[Paper Review] Large yet bounded: Spin gap ranges in carbenes

Max Schwilk, Diana N. Tahchieva+1 more|arXiv (Cornell University)|Apr 22, 2020

Catalysis and Oxidation Reactions8 references22 citations

TL;DR

This study presents a systematic quantum chemical analysis of 8,062 carbene structures using multireference MRCI calculations, revealing a hard upper bound of ~30 kcal/mol for the singlet-triplet spin gap across all carbene classes. Despite large variations in adiabatic spin gaps (exceeding 60 kcal/mol within classes), the singlet state is stabilized by π-donating α-substituents, while triplet states prevail with σ- and π-withdrawing groups, establishing a bounded yet highly tunable spin gap landscape in carbene electronic structure.

ABSTRACT

Despite its relevance for chemistry, the electronic structure of free carbenes throughout chemical space has not yet been studied in a systematic manner. We explore a large and systematic carbene chemical space consisting of eight thousand diverse and common carbene scaffolds in their singlet and triplet state computed at controlled accuracy (higher order multireference level of theory) and with verified carbene character in the electronic structure. Originating in strong electron correlation, a hard upper limit for the singlet-triplet gap is found to emerge at around 30 kcal/mol for all the carbene classes in this chemical space. We also observe large vertical and adiabatic spin gap ranges within many carbene classes ($>$100 and $>$60 kcal/mol, respectively), and we report novel relationships between compositional, structural, and electronic degrees of freedom. Our QMspin data base includes numerical results for $\approx$13'000 MRCI calculations on randomly selected carbene scaffolds.

Motivation & Objective

• To systematically explore the electronic structure of carbenes across a large chemical space using high-accuracy multireference quantum chemistry methods.
• To identify trends in singlet-triplet spin gaps (ΔEₛ₋ₜᵃᵈ) across diverse carbene classes and establish their limits.
• To validate genuine carbene character through intrinsic bond orbital (IBO) analysis and ensure electronic structure reliability.
• To establish a comprehensive, high-accuracy data set (QMspin) for future materials discovery and design.
• To uncover relationships between molecular composition, geometry, and electronic structure in carbenes.

Proposed method

• Generated 8,000 carbene scaffolds from the QM9 data set, focusing on molecules with up to nine heavy atoms (H, C, N, O, F).
• Performed geometry optimizations at the CASSCF(2e,2o) level for both singlet and triplet states, using state-averaged orbitals.
• Computed high-accuracy adiabatic and vertical singlet-triplet energy gaps using MRCISD+Q-F12 with explicitly correlated basis sets.
• Validated carbene character via intrinsic bond orbital (IBO) localization, requiring ≥30% contribution from the carbene carbon to non-bonding orbitals and no other carbon exceeding this threshold.
• Ensured wave function reliability by verifying reference configuration weights >0.75 in MRCI and RMSD <1 Å between singlet and triplet geometries.
• Filtered out non-genuine carbenes (e.g., those with bond breaking or incorrect orbital localization), retaining 5,021 singlet and 8,062 triplet structures.

Experimental results

Research questions

• RQ1 What is the maximum possible adiabatic singlet-triplet gap in carbenes across diverse chemical space?
• RQ2 How do different α-substituent types (e.g., π-donors, σ/π-withdrawers) influence the spin state preference and gap magnitude?
• RQ3 To what extent can the singlet-triplet gap be tuned within a single carbene class, and what structural and electronic factors enable large variations?
• RQ4 What are the limits of electronic structure stability and carbene character across a large, systematically generated chemical space?
• RQ5 Can a high-accuracy, validated data set of carbenes be constructed to support future materials design and discovery?

Key findings

• A hard upper bound of approximately 30 kcal/mol exists for the adiabatic singlet-triplet gap (ΔEₛ₋ₜᵃᵈ) across all carbene classes studied.
• Adiabatic spin gaps exceed 60 kcal/mol within certain carbene classes, indicating a broad tunability range despite the upper bound.
• Carbene classes with π-donating α-substituents (e.g., oxo- and amino-carbenes) strongly stabilize the singlet state, yielding gaps between -50 and -20 kcal/mol.
• Carbene classes with aliphatic or aromatic α-substituents (e.g., vinyl-, alkynyl-, aryl-carbenes) show near-zero spin gaps, with most values within ±10 kcal/mol.
• Carbonyl- and cyano-substituted carbenes (group c) exhibit large conformational changes between singlet and triplet states, contributing to high spin gaps.
• The QMspin data set contains 13,000 MRCISD+Q-F12 calculations on 8,000 distinct scaffolds, with 99.5% of singlet and 95% of triplet structures confirmed as genuine carbenes via IBO analysis and orbital localization.