Impact of Basis Set Selection on DFT Predictions: From Electronic Structure to Spectroscopy in Pyrimidine

Impact of Basis Set Selection on DFT Predictions: From Electronic Structure to Spectroscopy in Pyrimidine | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 13 July 2025 V1 Latest version Share on Impact of Basis Set Selection on DFT Predictions: From Electronic Structure to Spectroscopy in Pyrimidine Author : Hayder M. Hadi 0009-0006-4229-6884 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175238283.31368892/v1 542 views 288 downloads Contents Abstract Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this study, we systematically investigate the impact of basis set selection on the accuracy of Density Functional Theory (DFT) calculations for pyrimidine, a prototypical heterocyclic compound with biological and optoelectronic relevance. Six basis sets ranging from minimal (3-21G + ) to highly augmented correlation-consistent sets (aug-cc-pVQZ) were employed to compute key molecular properties, including HOMO–LUMO gaps, bond lengths and angles, donor–acceptor interactions, thermodynamic parameters ( ΔH, ΔG, S ), and UV-Vis and IR spectra. The results demonstrate that basis set quality significantly influences the accuracy of electronic and spectroscopic predictions. Augmented triple-zeta sets such as aug-cc-pVDZ and aug-cc-pVTZ yielded values closest to experimental references, particularly for λₘₐₓ and thermochemical quantities. In contrast, smaller basis sets introduced noticeable deviations. Benchmarking analysis revealed that accuracy plateaus beyond the triple-zeta level, suggesting that aug-cc-pVDZ offers an optimal balance between computational cost and predictive reliability. These findings highlight the crucial role of basis set selection in DFT studies and offer practical guidance for researchers seeking to optimise simulations of π-conjugated systems. The study holds direct implications for computational modelling in medicinal chemistry, photodynamic materials, and molecular environmental sensing. Introduction Density Functional Theory (DFT) has emerged as a cornerstone computational method in chemistry and materials science due to its favourable balance between computational cost and predictive accuracy in electronic structure calculations[1-3]. However, the reliability of DFT outcomes depends not only on the choice of exchange-correlation functional but also critically on the basis set employed, which governs how atomic orbitals are mathematically represented[4,5]. Basis sets serve as approximations to the true electronic wavefunctions, and their truncation inevitably introduces systematic errors. Therefore, the selection of a suitable basis set is not a trivial task[6-8]. Pople-style basis sets, such as 6-31+G and 6-311++G**, remain widely used in standard DFT workflows owing to their simplicity and ease of implementation. Conversely, Dunning’s correlation-consistent basis sets (cc-pVXZ, where X = D, T, Q), especially in their augmented forms (e.g., aug-cc-pVDZ, aug-cc-pVTZ), offer a more rigorous, hierarchical approach by systematically accounting for electron correlation[9,10]. The inclusion of diffuse functions (denoted as “+” or “aug”) and polarisation functions (“*” or “**”) further enhances the flexibility of the basis set. Diffuse functions are particularly important for accurately modelling anions, excited Rydberg states, and weakly bound systems[11,12], whereas polarisation functions improve the angular description of orbitals and are essential for capturing chemical bonding effects in most molecules[13]. While the incorporation of these functions generally improves calculated properties such as total energy, dipole moment, and excitation energies, the incremental gain often diminishes beyond a certain basis set level[13,14]. An additional consideration in basis set accuracy is the Basis Set Superposition Error (BSSE), which arises from artificial stabilisation when basis functions from neighbouring atoms overlap. While BSSE is most pronounced in weakly interacting complexes[15,16], it can still introduce subtle artefacts in smaller, covalently bonded systems. For this reason, counterpoise correction is often applied even in isolated molecules to ensure consistency and to quantify the energetic bias introduced by basis set incompleteness[17,18]. Moreover, as basis set size increases, the computational cost rises steeply, sometimes without a commensurate improvement in predictive accuracy. Large and highly augmented sets such as aug-cc-pVQZ may significantly burden computational resources, especially in high-throughput or large-scale systems[19-21]. Thus, identifying practical trade-offs between accuracy and efficiency is essential for sustainable computational design[22,24]. Although previous benchmarking efforts have explored basis set effects, many are limited in scope—focusing only on specific properties such as optimised geometry or ionisation energy—or are tailored to particular molecular classes[24,25]. Additionally, such