Draft:Nitrosyl tunneling in ruthenium complexes

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Nitrosyl tunneling in ruthenium complexes refers to a quantum mechanical process where the nitrosyl ligand (NO) migrates between different binding sites or orientations within a coordination sphere, even when classical thermal energy is insufficient to overcome activation barriers. This phenomenon has gained interest due to its relevance in low-temperature dynamics, spectroscopic signatures, and implications in catalytic mechanisms involving nitric oxide.

Overview

Ruthenium (Ru), a second-row transition metal, forms stable complexes with nitrosyl ligands in various coordination modes. In several of these complexes, NO can exhibit unusual dynamic behavior, including quantum tunneling — a process where the ligand moves through a potential energy barrier rather than over it. Nitrosyl tunneling has been observed spectroscopically, particularly via infrared (IR) spectroscopy, inelastic neutron scattering (INS), and low-temperature NMR. ^{[7,8,12,30,32]} This behavior is most prominent in environments where NO ligands are weakly bound or where multiple equivalent coordination geometries exist, especially in five-coordinate Ru(II) complexes and low-temperature crystal matrices.^[5,8,18,30]

Coordination chemistry of nitrosyl ligands

File:Chemdrawfornitrosylarticle.png

Linear and bent conformation of M-NO

Nitrosyl ligands can bind to metal centers in several ways:

• Linear (end-on) M–NO⁺ (bond angle ~180°)
• Bent (end-on) M–NO (bond angle ~120–140°)
• Side-on (η²-NO)

In ruthenium complexes, NO most commonly adopts the linear end-on geometry, indicative of a strong π-backbonding interaction and formal NO⁺ character.

The geometry and bonding mode are key factors in determining the likelihood and rate of tunneling.^[8,18]

Linkage isomerism and structural dynamics

Linkage isomerism involves the NO ligand binding through different atoms (N or O) or in different geometries. For instance, the transition from a linear Ru–N–O to a bent or side-on configuration can be induced by external stimuli like light or temperature changes. These isomers are often referred to as metastable states (MS), with MS1 representing the iso-nitrosyl form (Ru–O–N) and MS2 the side-on configuration. These states are separated by energy barriers, allowing for their isolation and study under specific conditions.^[30,31,32]

Ruthenium nitrosyl complexes, including derivative of Ru(NO)(PPh₃)₂Cl₂ have been shown to exhibit photo-induced linkage isomerism. Exposure to light can cause the nitrosyl ligand to switch from the ground state (GS) to metastable states (MS1 and MS2), corresponding to different bonding modes. One study showed in [RuCl(NO)Py₄](PF₆)₂.0.5H₂0, nearly 100% solid-state isomerization can be achieved.

Linkage isomerism is not only photochemically driven, but also closely related to non-classical behavior, particularly nitrosyl ligand tunneling. In the absence of sufficient thermal energy, interconversion between metastable and ground state isomers can proceed via tunneling of the NO ligand through the potential energy barrier separating coordination modes.^[5,30,31,32] In low temperature or rigid lattice environments, where classical barrier rotation is suppressed, the highly dynamic and sensitive interplay between structural characteristics and quantum effects can be observed.

Tunneling phenomenon

Quantum mechanical tunneling

File:Diagramfortunelingbarrierexplanation.png

C-H Tunneling Diagram

The JWKB approximation provides a semi-classical framework for estimating tunneling probability, revealing its exponential dependence on barrier width and inverse square root dependence on particle mass. As such, while light atoms like H and electrons traditionally dominate tunneling discussions, even heavier atoms (e.g., N, O) can tunnel given sufficiently narrow barriers and vibrational preorganization.^{[12,24,26,35]} Tunneling-dominated systems often:

• Exhibit large kinetic isotope effects (KIEs)
• Have anomalously low activation energies
• Deviate from classical Arrhenius behavior

Nitrogen-Based Heavy Atom Tunneling (HAT)

