/qua.560450505

B. J. Huang, J. M. Braams, and . Bowman, potential energy and dipole moment surfaces for H5O2+, The Journal of Chemical Physics, vol.122, issue.4, p.44308, 2005.
DOI : 10.1063/1.1834500

J. Braams and J. M. Bowman, Permutationally invariant potential energy surfaces in high dimensionality, International Reviews in Physical Chemistry, vol.28, issue.4, p.577, 2009.
DOI : 10.1063/1.3196178

. Sturmfels, Algorithms in Invariant Theory, 2008.
DOI : 10.1007/978-3-7091-4368-1

G. Mclellan, Invariant functions and homogeneous bases of irreducible representations of the crystal point groups, with applications to thermodynamic properties of crystals under strain, Journal of Physics C: Solid State Physics, vol.7, issue.18, p.3326, 1974.
DOI : 10.1088/0022-3719/7/18/015

G. Mclellan, The derivation of generalised integrity bases for finite orthogonal groups and counting rules for numerator invariants and covariants, Journal of Physics C: Solid State Physics, vol.12, issue.5, p.753, 1979.
DOI : 10.1088/0022-3719/12/5/007

A. Thionnet and C. Martin, A new constructive method using the theory of invariants to obtain material behavior laws, International Journal of Solids and Structures, vol.43, issue.2, p.325, 2006.
DOI : 10.1016/j.ijsolstr.2005.05.021

URL : https://hal.archives-ouvertes.fr/hal-00157256

G. Sartori and G. Valente, Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata, Journal of Physics A: Mathematical and General, vol.36, issue.7, p.1913, 2003.
DOI : 10.1088/0305-4470/36/7/308

G. Sartori and V. Talamini, Orbit spaces of compact coregular simple Lie groups with 2, 3 and 4 basic polynomial invariants: Effective tools in the analysis of invariant potentials, Journal of Mathematical Physics, vol.39, issue.4, p.2367, 1998.
DOI : 10.1063/1.532294

J. Lee, J. M. Martin, and P. R. Taylor, and isotopomers, The Journal of Chemical Physics, vol.102, issue.1, p.254, 1995.
DOI : 10.1063/1.469398

K. Oyanagi, T. Yagi, K. Taketsugu, and . Hirao, Highly accurate potential-energy and dipole moment surfaces for vibrational state calculations of methane, The Journal of Chemical Physics, vol.124, issue.6, p.64311, 2006.
DOI : 10.1063/1.2162891

Y. Cassam-chena¨?chena¨?, M. Bouret, S. A. Rey, A. V. Tashkun, V. G. Nikitin et al., Ab initio effective rotational Hamiltonians: A comparative study, International Journal of Quantum Chemistry, vol.69, issue.9, p.2201, 2012.
DOI : 10.1002/qua.23183

J. Cassam-chena¨?chena¨? and . Liévin, calculation of the rotational spectrum of methane vibrational ground state, The Journal of Chemical Physics, vol.136, issue.17, p.174309, 2012.
DOI : 10.1063/1.4705278

J. Cassam-chena¨?chena¨? and . Liévin, An improved third order dipole moment surface for methane, Journal of Molecular Spectroscopy, vol.291, p.77, 2013.
DOI : 10.1016/j.jms.2013.07.004

D. Schmidling, molecules, Journal of Computational Chemistry, vol.17, issue.32, p.2771, 2013.
DOI : 10.1002/jcc.23447

N. Yurchenko, J. Tennyson, R. J. Barber, and W. Thiel, Vibrational transition moments of CH4 from first principles, Journal of Molecular Spectroscopy, vol.291, p.69, 2013.
DOI : 10.1016/j.jms.2013.05.014

G. Derksen and . Kemper, Computational invariant theory, Encyclopaedia of mathematical sciences, 2002.

J. Benson, Polynomial Invariants of Finite Groups, 1993.
DOI : 10.1017/CBO9780511565809

P. Stanley and B. , New Series) Am, Math. Soc, vol.1, p.475, 1979.

R. T. Patera, P. Sharp, and . Winternitz, Polynomial irreducible tensors for point groups, Journal of Mathematical Physics, vol.19, issue.11, p.2362, 1978.
DOI : 10.1063/1.523595

. Burnside, Theory of groups of finite order, 1955.

X. Wang and J. Tucker-carrington, Deficiencies of the bend symmetry coordinates used for methane, The Journal of Chemical Physics, vol.118, issue.14, p.6260, 2003.
DOI : 10.1063/1.1557455

V. Nikitin, M. Rey, and V. G. Tyuterev, New dipole moment surfaces of methane, Chemical Physics Letters, vol.565, p.5, 2013.
DOI : 10.1016/j.cplett.2013.02.022

P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, American Journal of Physics, vol.28, issue.4, 1959.
DOI : 10.1119/1.1935822

G. Littlejohn and M. Reinsch, Gauge fields in the separation of rotations andinternal motions in the n-body problem, Reviews of Modern Physics, vol.69, issue.1, p.213, 1997.
DOI : 10.1103/RevModPhys.69.213