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High-level G4 and G4(MP2) theoretical study into the gas-phase thermodynamic and electronic properties of atmospherically relevant terrestrial vegetation derived C10H16 monoterpenes and C15H24 sesquiterpenes

This study employs high-level G4 and G4(MP2) computational methods to determine the gas-phase thermodynamic properties and adiabatic ionization energies of 74 atmospherically relevant C10 and C15 terpenes, revealing that compact, highly bridged structures are the most stable and that calculated values align well with experimental data while being governed by specific electronic and structural factors.

Original authors: Sierra Rayne, Kaya Forest

Published 2026-10-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sierra Rayne, Kaya Forest

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The air we breathe is not empty; it is a bustling chemical landscape shaped by the living world. Trees and plants constantly release a vast array of invisible gases, known as volatile organic compounds, which drift into the atmosphere and interact with sunlight and other chemicals. Among the most significant of these are terpenes, a large family of hydrocarbons that give forests their characteristic scent. While some of these molecules are simple, others are complex structures with carbon atoms arranged in rings and chains. Once released, these compounds do not simply vanish; they undergo a series of chemical transformations that can lead to the formation of tiny particles in the air, which in turn influence cloud formation and the Earth's climate. To understand how these molecules behave, scientists need to know their fundamental energy properties: how much energy is stored within their bonds, how stable they are compared to one another, and how easily they can lose an electron to become charged. These details are crucial for predicting how quickly they will react in the atmosphere, but for many of these complex plant-derived molecules, such data has been missing or difficult to measure directly.

A recent study has filled these gaps by using powerful computer simulations to map the energy landscape of seventy-four different terpene molecules found in terrestrial vegetation. The researchers focused on two main groups: monoterpenes, which have ten carbon atoms, and sesquiterpenes, which have fifteen. These molecules come in many different shapes, ranging from open chains to tightly packed, multi-ring structures. Because these compounds are often unstable or exist in such small quantities in nature, measuring their properties in a laboratory is frequently impossible. Instead, the team employed high-level theoretical methods, essentially performing precise mathematical calculations on a supercomputer to determine the exact energy required to form each molecule from its basic atoms, how much energy is released or absorbed when one shape changes into another, and the specific energy needed to strip an electron from the molecule. This approach allowed them to generate a complete and consistent set of data for a wide variety of structures, providing a reliable reference for atmospheric scientists.

The calculations revealed clear patterns in how the shape of a molecule dictates its stability. The study found that molecules with open, chain-like structures are generally the least stable, carrying a significant energy penalty compared to their ringed counterparts. When carbon atoms form rings, the molecule becomes more stable, but the degree of this stability depends heavily on how the rings are fused and where the double bonds are located. The most stable molecules were found to be those with compact, highly bridged frameworks where structural strain is efficiently distributed. For instance, a molecule with a double bond tucked inside a ring system was consistently more stable than one where the double bond stuck out from the ring. This preference for internal, more crowded double bonds follows a well-known chemical principle, but the study confirmed it across a vast array of complex structures. The researchers also discovered that the most stable sesquiterpenes were those with rigid, fused ring systems that minimized internal strain, while the least stable were the flexible, open-chain versions of the same chemical formula.

Beyond stability, the study mapped out how easily these molecules give up an electron, a property known as ionization energy. This value is critical because it helps predict how quickly a molecule will react with atmospheric scavengers like hydroxyl radicals. The results showed that the ease of removing an electron is governed by how well the molecule can spread out the resulting positive charge. Molecules with extended systems of conjugated double bonds, where electrons can move freely across the structure, were the easiest to ionize. Similarly, the presence of strained three-membered rings adjacent to double bonds provided a unique way to stabilize the charged state, lowering the energy required for ionization. In contrast, molecules with isolated double bonds that were poorly shielded by surrounding atoms required the most energy to ionize. The study found that the most stable, rigid molecules often had the highest ionization energies, while the most reactive, flexible ones had the lowest.

The researchers compared their calculated values against the limited experimental data available for a few of these compounds and found excellent agreement, confirming that their simulations were accurate. They also tested their results against other theoretical methods and found that some older, less sophisticated approaches produced incorrect rankings of stability, sometimes suggesting that a less stable molecule was actually the most stable. This highlights the necessity of using high-level computational tools to get the physics right. The study also clarified some historical confusion regarding the ionization energies of specific compounds like pinene and limonene, reconciling conflicting reports in the literature by providing a consistent, high-precision benchmark. By establishing these precise energy values, the work provides a solid foundation for improving models of atmospheric chemistry. These models rely on accurate data to predict how biogenic emissions will transform into secondary organic aerosols, which play a major role in climate regulation. With this new dataset, scientists can now better understand the fate of these plant-derived gases and their impact on the global environment.

Technical Summary: High-Level G4 and G4(MP2) Study of Terpenes

Problem Statement
Biogenic volatile organic compounds (BVOCs), specifically monoterpenes (C10H16) and sesquiterpenes (C15H24), are critical drivers of tropospheric chemistry, influencing the oxidizing capacity of the lower atmosphere and the formation of secondary organic aerosols (SOAs). Despite their environmental significance, a comprehensive understanding of their atmospheric degradation pathways is hindered by a scarcity of high-quality fundamental thermodynamic and electronic data. These compounds exhibit vast structural diversity, including acyclic, monocyclic, bicyclic, and tricyclic frameworks, many of which are unstable or difficult to isolate for direct experimental measurement. Consequently, reliable gas-phase standard state enthalpies of formation ( $\Delta_fH^\circ(g)$ ), enthalpies of isomerization ( $\Delta_{isom}H^\circ(g)$ ), and adiabatic ionization energies (AIEs) are often missing or inconsistent, limiting the accuracy of atmospheric kinetic models and structure-activity relationship (SAR) predictions.