studies often fall short of offering generalisable insights into how basis set selection influences a broad spectrum of molecular properties[25-27]. In this work, we systematically evaluate the impact of basis set selection on DFT-computed properties for pyrimidine, a heterocyclic compound of considerable biological and technological importance. By analysing six distinct basis sets, from the minimal 3-21G⁺ to the highly correlated aug-cc-pVQZ, we assess their influence on electronic, geometric, thermodynamic, and spectroscopic parameters—including HOMO–LUMO gaps, bond lengths and angles, donor–acceptor orbital transitions (via NBO analysis), Gibbs free energy, UV-Vis absorption, and infrared spectra. The findings provide actionable insights into how basis set complexity affects predictive accuracy, and whether intermediate sets such as aug-cc-pVDZ may serve as reliable, cost-effective alternatives for DFT modelling of π-conjugated organic systems Computational Method All quantum chemical calculations were performed using the Gaussian 16 software package[28]. The B3LYP exchange-correlation functional was employed throughout this study due to its proven reliability in predicting molecular geometries, vibrational spectra, and electronic properties across a wide range of organic molecules. Its consistent performance in describing π-conjugated systems, including heteroaromatics like pyrimidine, makes it a standard choice in basis set benchmarking studies. Although more recent functionals such as M06-2X and PBE0 may offer improved accuracy for specific classes of compounds, B3LYP remains widely used and computationally efficient, and a full comparison across functionals lies beyond the scope of this study[29,30]. The ionisation potential (IP) and electron affinity (EA) were calculated using standard Koopmans-based expressions given in equations (1) and (2): \begin{equation} \ \ \ \ \ \ \ \ \ \ \ IP=E^{+}-E^{0}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)\nonumber \\ \end{equation} \(EA=E^{0}-E^{-}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)\) where \(E^{0}\) is the ground-state energy of the neutral molecule, and\(E^{\mp}\) correspond to the ground-state energies of the cationic and anionic species, respectively[31]. A total of six basis sets was selected to assess the influence of basis set size and flexibility on calculated molecular properties: 3-21G + , 6-31 ++ G**, 6-311 ++ G**, aug-cc-pVDZ, aug-cc-pVTZ, and aug-cc-pVQZ. These were chosen to represent a systematic progression from minimal to highly extended basis sets, incorporating both Pople-style and correlation-consistent families[9,10,32]. All augmented basis sets include both diffuse and polarisation functions, which are essential for accurately describing electron delocalisation and excited-state transitions, particularly in π-systems [11,12]. Geometry optimisations were carried out without imposing symmetry constraints. Harmonic vibrational frequency calculations were then performed to confirm that each optimised structure represents a true minimum on the potential energy surface. Time-dependent DFT (TD-DFT) was employed to simulate the UV-Vis absorption spectra, allowing for a comparative analysis of vertical excitation energies across different basis sets. Infrared (IR) spectra were also calculated to examine the sensitivity of vibrational features to basis set quality [32]. RESULTS AND DISCUSSION HOMO–LUMO and Energy Gap One of the primary indicators of a molecule’s electronic stability and reactivity is the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). This HOMO–LUMO gap (Eg) is notably sensitive to the choice of basis set. In this study, we observed a systematic trend across all tested basis sets: the inclusion of diffuse and polarization functions led to a modest increase in the Eg, which subsequently stabilised as the basis set became more complete, particularly with the correlation-consistent families[33]. As shown in Table 1 , the minimal 3-21G⁺ basis set produced a gap of 5.47 eV, whereas 6-31++G** and 6-311++G** yielded slightly larger gaps of 5.74 eV and 5.65 eV, respectively. The aug-cc-pVDZ and aug-cc-pVTZ basis sets resulted in gap values around 5.63–5.65 eV, suggesting that improvements diminish beyond the triple-zeta level, consistent with previous benchmarks [23,34]. The HOMO energies generally decreased with increasing basis set quality, reflecting enhanced stabilization of occupied orbitals. Conversely, LUMO energies increased slightly, owing to the improved flexibility in describing unoccupied orbitals. This dual trend contributes to the widening of the HOMO–LUMO gap and aligns with observations reported in prior studies[35]. Ionization potentials (IP), estimated via Koopmans’ theorem, showed mild sensitivity to basis set complexity. Values increased from 9.22 eV (3-21G⁺) to 9.59 eV (aug-cc-pVDZ–QZ), closely approaching the experimental reference of 9.3–9.4 eV for pyrimidine [36]. The percentage error was reduced from ~0.9% in 