Single-molecule neuromorphic device with aJ-level power consumption per switching

Abstract

Artificial neural network-based machine learning provides foundations for artificial intelligence (AI), yet requires high energy costs for training. Beyond software-level simulation of neural networks, hardware-level implementation via neuromorphic devices becomes the next milestone in nanoscience towards energy-sustainable AI. Single-molecule devices have the potential for ultimate scale and energy efficiency, but challenges remain in achieving programmable multi-conductance states amidst room-temperature thermal fluctuations. Here we fabricated a bio-inspired single-molecule neuromorphic device consuming ~6.34 aJ/operation by electrochemically gating molecule-ion electrostatic interactions. This device realizes biomimetic emulation of neural plasticity from short-term to long-term memory featuring over 10 distinct conductance states, demonstrating the applications in Pavlovian conditioning for associative learning and pattern recognition in Morse code processing. Our approach enables multi-state synaptic emulation using an individual molecule toward energy-sustainable AI.

Molecular devices offer the potential for the scalability and energy efficiency required to develop energy-sustainable AI. Zhang et al. report a single-molecule neuromorphic device that consumes 6.34 aJ per operation and support both short-term to long-term memory, featuring over 10 distinct conductance states.

Introduction

Large-scale neural networks, such as GPT-4 with trillions of artificial neurons, have demonstrated great promise for artificial intelligence (AI) but also consumed large amounts of energy for the training of these networks^1,2. To address the exponentially growing energy demands of AI, inspired by the energy-efficient operations from biological neural systems, neuromorphic computing^3–7 has demonstrated the potential for the hardware-level simulation of neural networks, employing diverse materials from silicon-based semiconductors to organic electrochemical transistors^8–10. Long-term efforts to reduce operating energy have made substantial progress through the evolution from HP’s memristor¹¹ to current state-of-the-art inorganic^12,13 and organic¹⁴ devices, but the most advanced transistors still consume ~240 aJ (10⁻¹⁸ J) per operation¹⁵. As neuromorphic devices at the ultimate scale, single-molecule neuromorphic devices represent a promising solution with potential energy consumption of several aJ per operation, leveraging their atomic-scale dimensions and electron tunneling mechanisms with low inter-state energy barriers^16–22.

Molecular materials have demonstrated potential for neuromorphic computing due to their unique tunable band structures and multiple conductance states with high energy efficiency²³. To further minimize channel length, self-assembled monolayers (SAMs)^24,25 with ~2 nm thickness have been employed to implement neuromorphic functions, but still more than thousands of molecules involved in the switching, and then single fullerene within ~1 nm length was used to achieve logic operations^26–28 through external electric field-induced dipole inversion. However, current state-of-the-art single-fullerene logic-in-memory devices remain limited to two conductance states due to the restricted number of thermodynamically stable conformations at room temperature^29–31. Drawing inspiration of the ion channel dynamics from biological synapses, recent advances in elegantly controlling electrostatic molecule–ion interactions at the single-molecule scale offer a promising approach to fix the molecular conformations^32–34, thereby enabling multiple nonvolatile conductance states with minimal energy consumption.

Here, we fabricated single-molecule neuromorphic devices by modulating electrostatic coupling between a single 5,5’-(2,5-dimethoxy-1,4-phenylene) bis(2-(methylthio)thiophene) (MeO-TBT) molecule and tetrabutylammonium cations (TBA⁺) (Fig. 1a) using electrochemical scanning tunneling microscopy break junction (EC-STMBJ) techniques^35–40. Through synchronized application of a bias pulse (reducing the dihedral thiophenyl-phenyl angle in MeO-TBT molecule) and a gate voltage pulse (driving TBA⁺ to disrupt the S–O interactions for tuning the dihedral angle in MeO-TBT molecule)⁴¹, we achieved an operation energy consumption of ~6.34 aJ, six orders of magnitude lower than that of a conventional 2-CMOS-transistor neuron implementation (~415 pJ)⁴². By controlling molecule–cation interactions (Fig. 1b), the device emulates both short-term plasticity (STP) with 307.99% paired-pulse facilitation and long-term synaptic plasticity (LTP) featuring over ten nonvolatile conductance states, thereby performing associative learning through Pavlovian conditioning while enabling recognition of Morse code and handwritten digits. Theoretical calculations reveal that the averaged energy consumption of displacing TBA⁺ cations reaches ~2.1 aJ per cation, thus inducing multiple conductance states through varying degrees of conformational locking by S–O interactions.