Nitrogen lies in a unique mass regime: light enough for quantum activity, but heavy enough to demand specific conditions for tunneling. Nitrogen tunneling has been observed in:

• Matrix-isolated ring rearrangements
• Cryogenic photochemistry (e.g., trifluoroacetyl nitrene)
• Spin crossover systems (via instanton theory)

In organometallics, coordination to metals modifies the electronic structure of ligands, often enhancing or modulating tunneling probabilities by adjusting barrier heights, vibrational coupling, and ligand dynamics. ^{[6,12,16,24,26,28,35]}

Observed examples:

• Nitrogen tunneling in iron-nitrosyl myoglobin
• Orbital delocalization in Ru–NO complexes
• Labile and hemilabile NO ligands in dynamic Ru environments

Quantum tunneling of nitrosyl ligands

Quantum mechanical tunneling (QMT) is a critical phenomenon arising from the wave–particle duality of matter, allowing particles to penetrate energy barriers that would be classically insurmountable. In the context of organometallic chemistry, nitrosyl tunneling in ruthenium complexes represents a particularly compelling example of this effect, wherein the NO ligand migrates between different orientations or binding sites within the coordination sphere of a ruthenium center—even under conditions of insufficient thermal energy.^{[7,8,10,12,19,21,30]}

This behavior is especially significant at low temperatures (<30 K), where classical motions are effectively frozen out. Tunneling is supported by multiple experimental and theoretical approaches, with implications in catalysis, spectroscopy, and molecular design.^{[21,30,31,32,35]}

Mechanistic types

There are three common types of nitrosyl tunneling observed in ruthenium complexes:

File:RuNObindingmodes.png

1. Site-to-site tunneling (e.g., cis ⇌ cis′)
2. Orientation tunneling (e.g., end-on ⇌ bent)
3. Inversion tunneling (change in NO geometry through inversion at nitrogen

The linear configuration is most common and often associated with formally NO⁺ species. Geometry and bonding strongly influence the tunneling probability of the ligand. Complexes with multiple nearly equivalent binding sites or weakly bound NO groups are especially prone to QMT.^[30,31,32]

Notable examples and structural motifs

Ru-NO and related omplexes

[Ru(NH₃)₅(NO)]²⁺

File:Rupentamminenoclustermodel.png

[Ru(NH₃)₅(NO)]³⁺+·10H₂0 cluster

Density functional theory combined with Monte Carlo simulations examining [Ru(NH₃)₅(NO)]³⁺·10H₂0 indication the presence of minimum-energy crossing points which facilitates nonadiabatic transitions. Associated with lowered activation energy for NO release, this the electronic behavior and mechanisms of this complex are indicative of tunneling.^[38]

[RuCl(NO)(PPh₃)₂]X

File:Orbitalinteractionsforruno.png

The weighted sums of involved orbitals in the low-lying transitions in the [RuNOPy4Cl]2+ complex (Vorobyev et al)

In five-coordinate ruthenium nitrosyl phosphine complexes, such as [RuCl(NO)(PPh₃)₂]X, NO often adopts a bent coordination geometry. Tunneling in these systems may involve reorientation about the Ru–NO axis or movement between two axial sites.

These systems are studied using low-temperature IR spectroscopy, where splitting or broadening of the ν(NO) stretching band reveals dynamic behavior. ^[32]

Spectroscopic evidence

Infrared (IR) Spectroscopy

File:Irspectraforruno.png

IR spectral ranges of Ru-NO conformations reported by Rose et al

The ν(NO) stretching frequency is sensitive to NO bonding and orientation.^[25] Tunneling leads to:

• Band splitting (due to tunneling between inequivalent sites)
• Line broadening (due to fast tunneling on the IR time scale)
• Temperature-dependent frequency shifts

Typical ν(NO) ranges:

• Linear Ru–NO⁺: 1850–1900 cm⁻¹
• Bent Ru–NO: 1600–1750 cm⁻¹

Inelastic Neutron Scattering (INS)