6-31++G** to less than 0.3% in aug-cc-pVTZ, indicating improved predictive accuracy with higher-quality sets. Electron affinities (EA) fluctuated within a narrow range, with the most negative value recorded for aug-cc-pVQZ (−0.21 eV), suggesting a more refined estimation of electron capture at the highest basis set level. Dipole moments varied slightly between 2.35 and 2.47 Debye across the basis sets. These values remain close to the experimental gas-phase dipole moment of 2.33 D, with a maximum deviation below 6%. This minor variation is expected for symmetric systems like pyrimidine, where electron distribution remains relatively stable with increasing basis set flexibility[37]. Collectively, the results confirm that while high-level basis sets offer incremental accuracy gains, intermediate sets like aug-cc-pVDZ strike a desirable balance between reliability and computational cost. Such sets are especially suitable for larger molecular systems or high-throughput studies where efficiency is a key concern. Bond Lengths and Bond Angles Accurate prediction of molecular geometry is one of the core strengths of DFT. In this study, the influence of basis set selection on bond lengths and bond angles in pyrimidine was systematically investigated. The calculated geometrical parameters demonstrated a gradual improvement with increasing basis set quality, reflecting more accurate electron distribution and orbital flexibility. As summarised in Table 2 , the average C–N bond length predicted by the minimal 3-21G⁺ basis set was 1.350 Å, while the aug-cc-pVTZ and aug-cc-pVQZ basis sets gave values of 1.333 Å and 1.332 Å, respectively. These are in close agreement with the experimental C–N bond length of 1.331 Å, with a maximum absolute error (|Δ|) of 0.019 Å. Likewise, the C–C bond length improved from 1.395 Å (3-21G⁺) to 1.388–1.387 Å (augmented sets), approaching the reference value of 1.393–1.396 Å[38] . The C–H bond length, which is typically underestimated by lower basis sets, showed convergence near the experimental value of ~1.084 Å only with the larger set\RL.[39] Bond angles also showed systematic improvement with increasing basis set quality, as seen in Table 3. For instance, the N–C–C angle (A5) shifted from 122.04° with 3-21G⁺ to 122.16° with aug-cc-pVQZ, closely matching the experimental angle of 122.2° . The N–C–N angle (A1), calculated as 126.07° (3-21G⁺), increased to 126.85° (aug-cc-pVQZ), closely approaching the experimental value of 126.8° [38]. The optimised molecular geometry, illustrated in Figure 1 , reflects the planarity of the pyrimidine ring and demonstrates convergence of structural parameters at the triple-zeta level. Notably, the transition from aug-cc-pVTZ to aug-cc-pVQZ yielded minimal changes (<0.001 Å in bond lengths), indicating geometric saturation. These findings support the view that aug-cc-pVTZ provides a reliable compromise between computational cost and geometric accuracy in medium-sized organic molecules. For applications requiring high structural precision—such as vibrational analysis or intermolecular interaction energy calculations—careful basis set selection remains essential to avoid measurable deviations from experimental geometry. The Effect of Basis Sets on Orbital Transitions and Donor–Acceptor Interactions Natural Bond Orbital (NBO) analysis provides valuable insights into electron density distribution, hybridisation patterns, and donor–acceptor interactions within molecules. In this study, we examined how different basis sets influence second-order perturbation energies (E²), which reflect the strength of orbital delocalisation and charge transfer in pyrimidine. As shown in Table 4 , delocalisations of the type lone pair (n) → π* and π → π* were consistently observed across all basis sets. These interactions are characteristic of the conjugated aromatic structure of pyrimidine. The stabilisation energies associated with these transitions increased with basis set quality, indicating enhanced orbital overlap and more accurate electron delocalisation. For instance, the E² value for the π(C1–N2) → π*(C3–C4) interaction increased from 28.45 kcal/mol (3-21G⁺) to 30.01 kcal/mol (aug-cc-pVTZ), while the π(C5–N6) → π*(C1–N2) interaction rose from 31.47 to 32.31 kcal/mol over the same basis set range. Notably, Pople-type basis sets like 6-31++G** and 6-311++G** tended to slightly underestimate the E² values compared to their correlation-consistent counterparts. This underestimation stems from the limited polarisation and spatial flexibility in Pople sets, which impedes their ability to accurately describe electron-rich and delocalised orbitals. In contrast, augmented correlation-consistent sets (e.g., aug-cc-pVDZ, aug-cc-pVTZ) offered consistently higher E² values and smaller energy gaps E(j) − E(i), reflecting stronger donor–acceptor interactions and a more reliable representation of electron delocalisation[40]. Furthermore, the σ → σ* hyperconjugative interactions (e.g., N2 → C1–N6) also followed a similar trend, with