Fig. 1. Single-molecule neuromorphic device.

a Comparison between a biological synapse (left) and the artificial single-molecule neuromorphic device (right). CE and RE are abbreviations for counter electrode and reference electrode, respectively. MeO-TBT is the abbreviation for 5,5’-(2,5-dimethoxy-1,4-phenylene) bis(2-(methylthio)thiophene). b Scaling of information processing and storage capacity with the number of nonvolatile conductance states.

Results

Emulating synaptic plasticity in a single-molecule neuromorphic device

Inspired by ion-mediated biological information processing, we demonstrate dynamic modulation of molecular junction transport properties through electrostatic coupling/decoupling between MeO-TBT molecules and cations, emulating synaptic multi-conductance behavior (Fig. 2a). Initially, at V_G = –0.4 V (vs. Ag/AgCl), cations migrate to the junction under the applied field and form electrostatic couplings that disrupt molecular planarity through S–O interaction breaking, establishing a low-conductance state (State I). Subsequent application of a positive gate voltage pulse (State II) drives cations away from the junction (State III), weakening coupling effects and restoring molecular planarity. This enhances π-electron delocalization to increase conductance. Upon pulse removal (State IV), ion diffusion returns the system to equilibrium while the conductance gradually decays to its initial value, replicating synaptic plasticity. Upon thousands of single-molecule break-junction measurements, we have observed a gate voltage-dependent conductance modulation (Supplementary Figs. 1–6) that aligns with theoretical predictions, thereby corroborating the molecule–ion coupling mechanism. And this phenomenon exhibits robust reproducibility across systems composed of different tip and substrate electrodes, which further verifies the excellent device-to-device consistency and repeatability of our molecular junctions.

Fig. 2. Synaptic plasticity emulation in a single-molecule neuromorphic device.

a Schematic of ion redistribution in the MeO-TBT-based molecular transistor under electrical stimulation. CE counter electrode. b Conductance statistics (105 traces) under single V_G pulses (–0.4 to 0.5 V) at V_B = 1 mV, with black curve showing the fitted trend (inset). Energy consumption comparisons at V_B = 1, 10, and 100 mV are shown (inset), where the blue curve represents experimental data. c Benchmarks of published neuromorphic devices by channel length versus energy consumption (see Supplementary Information). d I-V_B characteristics (2184 traces) and fitting (blue line) for forward and reverse scans at V_G = –0.4 V, using 0.5 mM MeO-TBT in 0.2 M solution of tetrabutylammonium hexafluorophosphate (TBAPF₆) in propylene carbonate (PC). e Paired-pulse facilitation (PPF) under combined V_G = 0.5 V and V_B = 0.6 V pulses (1136 traces). PPF = (G₂/G₁) × 100% = (220.97 nS/ 73.40 nS) × 100% = 301%. f Long-term plasticity and multiple conductance (right histograms) achieved with combined stimulation of gate voltage pulses and bias voltage pulses (V_G = 0.5 V, V_B = 0.6 V, t_p = 50 ms, ∆t = 150 ms).

To investigate the neuromorphic functionality of our single-molecule device, we analyzed its current-gate voltage (I-V_G) characteristics and observed pronounced hysteresis effects (Fig. 2d and Supplementary Figs. 7–10). The device emulates excitatory postsynaptic conductance (EPSC) through single gate voltage pulses. At 1 mV bias with 1 ms pulse width, it demonstrates ultra-low energy consumption averaging ~6.34 aJ per synaptic event, while the minimum operation energy reaching ~4.34 aJ (blue curve in Fig. 2b). This total energy includes contributions from both the source-drain and gate circuits (Supplementary Figs. 11–13 and Supplementary Note 1), and the corresponding static power consumption is ~0.25 fW. Statistical analysis of operational energy consumption across different bias voltages (1, 10, and 100 mV; Fig. 2b inset) reveals a voltage-dependent trend. Gaussian fitting of over 100 independent measurements shows the per-operation energy increasing from 6.34 aJ to 229.45 fJ with applied voltage. Figure 2c presents a comprehensive benchmarking framework that compares channel length versus energy consumption. Current technologies exhibit a fundamental trade-off, as monolayer devices achieve sub-nm channels but require μJ-level energy, whereas carbon nanotube devices reach aJ-level consumption with μm-scale dimensions. The dashed lines indicate theoretical projections for Si CMOS and NEMS devices (Supplementary Table 1) provided by International Roadmaps for Devices and Systems (IRDS)^43,44. Remarkably, our device achieves breakthroughs on both axes, attaining sub-nanometer channel dimensions (X-axis) and aJ-level energy consumption (Y-axis), thereby demonstrating advantages of miniaturization and low-power operation.