Methodology
To address these data gaps, the study employed high-level composite ab initio quantum-chemical protocols, specifically the Gaussian-4 (G4) and Gaussian-4 modified second-order Møller-Plesset perturbation theory (G4(MP2)) methods. The research focused on a dataset of 74 atmospherically relevant hydrocarbons: 20 monoterpene isomers and 54 sesquiterpene isomers derived from terrestrial vegetation.

The computational workflow involved:

Structure Generation: Initial 3D structures were retrieved from the PubChem database and optimized using the MMFF94 force field via a systematic rotor search to identify the global minimum energy conformers.
Quantum Calculations: High-level calculations were performed using the Gaussian 16 software package on the Digital Research Alliance of Canada grid.
Thermodynamic Properties: Gas-phase standard state enthalpies of formation ( $\Delta_fH^\circ(g)$ ) were calculated using the atomization approach, utilizing experimental atomic enthalpies for hydrogen and carbon. Enthalpies of isomerization ( $\Delta_{isom}H^\circ(g)$ ) were derived relative to the lowest-enthalpy isomer in each class.
Electronic Properties: Gas-phase standard state (298.15 K) and 0 K adiabatic ionization energies (AIEs) were computed.
Validation: The calculated values were compared against available experimental data from the NIST Chemistry WebBook and prior literature, as well as against lower-level methods (e.g., DFT, group contribution methods) to assess accuracy and consistency.

Key Results
The study generated a self-consistent dataset of thermodynamic and electronic properties for all 74 compounds. Key findings include:

Methodological Consistency: G4 and G4(MP2) methods yielded highly self-consistent results. G4(MP2) values for $\Delta_fH^\circ(g)$ and $\Delta_{isom}H^\circ(g)$ were systematically lower than G4 values by several kJ mol⁻¹ (ranging from -0.2 to -6.6 kJ mol⁻¹). Similarly, G4(MP2) AIEs were systematically lower than G4 counterparts by 0.01–0.05 eV (mean deviation ≈0.03 eV or 2.9 kJ mol⁻¹).
Thermodynamic Accuracy: The calculated $\Delta_fH^\circ(g)$ values showed good agreement with limited available experimental data (e.g., for camphene and $\alpha$ -carene), indicating effective thermochemical accuracy within $\pm 4.2$ kJ mol⁻¹.
Stability Trends:
- Monoterpenes: Acyclic trienes were identified as the least thermodynamically stable isomers. Stability increased with cyclization, with compact, highly bridged polycyclic frameworks (e.g., tricyclene, camphene, $\alpha$ -fenchene) representing the most stable motifs. Stability was governed by ring strain, double-bond substitution (adhering to Zaitsev's rule), and hyperconjugation. Endocyclic double bonds were consistently more stable than exocyclic counterparts.
- Sesquiterpenes: Similar trends were observed, with acyclic isomers ( $\alpha$ - and $\beta$ -farnesene) being the least stable. The global minimum was identified as $\beta$ -patchoulene, a rigid, fused tricyclic structure. Macrocyclic and monocyclic frameworks (e.g., germacrenes) displayed intermediate stability.
Ionization Energies (AIEs): AIEs ranged from ~7.2 eV to ~8.6 eV. The values were governed primarily by $\pi$ $π$ -conjugation, alkyl substitution, and specific orbital interactions.
- Extended $\pi$ -conjugation (e.g., in acyclic trienes and conjugated dienes) significantly lowered AIEs.
- Interactions between alkenes and strained rings (specifically alkene–cyclopropyl Walsh orbital interactions) provided additional stabilization, lowering AIEs in compounds like thujenes and sabinene.
- Highly substituted endocyclic double bonds generally resulted in lower AIEs compared to isolated or exocyclic double bonds.
Comparison with Other Methods: The study highlighted significant discrepancies between the high-level G4/G4(MP2) results and lower-level Density Functional Theory (DFT) or group contribution methods (GCMs). In several cases, lower-level methods produced incorrect stability rankings or erroneous magnitude estimates, underscoring the necessity of high-level composite methods for these complex systems.

Significance and Claims
The authors claim that this work provides a comprehensive, internally consistent reference dataset that resolves long-standing ambiguities in terpene thermochemistry. By filling critical data gaps for structurally complex isomers, the study offers accurate structural and energetic inputs required for:

Refining atmospheric chemistry mechanisms and oxidation pathways.
Improving structure–activity relationships for predicting oxidant attack rates (e.g., by $\cdot$ OH, O $_3$ , $\cdot$ NO $_3$ ).
Parameterizing secondary organic aerosol yields.
Supporting robust models of tropospheric oxidizing capacity and aerosol-driven climate regulation.

The paper emphasizes that the mutual consistency between G4 and G4(MP2) across both rigid and flexible frameworks validates the use of these protocols for extending such datasets to further terpenoid isomers. Furthermore, the discrepancies observed with common lower-level methods serve to underscore the value of these high-level composite benchmarks for atmospheric science applications.

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