INS is a powerful probe for low-energy vibrational modes and ligand dynamics. It can directly observe NO tunneling transitions and determine energy level splitting due to tunneling.^[32}

Nuclear Magnetic Resonance (NMR)

Low-temperature ¹⁵N NMR of labeled NO can reveal exchange broadening due to tunneling and is complementary to IR studies.^{[2,16,18,26,30,33]}

Theoretical models and quantum chemical calculations

Potential Energy Surfaces (PES)

Theoretical studies involve calculating PES as a function of NO position and orientation. The presence of shallow double-well potentials is a hallmark of systems likely to undergo tunneling.^{[7,8,17,30,31,32]}

File:Runoisomerizationshallowpes.png

Shallow double well potential energy surface indicative of tunneling from ground state to meta-stable states in Ru-NO complex

Computational methods:

• Density Functional Theory (DFT)
• Multiconfigurational wavefunction methods (CASSCF, MRCI)
• Path integral molecular dynamics (PIMD)

Factors Influencing Tunneling

Parameter	Effect on Tunneling
Ru oxidation state	Higher oxidation can tighten NO bonding, reducing tunneling
Ligand field strength	Strong fields reduce flexibility of NO orientation
NO geometry (linear vs bent)	Bent NO more prone to tunneling reorientation
Matrix environment	Solid-state matrices may inhibit or enable tunneling
Temperature	Tunneling dominates at low temperatures; thermal hopping at higher T

Implications in catalysis

Nitrosyl ligands are key intermediates in various catalytic processes involving ruthenium, such as:

• NO reduction
• Nitric oxide disproportionation
• Nitrate/nitrite conversion in biological mimics

Tunneling behavior may influence:

• Reaction pathways by altering ligand accessibility
• Activation barriers via zero-point energy corrections
• Ligand substitution kinetics

Understanding tunneling dynamics is thus relevant for the rational design of NO-based sensors, therapeutic agents, and catalysts.

Experimental techniques summary

Technique	What It Probes	Key Observations
IR spectroscopy	ν(NO) stretching	Band broadening, splitting
Neutron scattering	Tunneling modes	Direct observation of splittings
Low-T NMR	Ligand motion	Exchange broadening
X-ray diffraction (variable T)	Average geometry	Changes in NO orientation or disorder

Recent advances and possible applications

Biomedical applications

File:Reactionpathway.png

The reaction mechanism of trans-[Ru(cyclam)(NO)Cl]2+ involving reduction, NO release, and the catalytic cycle for NO2 according to Stepanenko et al.

Ruthenium nitrosyl complexes have been explored as NO donors in therapeutic contexts. Their ability to release NO upon stimulation makes them candidates for treatments requiring controlled NO delivery, such as vasodilation or antimicrobial therapies.^{[1,2,7,8,17,21,30,37]\}

Photochemical applications

File:Photoregenerationnolinkage.png

Scheme illustrating the photogeneration of nitrosyl linkage isomers in RuCl(NO)2(PCy3)2BF4 according to Stepanenko et al

The photoresponsive nature of these complexes allows for their use in light-activated processes. Upon irradiation, the NO ligand can undergo isomerization or be released, enabling applications in areas like photodynamic therapy or as components in molecular switches.^[30,31]

Data storage and molecular electronics

The distinct optical properties of the different NO isomers enable their use in data storage devices. By toggling between isomeric states using light, information can be encoded at the molecular level, paving the way for high-density storage solutions. ^{{17,18,30,32}}

Additional directions

• Femtosecond IR spectroscopy to observe tunneling on ultrafast timescales
• Pressure-dependent studies to modulate NO coordination
• Isotopic substitution (e.g., ¹⁵NO vs ¹⁴NO) to probe mass effects on tunneling
• Metal–organic frameworks (MOFs) containing Ru–NO centers for tunable tunneling environments
• Cryogenic single-molecule studies combining STM with tunneling spectroscopy

See also

• Nitrosyl ligand
• Quantum tunneling
• Transition metal nitrosyl complexes
• Ruthenium coordination chemistry

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