Further, exclusively driven by gate voltage pulses, the device demonstrates a bias voltage-dependent transition from volatile to nonvolatile behavior. Current-bias voltage (I-V_B) statistical analysis further reveals distinct hysteresis effects (Fig. 2d and Supplementary Figs. 8, 9, 14). By optimizing experimental conditions with synchronized gate and bias voltage pulses at a low operating voltage of 0.1 V, we achieve enhanced device non-volatility through synergistic electrical stimulation (Supplementary Figs. 15–19). This configuration enables EPSC emulation across varying pulse durations, with amplitudes significantly exceeding the algebraic sum of individual pulses (Supplementary Table 2), thereby mimicking the supralinear integration properties of neuronal dendrites. The simultaneous demonstration of synaptic plasticity and dendritic integration at the single-molecule scale establishes a new paradigm for energy-efficient neuromorphic device design.

To induce the transition from short-term to long-term plasticity (Fig. 2e and Supplementary Figs. 20–21), we implemented paired-pulse facilitation (PPF) by applying consecutive double-pulse stimulation (Supplementary Note 2). Based on 1136 device tests, we observe a maximum PPF index of ~301% at a pulse interval of 10 ms, demonstrating robust cycle-to-cycle endurance. Furthermore, as the interval extended to 300 ms, the PPF index exhibits a clear exponential decay trend. Compared to the 236% achieved with gate voltage pulses alone (Supplementary Fig. 22), this value shows a significant increase. This result further demonstrates that the simultaneous application of gate and bias voltage pulses can effectively enhance the memristive performance of the device. With twelve consecutive pulses, the device exhibits progressive enhancement of EPSC conductance states while maintaining frequency sensitivity (Supplementary Fig. 23), exhibiting biological synapse-like multilevel plasticity and frequency-dependent potentiation similar to biological systems. Control of pulse intervals and durations enables the identification of more than 10 distinct conductance states (including baseline; Fig. 2f, Supplementary Figs. 24 and 25, and Supplementary Table 3)⁴⁵, highlighting the potential of this single-molecule device for programmable neuromorphic computing and multilevel memory applications.

Expanding these findings, we emulated the “learn-forget-relearn” behavior using the single MeO-TBT synapse (Supplementary Fig. 26, Supplementary Table 4, and Supplementary Note 3). The initial learning phase requires six pulses to achieve conductance saturation, whereas relearning attains the same state with only three pulses (a 50% increase in learning efficiency). Notably, conductance retention improves from 21.15 to 45.57% during short-term forgetting (10 ms intervals) and from 4.18 to 7.61% in long-term forgetting (400 ms intervals). Beyond implementing spike-timing-dependent plasticity (STDP)⁴⁶, the device exhibits memory reconsolidation through cumulative ion migration, establishing a platform for autonomous neuromorphic computing systems.

Associative learning and recognition using a single-molecule neuromorphic device

To demonstrate the potential of neuromorphic computing with the single-molecule device, we emulated associative learning behavior under the synergistic stimulation of V_G and V_B pulses. The single-molecule conductance curve (Fig. 3a, for more details, see Supplementary Fig. 27 and the corresponding caption), together with the two-dimensional histogram compiled from 134 individual traces (Fig. 3b and Supplementary Fig. 28), conclusively demonstrates that our single-molecule device can implement classical Pavlovian conditioning⁴⁷. Electrical pulse sequence 1 is used as the conditioned stimulus (CS), emulating the scenario in which a dog hears a bell without response. Sequence 2 serves as the unconditioned stimulus (UCS), representing the dog’s response upon seeing food. The device is trained by simultaneously applying both sequences, mimicking the experience of the dog hearing the bell while seeing food. Finally, when sequence 1 is applied again to emulate the dog hearing the bell once more, the device exhibits a response. This indicates that the device is capable of emulating associative learning behavior after pretraining.