E² values increasing from in higher-level basis sets. This reinforces the importance of diffuse and polarisation functions in capturing both π-conjugation and σ-delocalisation effects[41]. These NBO-based observations align well with TD-DFT results, where transitions such as n → π* and π → π* experienced small red shifts (i.e., lower excitation energies) with more complete basis sets, further supporting the need for enhanced basis flexibility when modelling excited-state behaviour. Overall, this analysis confirms that the choice of basis set significantly influences the computed donor–acceptor interactions. For systems with delocalised π-electron networks—such as heteroaromatic rings—the use of augmented correlation-consistent basis sets is essential for quantitatively reliable interpretations. Thermodynamic Properties: Gibbs Free Energy, Enthalpy, and Entropy Thermodynamic parameters such as Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (S) offer valuable insights into the energetic stability and spontaneity of molecular systems. In this study, these properties were computed for pyrimidine using six different basis sets to evaluate how basis set sophistication influences thermodynamic predictions. As summarised in Table 5 , the calculated enthalpy (ΔH) values ranged from −90.68 kcal/mol with the minimal 3-21G⁺ set to −91.80 kcal/mol with the aug-cc-pVTZ and aug-cc-pVQZ sets. A similar trend was observed for Gibbs free energy (ΔG), which varied from −74.23 kcal/mol to −75.43 kcal/mol across the same range. The difference of basis sets reflects the gradual improvement in accounting for electron correlation and vibrational zero-point energy with increased basis set quality. These findings align with prior benchmark thermochemical studies on similar heteroaromatic systems[42]. Entropy values (S), by contrast, exhibited minimal variation—ranging from 75.4 to 76.1 cal/mol·K. This stability is expected, as entropy largely depends on mass distribution and low-frequency vibrational modes, which are less sensitive to the electronic flexibility introduced by diffuse or polarisation functions. While the aug-cc-pVTZ and aug-cc-pVQZ basis sets delivered the most accurate and consistent thermodynamic predictions, the aug-cc-pVDZ set yielded results within 0.1–0.2 kcal/mol of them, but at a significantly reduced computational cost. This makes aug-cc-pVDZ a highly practical choice for routine simulations, especially in larger systems where efficiency is critical. In summary, the basis set selection has a measurable impact on computed thermodynamic properties—particularly ΔH and ΔG—where even modest numerical differences can meaningfully influence reaction modelling, equilibrium assessments, and temperature-dependent behaviour. For most medium-sized systems, a well-chosen triple-zeta basis set with diffuse functions offers a sound balance between accuracy and computational cost. UV-Vis and IR Spectra Time-dependent density functional theory (TD-DFT) calculations were employed to simulate the UV-Vis absorption spectrum of pyrimidine using six different basis sets. The predicted absorption maxima (λₘₐₓ) ranged from 303.7 nm with 3-21G⁺ to 290.8 nm with aug-cc-pVQZ, reflecting a consistent trend where higher-level basis sets result in blue-shifted transitions. The complete values are presented in Figure 2 for clarity. When compared with the experimental gas-phase absorption maximum of 240 nm, all theoretical results significantly overestimated λₘₐₓ. The deviation was most pronounced for 3-21G⁺ (+63.7 nm), whereas the aug-cc-pVTZ and aug-cc-pVDZ basis sets yielded much closer values (290.8 and 291.4 nm, respectively), corresponding to deviations of known limitation of TD-DFT with B3LYP for π→π* transitions in aromatic systems[43]. A smooth dashed curve representing the experimental profile is superimposed in Figure 2 to visualise the discrepancy. The improvement in spectral accuracy with larger basis sets begins to plateau at the triple-zeta level. Thus, aug-cc-pVDZ and aug-cc-pVTZ may be recommended for routine excited-state simulations, balancing efficiency and accuracy. In contrast, infrared vibrational spectra \RL Figure 3 exhibited minimal dependence on the basis set. Key peaks such as the C=C stretching mode near 1610 cm⁻¹ and the C–H stretching near 3150 cm⁻¹ were reproduced with minor deviations. For instance, 3-21G⁺ underestimated the C=C stretch to 1561 cm⁻¹, while aug-cc-pVQZ remained close to 1611 cm⁻¹. These shifts, although present, did not significantly affect the overall spectral shape. Therefore, while UV-Vis predictions require careful basis set selection with diffuse functions, IR spectra of small rigid molecules like pyrimidine can be reliably obtained using moderate-level basis sets. Augmented triple-zeta sets do offer enhanced precision, but their computational cost must be justified by the application. BSSE Analysis Although Basis Set Superposition Error (BSSE) is typically more significant in weakly bound systems and non-covalent interactions, it was also evaluated in this study for a single-molecule system (pyrimidine) to quantify subtle artefacts introduced by basis set incompleteness and to ensure methodological consistency across all comparisons.