As noted above, the components of a PES include the internal coordinates (bond lengths, bond angles, dihedral angles) and the total energies of a molecule. Given a PES, _Survibtm_ solves for spectroscopic constants which include anharmonicity through quartic terms according to second-order RSPT, as shown in Equations (7)-(10). _RSperturb_ and _DiatomicVibRot_ are _Mathematica_ codes that analyze high-order perturbation methods using symbolic mathematics [10]. _Risperturb_ provides algebraic solutions to the quantum mechanical molecular vibrational-rotational problems for a diatomic molecule, given its potential energy curve (PEC) (a PEC is the limiting case of a PES involving just two atoms). For example, differences observed between the theoretical sixth-order RSPT results and experimental energies for H\({}_{2}\), N\({}_{2}\), CO and HF spectral lines are typically less than 0.1%. Vibrational and rotational energies for H\({}_{2}\), calculated using _DiatomicVibRot_, indicate how accuracy degrades slowly for higher-lying vibrational and rotational states, as is expected in perturbation theory [2]. It is noteworthy that current state-of-the-art solutions for polyatomic systems have been derived only up to the second order of perturbation theory for polyatomic molecules [11]. Expanding on previous published work's theoretical developments will be necessary in order to calculate the arbitrary-order correction terms to vibrational-rotational energies that allow for accurate calculations of polyatomic vibrational-rotational spectra for spherical, symmetric, and asymmetric top molecules. The algebraic equations resulting from high-order perturbation theory can be properly and efficiently treated to the appropriate level of approximation as dictated by the accuracy of Born-Oppenheimer PESs. The Born-Oppenheimer approximation is an assumption which states nuclear and electronic motion within molecules can be separated. In a follow-up study, the _RSperturb_ and _Survibtm_ codes will be combined, modified and extended to be applicable to polyatomic molecules. The derivation includes the terms in the Hamiltonian operator required to calculate, to arbitrary-order, anharmonicity effects, intensities, non-rigid rotations, vibration-rotation couplings, wave functions and property expectation values. The requisite correction formulae in terms of universal constants, molecular constants, and quantum numbers are to be generated using symbolic computation through a generalization of the \(q[n]\) procedural program [10] to polyatomic systems within _Mathematica_. The necessary equations, governing such high-order effects as resonances, Coriolis couplings and centrifugal distortions, are to be incorporated. The algebraic results will be translated into computer code at runtime using a supplied analytical representation of a molecular PES and will be executed on an advanced computing platform to calculate ab initio spectra and related properties [5]. When calculating spectra there are several different properties that can be compared with what is observed: e.g, fundamental transitions, hot bands, combinations and overtones. A _fundamental transition_ is a symmetric stretch or bend, or asymmetric stretch corresponding to an excitation from the ground vibrational state to the first excited vibrational level in bent triatomic molecules. _Hot bands_ are transitions from excited-to-excited vibrational states. _Combinations_ are simultaneous excitations of multiple normal modes with a single photon. _Overtones_ are also observed in IR spectroscopy and occur when a molecule undergoes a transition from the ground state to the second or higher excited state, meaning that the vibrational quantum number of the upper state is greater than one excitation. Consequently, through the execution of the _MolecGeom_ code, a swift and reliable generation of spectra for polyatomic molecules is within reach.