Fig. 3. Associative learning and Morse code recognition.

a, b Mimicking Pavlov’s experiment using a single-molecule device. A representative single-molecule conductance curve (right panel of Fig. a) and statistical results from 134 traces (Fig. b) demonstrate the emulation of Pavlov’s experiment. The conductance was enhanced by ~401% after training (see histograms in the right column). The blue dog icon represents the no-response scenario, and the red dog icon represents the response scenario. c Morse code decoding of the six characters of “PI-LAB” is achieved with tunable pulse durations (V_G = 0.5 V, V_B = 0.6 V, t_p = 50 ms, ∆t = 10 ms): 25 ms for “.” and 75 ms for “-” with distinguishable output conductance states, as indicated in the histograms at right.

Morse code recognition was further performed to demonstrate the information processing capabilities of this single-molecule neuromorphic device⁴⁸. Here, excitatory postsynaptic conductance (EPSC) values generated by 25 and 75 ms electrical pulses are used to encode the dot (“.”) and dash (“-”) signals, respectively (Fig. 3c and Supplementary Figs. 29 and 30). As shown, the name of our laboratory, “PI-LAB”, can be represented using low and high EPSC amplitudes through temporally coded pulse input signals. Importantly, comparative analysis of the steady-state conductance after pulse termination reveals distinct differences corresponding to the encoded Morse code patterns. This clear conductance differentiation demonstrates the intrinsic capability of the single-molecule device for temporal pattern recognition. Furthermore, key feature parameters extracted from the conductance data of this single-molecule neuromorphic device are used to construct an artificial spiking neural network (SNN) model (Supplementary Fig. 31) for the task of MNIST handwritten digit recognition^49,50. Experimental results show that this model achieves a classification accuracy of 97.4% and notably exhibits human-like cognitive confusion when handling blurred images (accuracy of 96%), highlighting the potential of single-molecule devices in image and voice processing applications.

Mechanism of the single-molecule neuromorphic device

To elucidate the operational mechanism of single-molecule neuromorphic devices, we performed large-scale force-field molecular dynamics (FFMD) simulations to investigate electric field-driven ionic migration of TBA⁺ and PF₆⁻ (Fig. 4a and Supplementary Movie 1)⁵¹. Validation of the force field is achieved by simulating TBA⁺ and PF₆⁻ self-diffusion in 0.2 M propylene carbonate solution (Supplementary Fig. 32a). The simulated self-diffusivity of TBA⁺ and PF₆⁻ is 3.83 ×  10⁻¹⁰ m²·s⁻¹ and 4.74 × 10⁻¹⁰ m²·s⁻¹, respectively, consistent with experimental pulsed field gradient-NMR measurements. (Supplementary Figs. 32b and 33)⁵². Under an applied electric field (positive X-axis as gate voltage and positive Y-axis as bias voltage), TBA⁺ ions migrated along the field direction, while PF₆⁻ ions moved oppositely, with preferential accumulation near the MeO-TBT bottom (Supplementary Fig. 34). Ion mobilities are quantified as (5.92 ± 3.37) × 10⁻⁵cm²·V⁻¹·s⁻¹ (TBA⁺) and (6.96 ± 2.98) × 10⁻⁴cm²·V⁻¹·s⁻¹ (PF₆⁻). FFMD simulations further reveal three distinct states: coupling (State I) and decoupling (States II and III) between MeO-TBT and TBA⁺.

Fig. 4. Mechanism of multiple conductance states in single-molecule neuromorphic devices.

a Simulated ion migration under an external electric field (positive X- and Y-axis components) using nonequilibrium molecular dynamics (MD). TBA⁺ and PF₆⁻ represent tetrabutylammonium cation and hexafluorophosphate anion, respectively. b Transmission spectra calculations for the single-molecule junction in State I, State II, and State III (corresponding to Fig. 2a). To simplify computations while preserving key chemical characteristics, we substituted tetrabutylammonium with tetramethylammonium cations in the model. c Theoretical time-dependent cumulative energy profile for TBA⁺ migration around MeO-TBT. The TBA⁺ (1), TBA⁺ (2), TBA⁺ (3), and TBA⁺ (4) correspond to the four tetrabutylammonium cations in Fig. 4a, respectively.