[44] The counterpoise correction method was applied using Gaussian 16, and the results are summarised graphically in Figure 4. As shown in Figure 4 , a distinct downward trend is observed in BSSE values as the basis set quality improves. The 3-21G⁺ basis set exhibits the highest correction (~0.45 kcal/mol), which reflects its limited orbital flexibility and poor description of the electron density. With the inclusion of diffuse and polarisation functions, the BSSE correction steadily decreases. For example, the 6-31++G** and 6-311++G** basis sets reduce the error to Correlation-consistent sets, such as aug-cc-pVDZ and aug-cc-pVTZ, show much smaller corrections (~0.12 and ~0.08 kcal/mol), while aug-cc-pVQZ approaches near-negligible levels (~0.06 kcal/mol). These findings confirm that even in isolated molecular systems, artificial stabilisation due to basis set incompleteness can occur and should not be overlooked when low-level basis sets are used. Although the absolute magnitude of BSSE in this context is small, its systematic nature may impact total energy comparisons and thermodynamic calculations. The near convergence observed for aug-cc-pVTZ and aug-cc-pVQZ confirms the reliability of these high-quality basis sets for accurate energy estimations. Therefore, the evaluation of BSSE—despite its minor quantitative influence in this case—serves as a valuable methodological control that enhances confidence in the basis set convergence behaviour across the study[45]. Benchmarking Accuracy and Efficiency of Basis Sets: A Comparative Analysis To comprehensively evaluate the performance of the selected basis sets, a benchmarking analysis was performed to assess the balance between computational accuracy and cost. This analysis focused on two key aspects: the precision in predicting UV-Vis absorption maxima (λₘₐₓ) and the convergence of thermodynamic parameters such as enthalpy (ΔH) and Gibbs free energy (ΔG), with particular emphasis on how these metrics evolve with increasing basis set complexity. As depicted in Figure 5 , the percentage error in λₘₐₓ predictions relative to the experimental gas-phase reference (240 nm) shows a clear trend. The minimal 3-21G⁺ basis set yielded the largest deviation, with an error exceeding 33%. Upon incorporating diffuse and polarization functions—as in 6-31++G** and 6-311++G**—the error dropped sharply to approximately 27%, indicating a substantial improvement in spectral accuracy. However, further increases in basis set quality (e.g., aug-cc-pVDZ and aug-cc-pVTZ) resulted in only marginal gains, suggesting a plateau in predictive improvement beyond the double-zeta level. This diminishing return was also observed in thermodynamic calculations. Both ΔH and ΔG values exhibited convergence behavior between the aug-cc-pVDZ and aug-cc-pVTZ basis sets, with negligible differences beyond this point. These findings imply that for medium-sized organic molecules like pyrimidine, larger basis sets such as aug-cc-pVQZ offer minimal added value for standard thermodynamic assessments. When computational efficiency is considered, the 6-311++G** and aug-cc-pVDZ basis sets emerge as optimal choices. They deliver reliable accuracy in both excited-state and ground-state properties while maintaining feasible computational demands. This trade-off renders them particularly suitable for large-scale simulations or high-throughput studies where both accuracy and speed are essential Conclusions This study systematically evaluated the impact of basis set selection on a broad range of DFT-computed properties of pyrimidine, encompassing electronic, structural, thermodynamic, and spectroscopic parameters. By comparing six basis sets—from the minimal 3-21G⁺ to the highly augmented aug-cc-pVQZ—we demonstrated that the level of basis set sophistication plays a pivotal role in determining the reliability and interpretability of theoretical predictions. The findings showed that smaller basis sets tend to misrepresent key electronic properties such as the HOMO–LUMO gap and donor–acceptor characteristics, whereas larger and augmented sets yielded significantly better agreement with both experimental and high-level theoretical references. Structural parameters, particularly bond lengths and angles, displayed improved convergence when using triple-zeta augmented sets, confirming the suitability of aug-cc-pVTZ for accurate geometry optimisation. Thermodynamic and spectroscopic descriptors, including ΔH, ΔG, λₘₐₓ, and vibrational frequencies, also benefited from the enhanced flexibility and completeness of correlation-consistent basis sets. Although the basis set superposition error (BSSE) was minor in this single-molecule system, its evaluation reinforced the energetic reliability of high-quality basis sets. Among all tested sets, aug-cc-pVDZ and aug-cc-pVTZ emerged as optimal compromises between computational efficiency and accuracy. Their performance makes them particularly attractive for simulating π-conjugated aromatic systems, such as nucleobases, organic dyes, and heterocycles employed in drug design, photodynamic therapy, and molecular sensing. Overall, the results of this study highlight that basis set selection is not a mere technical detail, but a central factor that governs the fidelity, reproducibility, and applicability of DFT predictions. Future work may extend this investigation to explore the effects of functional choice, solvation, and relativistic corrections, particularly for larger systems or biologically relevant scaffolds. Acknowledgement The author would like to thank the Departments of Physics and Medical Physics in the Colleges of Science and Education and their staff for their support and assistance in completing this research’s requirements. in the public, commercial, or not-for-profit sectors.\RL” References [1] F. Jensen, “Atomic orbital basis sets,” WIREs Computational Molecular Science , vol. 3, no. 3, pp. 273–295, May 2013, doi: 10.1002/wcms.1123. [2] E. G. Lewars, Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics , 2nd Edition. New York: Springer Netherlands, 2011. doi: 10.1007/978-90-481-3862-3. [3] J. S. B. J. A. P. W. J. Pietro M. S. Gordon, “Basis Sets Used in Molecular Orbital Calculations,” J. Am. Chem. Soc. 1980, 102, 939. [4] E. R. Davidson’ and D. Feller I M N N ~~, “Basis Set Selection for Molecular Calculations.” [5] F. Muniz-Miranda, M. C. Menziani, and A. Pedone, “Assessment of the basis set effect on the structural and electronic properties of organic-protected gold nanoclusters,” Theor Chem Acc , vol. 135, no. 4, p. 94, Apr. 2016, doi: 10.1007/s00214-016-1856-2. [6] F. Jensen, Introduction to Computational Chemistry , Second Edition. John Wiley & Sons Ltd, 2006. [7] Y. Nomura and R. Akashi, “Density functional theory,” in Encyclopedia of Condensed Matter Physics , vol. 1, Elsevier, 2024, pp. 867–878. doi: 10.1016/B978-0-323-90800-9.00148-7. [8] T. H. Dunning, “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen,” J Chem Phys , vol. 90, no. 2, pp. 1007–1023, Jan. 1989, doi: 10.1063/1.456153. [9] P. Manninen and J. Vaara, “Systematic Gaussian basis‐set limit using completeness‐optimized primitive sets. A case for magnetic properties,” J Comput Chem , vol. 27, no. 4, pp. 434–445, Mar. 2006, doi: 10.1002/jcc.20358. [10] W. J. Hehre, R. F. Stewart, and J. A. Pople, “Self-Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals,” J Chem Phys , vol. 51, no. 6, pp. 2657–2664, Sep. 1969, doi: 10.1063/1.1672392. [11] A. Rosa, A. W. Ehlers, E. J. Baerends, J. G. Snijders, and G. te Velde, “Basis Set Effects in Density Functional Calculations on the Metal−Ligand and Metal−Metal Bonds of Cr(CO) 5 −CO and (CO) 5 Mn−Mn(CO) 5 ,” J Phys Chem , vol. 100, no. 14, pp. 5690–5696, Jan. 1996, doi: 10.1021/jp953381p. [12] S. Hayashi, T. Nishide, K. Ueda, K. Hayama, and W. Nakanishi, “Effects from Basis Sets and Levels of Calculations on the Nature of Interactions Predicted by QTAIM Dual Functional Analysis with QTAIM Functions,” ChemistrySelect , vol. 4, no. 20, pp. 6198–6208, May 2019, doi: 10.1002/slct.201900998. [13] A. D. Boese, J. M. L. Martin, and N. C. Handy, “The role of the basis set: Assessing density functional theory,” J Chem Phys , vol. 119, no. 6, pp. 3005–3014, Aug. 2003, doi: 10.1063/1.1589004. [14] W. J. Hehre, “Ab initio molecular orbital theory,” Acc Chem Res , vol. 9, no. 11, pp. 399–406, Nov. 1976, doi: 10.1021/ar50107a003. [15] A. N. Hill, A. J. H. M. Meijer, and J. G. Hill, “Correlation Consistent Basis Sets and Core Polarization Potentials for Al–Ar with ccECP Pseudopotentials,” J Phys Chem A , vol. 126, no. 34, pp. 5853–5863, Sep. 2022, doi: 10.1021/acs.jpca.2c04446. [16] S. Saravanan and V. Balachandran, “Quantum chemical studies, natural bond orbital analysis and thermodynamic function of 2,5-dichlorophenylisocyanate,” Spectrochim Acta A Mol Biomol Spectrosc , vol. 120, pp. 351–364, Feb. 2014, doi: 10.1016/j.saa.2013.10.042. [17] N. Mehta and J. M. L. Martin, “MP2-F12 Basis Set Convergence near the Complete Basis Set Limit: Are h Functions Sufficient?,” J Phys Chem A , vol. 126, no. 24, pp. 3964–3971, Jun. 2022, doi: 10.1021/acs.jpca.2c02494. [18] Á. Vidal Vidal, L. C. de Vicente Poutás, O. Nieto Faza, and C. Silva López, “On the Use of Popular Basis Sets: Impact of the Intramolecular Basis Set Superposition Error,” Molecules , vol. 24, no. 20, p. 3810, Oct. 2019, doi: 10.3390/molecules24203810. [19] A. S. Rosen, J. M. Notestein, and R. Q. Snurr, “Comparing GGA, GGA+ U, and meta-GGA functionals for redox-dependent binding at open metal sites in metal–organic frameworks,” J Chem Phys , vol. 152, no. 22, Jun. 2020, doi: 10.1063/5.0010166. [20] E. Giner, D. Traore, B. Pradines, and J. Toulouse, “Self-consistent density-based basis-set correction: How much do we lower total energies and improve dipole moments,” J Chem Phys , vol. 155, no. 