To elucidate the nature of interactions between MeO-TBT and the ammonium cations, we constructed models representing the interaction of MeO-TBT with one and two ammonium cations, optimizing them to obtain the lowest energy configurations (Fig. 4b and Supplementary Fig. 35). In the absence of molecule–ion interactions, the O–S distance measures 2.7 Å and the S–C1–C2–C3 dihedral angle is 15° on both sides of the molecule (Supplementary Fig. 36a). Applying a weak electric field (2 a.u.) along the S–S direction results in O–S distances of 2.7 Å and dihedral angles of 10° and 19° (Supplementary Fig. 36b), respectively. When the electric field strength is increased to 20 a.u., positive ions migrate closer to the molecule. As a result, both the O–S distance and the dihedral angle increase, reaching values of 2.80 Å and 28° (Supplementary Fig. 36c), respectively, with consistent values observed on both sides. The sulfur and oxygen atoms in the MeO-TBT molecule electrostatically interact with the hydrogen atoms from the cations of TBA⁺, with distances of 2.97 and 2.41 Å, respectively. In addition to these electrostatic interactions, there is a potential electrostatic attraction between the hydrogen atoms and the conjugated plane of MeO-TBT. To clarify the changes in conductance of MeO-TBT during the coupling and decoupling processes with ammonium cations, we calculated the transmission spectra on State I, State II, and State III corresponding to Figs. 2a and 4a (Fig. 4b). The results indicate that when MeO-TBT is in a coupled state with two cations, the transmittance is at its lowest, gradually increasing as the decoupling proceeds. Therefore, we propose the conformational assignments for State I and State III in Fig. 2a, and reasonably infer that States II and IV are the transition intermediates between them. Furthermore, our calculations yield a cumulative energy consumption profile for single TBA⁺ ion migration around MeO-TBT (Fig. 4c), showing an average energy consumption of ~2.10 aJ. This theoretical value agrees well with the experimental energy consumption range of ~6.34 aJ per operation. Together, these results provide strong theoretical evidence for the ion migration-mediated molecule–ion dynamic coupling mechanism.

To further elucidate the mechanism of multiple conductance states, we performed energy calculations on possible conformations of the MeO‑TBT molecular junction. The results show that the molecule possesses multiple low‑energy stable states (i.e., energy minima, such as States 1, 2, 4, and 5; Supplementary Fig. 37a), and their corresponding transmission spectra reveal distinct conductance plateaus (Supplementary Fig. 37b). This theoretically confirms the existence of multiple non‑volatile states, all of which are associated with molecular configurations of relatively high planarity. Both prior experimental work⁴¹ and electrochemical UV-Vis spectroscopy of MeO-TBT (Supplementary Fig. 38 and Supplementary Discussion)⁵³ show that raising the bias voltage or electrode potential facilitates planarization of the molecular junction. On this basis, we propose the following mechanism: electrical pulses drive the molecular structure toward a planarized transformation, causing it to relax and stabilize at specific non‑volatile conductance states. When combined bias/gate voltage pulses are applied consecutively, a synergistic effect emerges—the bias pulse promotes planarization of the molecular backbone, while the gate pulse modulates the S–O interaction by regulating TBA⁺ ions, thereby stabilizing a specific dihedral angle and gradually driving the molecule into a more planar (Supplementary Fig. 39), more stable low‑energy conformation. This process achieves the transition from short‑term to long‑term plasticity.

To further verify the operation mechanism of the single-molecule neuromorphic device, we conducted control experiments on the target molecule and the electrolyte. The results indicate that the I-V_G curves of 5,5’-(2,5-diethyl-1,4-phenylene) bis(2-(methylthio)thiophene) (Et-TBT) without the S–O non-covalent interactions show a much smaller hysteresis area, while the I-V_B curves exhibit almost no hysteresis (Supplementary Figs. 40 and 41). This suggests that the memory function of the device is closely related to the non-covalent S–O interactions in MeO-TBT. Control experiments using different electrolytes (Fig. 2d and Supplementary Figs. 7-–10, 42–44) reveal that devices containing ammonium ions exhibited significant hysteresis effects in both I-V_G and I-V_B tests, whereas the control group exhibits negligible hysteresis, confirming the critical role of ammonium ions in achieving memory functionality. Furthermore, it is observed that the lower-mobility tetrabutylammonium cations generate a larger hysteresis area in the I-V_G tests compared to tetraethylammonium cations (Supplementary Table 5), which aligns perfectly with theoretical predictions and indicates that the ion migration rate plays a critical role in modulating the memory effects of the device⁵⁴. In summary, both the theoretical and experimental findings demonstrate that a single molecule with S–O non-covalent interactions can endow the device with a history-dependent memory function through interactions with surrounding ammonium cations.