4, Jul. 2021, doi: 10.1063/5.0057957. [21] S. Huzinaga, “Basis sets for molecular calculations,” Computer Physics Reports , vol. 2, no. 6, pp. 281–339, May 1985, doi: 10.1016/0167-7977(85)90003-6. [22] B. Nagy and F. Jensen, “Basis Sets in Quantum Chemistry,” vol. 30, 2017, pp. 93–149. doi: 10.1002/9781119356059.ch3. [23] V. Mahamiya, P. Bhattacharyya, and A. Shukla, “Benchmarking Gaussian Basis Sets in Quantum-Chemical Calculations of Photoabsorption Spectra of Light Atomic Clusters,” ACS Omega , vol. 7, no. 51, pp. 48261–48271, Dec. 2022, doi: 10.1021/acsomega.2c06373. [24] K. A. Peterson, “Correlation consistent basis sets for actinides. I. The Th and U atoms,” J Chem Phys , vol. 142, no. 7, Feb. 2015, doi: 10.1063/1.4907596. [25] C. W. Bauschlicher and H. Partridge, “A comparison of correlation-consistent and Pople-type basis sets,” Chem Phys Lett , vol. 245, no. 2–3, pp. 158–164, Oct. 1995, doi: 10.1016/0009-2614(95)00972-7. [26] A. S. P. Gomes, K. G. Dyall, and L. Visscher, “Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the lanthanides La–Lu,” Theor Chem Acc , vol. 127, no. 4, pp. 369–381, Nov. 2010, doi: 10.1007/s00214-009-0725-7. [27] T. H. Dunning, K. A. Peterson, and D. E. Woon, “Basis Sets: Correlation Consistent Sets,” in Encyclopedia of Computational Chemistry , Wiley, 1998. doi: 10.1002/0470845015.cca053. [28] “Gaussian 16, Revision C.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N.”. [29] M. C. Daza, J. A. Dobado, J. M. Molina, P. Salvador, M. Duran, and J. L. Villaveces, “Basis set superposition error-counterpoise corrected potential energy surfaces. Application to hydrogen peroxide⋯X (X=F−, Cl−, Br−, Li+, Na+) complexes,” J Chem Phys , vol. 110, no. 24, pp. 11806–11813, Jun. 1999, doi: 10.1063/1.479166. [30] Y. Zhao and D. G. Truhlar, “The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06 functionals and 12 other functionals,” Theor Chem Acc , vol. 119, no. 5–6, pp. 525–525, Apr. 2008, doi: 10.1007/s00214-007-0401-8. [31] E. Louis, E. San-Fabián, M. A. Díaz-García, G. Chiappe, and J. A. Vergés, “Are Electron Affinity and Ionization Potential Intrinsic Parameters to Predict the Electron or Hole Acceptor Character of Amorphous Molecular Materials?,” Jun. 01, 2017, American Chemical Society . doi: 10.1021/acs.jpclett.7b00681. [32] X. J. Yang, A. Li, R. Glaser, and J. X. Zhong, “Polycyclic Aromatic Hydrocarbons with Aliphatic Sidegroups: Intensity Scaling for the C–H Stretching Modes and Astrophysical Implications,” Astrophys J , vol. 837, no. 2, p. 171, Mar. 2017, doi: 10.3847/1538-4357/aa5fa9. [33] G. López Arvizu and P. Calaminici, “Assessment of density functional theory optimized basis sets for gradient corrected functionals to transition metal systems: The case of small Nin (n⩽5) clusters,” J Chem Phys , vol. 126, no. 19, May 2007, doi: 10.1063/1.2735311. [34] K. B. Wiberg, “Basis set effects on calculated geometries: 6‐311++G** vs. aug‐cc‐pVDZ,” J Comput Chem , vol. 25, no. 11, pp. 1342–1346, Aug. 2004, doi: 10.1002/jcc.20058. [35] E. Louis, E. San-Fabián, M. A. Díaz-García, G. Chiappe, and J. A. Vergés, “Are Electron Affinity and Ionization Potential Intrinsic Parameters to Predict the Electron or Hole Acceptor Character of Amorphous Molecular Materials?,” J Phys Chem Lett , vol. 8, no. 11, pp. 2445–2449, Jun. 2017, doi: 10.1021/acs.jpclett.7b00681. [36] S. Cherukupalli et al. , “An appraisal on synthetic and pharmaceutical perspectives of pyrazolo[4,3-d]pyrimidine scaffold,” Bioorg Med Chem , vol. 26, no. 2, pp. 309–339, Jan. 2018, doi: 10.1016/j.bmc.2017.10.012. [37] I. Kulakowska and A. Rabczenko, “Conformation of nucleosides Dipole moments of pyrimidine nucleosides,” Biochimica et Biophysica Acta (BBA) - Nucleic Acids and Protein Synthesis , vol. 361, no. 2, pp. 131–139, Aug. 1974, doi: 10.1016/0005-2787(74)90340-2. [38] S. Breda, I. D. Reva, L. Lapinski, M. J. Nowak, and R. Fausto, “Infrared spectra of pyrazine, pyrimidine and pyridazine in solid argon,” J Mol Struct , vol. 786, no. 2–3, pp. 193–206, Apr. 2006, doi: 10.1016/j.molstruc.2005.09.010. [39] G. Herzberg and B. L. Crawford, “Infrared and Raman Spectra of Polyatomic Molecules.,” J Phys Chem , vol. 50, no. 3, pp. 288–288, Mar. 1946, doi: 10.1021/j150447a021. [40] F. Weinhold and C. R. Landis, Discovering Chemistry with Natural Bond Orbitals . Wiley, 2012. doi: 10.1002/9781118229101. [41] E. D. Glendening, C. R. Landis, and F. Weinhold, “ NBO 6.0 : Natural bond orbital analysis program,” J Comput Chem , vol. 34, no. 16, pp. 1429–1437, Jun. 2013, doi: 10.1002/jcc.23266. [42] G. L. Su et al. , “An investigation of valence shell orbital momentum profiles of difluoromethane by binary (e,2e) spectroscopy,” J Chem Phys , vol. 122, no. 5, Feb. 2005, doi: 10.1063/1.1839851. [43] B. Samir, C. Kalalian, E. Roth, R. Salghi, and A. Chakir, “Gas-phase UV absorption spectra of pyrazine, pyrimidine and pyridazine,” Chem Phys Lett , vol. 751, p. 137469, Jul. 2020, doi: 10.1016/j.cplett.2020.137469. [44] S. F. Boys and F. Bernardi, “The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors,” Mol Phys , vol. 19, no. 4, pp. 553–566, Oct. 1970, doi: 10.1080/00268977000101561. [45] T. H. Dunning, “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen,” J Chem Phys , vol. 90, no. 2, pp. 1007–1023, Jan. 1989, doi: 10.1063/1.456153. Table 1. HOMO–LUMO Energies, Energy Gaps, and Dipole Moments Calculated Using Various Basis Sets Table 2. Computed Bond Lengths (in Å) of Pyrimidine Using Different Basis Sets. Table 3. Computed Bond Angles (in degrees) of Pyrimidine Using Different Basis Sets. Table 4. Second-Order Perturbation Energies (\(E²\)) for Key Donor–Acceptor Interactions from NBO Analysis Table 5\RL. Thermodynamic Properties (\(\Delta H,\ \Delta G,\ S\)) of Pyrimidine in kcal/mol and cal/mol·K Table 1. 3-21G + -6.61 -1.14 9.22 -1.34 5.47 2.35 6-31 ++ G** -7.25 -1.52 9.61 -0.52 5.74 2.47 6-311G ++ G** -7.28 -1.63 9.64 -0.48 5.65 2.46 aug\RL-cc-pVDZ -7.25 -1.62 9.59 -0.47 5.63 2.38 aug\RL-cc-pVTZ -7.25 -1.59 9.59 -0.49 5.65 2.36 aug\RL-cc-PVTQZ -7.25 -1.59 9.59 -0.21 5.65 2.36 Table 2. R1 C-N 1.350 1.339 1.336 1.339 1.333 1.332 R2 C-N 1.350 1.339 1.336 1.339 1.333 1.332 R3 C-H 1.082 1.087 1.086 1.092 1.084 1.084 R4 C-N 1.353 1.340 1.336 1.340 1.333 1.332 R5 C-C 1.395 1.395 1.391 1.396 1.388 1.387 R6 C-H 1.084 1.088 1.087 1.093 1.085 1.084 R7 C-C 1.395 1.395 1.391 1.396 1.388 1.387 R8 C-H 1.082 1.085 1.083 1.090 1.080 1.080 R9 C-N 1.353 1.340 1.336 1.340 1.333 1.332 R10 C-H 1.084 1.088 1.087 1.093 1.085 1.084 Table 3. A1 N-C-N 126.070 127.044 127.013 127.086 126.900 126.851 A2 N-C-H 116.965 116.478 116.494 116.457 116.550 116.574 A3 N-C-H 116.965 116.478 116.494 116.457 116.550 116.574 A4 C-N-C 116.386 115.939 115.977 115.947 116.063 116.114 A5 N-C-C 122.038 122.297 122.254 122.235 122.177 122.160 A6 N-C-H 116.808 116.477 116.544 116.632 116.642 116.658 A7 C-C-H 121.155 121.226 121.202 121.133 121.181 121.183 A8 C-C-C 117.083 116.483 116.524 116.550 116.619 116.602 A9 C-C-H 121.459 121.759 121.738 121.725 121.690 121.699 A10 C-C-H 121.459 121.759 121.738 121.725 121.690 121.699 A11 C-C-N 122.038 122.297 122.254 122.235 122.177 122.160 A12 N-C-H 121.155 121.226 121.202 121.133 121.181 121.183 A13 N-C-H 116.808 116.477 116.544 116.632 116.642 116.658 A14 C-N-C 116.386 115.939 115.977 115.947 116.063 116.114 Table 4. 3-21G + C1-N2 π 1.69 C3-C4 π* 0.30 28.45 0.32 0.09 C5-N6 π 1.69 C1-N2 π* 0.35 31.47 0.31 0.09 N2 σ 1.91 C1-N6 σ* 0.03 11.50 0.85 0.09 N6 σ 1.91 C4-C5 σ* 0.03 8.72 0.86 0.08 6-31 ++ G** C1-N2 π 1.69 C3-C4 π* 0.29 29.99 0.33 0.09 C5-N6 π 1.69 C1-N2 π* 0.35 32.14 0.33 0.09 N2 σ 1.91 C1-N6 σ* 0.03 13.23 0.90 0.10 N6 σ 1.91 C4-C5 σ* 0.03 11.24 0.88 0.09 6-311 ++ G** C1-N2 π 1.69 C3-C4 π* 0.29 30.23 0.33 0.09 C5-N6 π 1.69 C1-N2 π* 0.35 32.18 0.33 0.09 N2 σ 1.91 C1-N6 σ* 0.03 11.19 0.90 0.09 N6 σ 1.91 C4-C5 σ* 0.03 10.20 0.88 0.09 aug\RL-cc-pVDZ C1-N2 π 1.69 C3-C4 π* 0.29 30.01 0.33 0.09 C5-N6 π 1.69 C1-N2 π* 0.35 32.38 0.32 0.09 N2 σ 1.91 C1-N6 σ* 0.03 13.23 0.90 0.10 N6 σ 1.91 C4-C5 σ* 0.03 11.37 0.89 0.09 aug\RL-cc-pVTZ C1-N2 π 1.69 C3-C4 π* 0.29 30.01 0.32 0.09 C5-N6 π 1.69 C1-N2 π* 0.35 32.31 0.32 0.09 N2 σ 1.91 C1-N6 σ* 0.03 12.42 0.89 0.10 N6 σ 1.91 C4-C5 σ* 0.03 11.54 0.86 0.09 aug\RL-cc-pVQZ C1-N2 π 1.69 C3-C4 π* 0.29 29.72 0.32 0.09 C5-N6 π 1.69 C1-N2 π* 0.35 31.84 0.32 0.09 N2 σ 1.91 C1-N6 σ* 0.03 13.23 0.88 0.10 N6 σ 1.91 C4-C5 σ* 0.03 11.24 0.84 0.09 Table 5. 3-21G + -90.68 -74.23 75.4 6-31 ++ G** -91.18 -74.74 75.5 6-311 ++ G** -91.37 -74.99 75.6 aug-cc-pVDZ -91.68 -75.24 75.9 aug-cc-pVTZ -91.8 -75.36 76.0 aug-cc-pVQZ -91.8 -75.43 76.1 Figure 1. Optimised ground-state structure of the pyrimidine molecule obtained using DFT at the B3LYP level\RL. Figure 2. Simulated UV-Vis absorption spectra of pyrimidine computed with various basis sets. The dashed curve indicates the experimental \RL Absorption Maxima \(\lambda ₘₐₓ\) at 240 nm for comparison. Figure 3. Simulated IR Spectra of Pyrimidine: Comparison of Vibrational Modes Across Basis Sets Figure 4. Basis set superposition error (BSSE) values for pyrimidine computed via the counterpoise method using various basis sets. Figure 5. \RL Percentage deviation of calculated \RL Absorption Maxima \(\lambda ₘₐₓ\) values from experimental reference (240 nm) for pyrimidine across different basis sets. Figure 1. Figure 2. Figure 3. Figure 4. Figure 5. Information & Authors Information Version history V1 Version 1 13 July 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords basis set dft electronic properties homo lumo Authors Affiliations Hayder M. Hadi 0009-0006-4229-6884 [email protected] University of Al-Qadisiyah View all articles by this author Metrics & Citations Metrics Article Usage 542 views 288 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Hayder M. Hadi. Impact of Basis Set Selection on DFT Predictions: From Electronic Structure to Spectroscopy in Pyrimidine. Authorea . 13 July 2025. DOI: https://doi.org/10.22541/au.175238283.31368892/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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