Discussion

In conclusion, we demonstrated a single-molecule neuromorphic device by fine tuning of the molecule–ion coupling via electrochemical gating. This bio-inspired single-molecule electrochemical synapse integrates synaptic and dendritic functionalities, achieving ultra-low energy consumption of ~6.34 aJ/operation. Through programmable molecule–cation electrostatic interactions, this device realizes biomimetic emulation of neural plasticity transitions from short-term (PPF index of about 307.99%) to long-term memory featuring over ten distinct conductance states, fulfilling the associative learning of Pavlovian experiment and pattern recognition of Morse code. Our findings provide the first experimental demonstration of neuromorphic devices at the single-molecule scale, which offer unique potential for energy-sustainable artificial intelligence.

Methods

Materials

MeO-TBT and Et-TBT were synthesized by H. Z. in D. Z.’s group⁴⁰. See Supplementary Method 2 for details. ¹H NMR and ¹³C NMR spectra are measured with Fourier 300 MHz (Supplementary Figs. 45–48). Mass spectra were collected on a Bruker Solarix-XR high-resolution mass spectrometer.

Conductance measurements

Conductance measurements were performed using a home-built EC-STMBJ system. The distance between the gold tip electrode and the gold substrate electrode was adjusted using a stepper motor and a piezoelectric ceramic. When a nanogap was formed between the two electrodes, the sample molecule enters the gap, connecting to the substrate and tip electrodes via methylthio groups to form a single-molecule junction. The tip and substrate electrodes were repeatedly brought together and separated to perform multiple cycles of break junction⁵⁵. A platinum electrode serves as the counter electrode, and an Ag/AgCl electrode acts as the reference electrode while recording the distance between the gold electrodes and the conductance of the single-molecule junction under various potential conditions. To minimize interference from leakage currents under electrochemical conditions, the gold tips obtained through electrochemical etching were encapsulated with apiezon wax. Finally, the dynamic break junction process and the electrochemical behavior of the single-molecule junctions were analyzed using a custom-developed Python program to process large volumes of experimental data. We conduct measurements of the single-molecule conductance of 0.5 mM MeO-TBT in a propylene carbonate (PC) solution containing 0.1 M tetrabutylammonium hexafluorophosphate (TBAPF₆) as the electrolyte at electrode potentials within the non-Faradaic region (gate voltage V_G ranging from –0.4 to 0.5 V) under a bias voltage of 0.1 V (Supplementary Figs. 2–6).

To optimize the memory characteristics of the device, we optimized the concentration used in the tests as well as the solvents³³. First, we adjust the electrolyte concentration and compare the test results of TBAPF₆ at concentrations of 0.05, 0.1, and 0.2 M (Supplementary Figs. 7–9). The results show that as the electrolyte concentration increases, the on/off ratio of the I-V_G and I-V_B hysteresis curves also increases. This indicates that electrolyte concentration plays a crucial role in adjusting the memory characteristics of the device. However, when the concentration exceeds 0.2 M, partial precipitation occurs due to its limited solubility in the PC solvent. Therefore, 0.2 M was selected as the optimal concentration for subsequent experimental investigations. Next, we further explore the impact of the solvent on the device memory characteristics (Supplementary Figs. 10 and 11). On this basis, we compare the I-V_G and I-V_B curves of the device in PC, acetonitrile, and ionic liquid (1-hexyl-3-methylimidazolium hexafluorophosphate) solutions, respectively. The experimental data demonstrate that the hysteresis effect is most pronounced in PC, which was therefore selected as the optimized solvent for subsequent studies. Our findings reveal that the single-molecule synaptic transistor based on MeO-TBT exhibits relatively good memory characteristics in a PC solution of 0.2 M TBAPF₆.

The characterization of current-voltage (I-V_B) curves was conducted in a “hover” mode, where the conductance changes between the working electrodes were monitored under set bias voltage and potential conditions. The transition into hover mode was determined by built-in judgment logic within our custom-developed testing software. When sampling points within a preset conductance range (based on the statistical conductance range of the target molecule) were detected and exceed a certain threshold, this indicates that the “hover” mode has been achieved, signaling the formation of a single-molecule junction. At this point, the piezoelectric ceramic ceases movement, and the I-V_B curve measurement was performed at a scanning speed of 10 V/s. After testing, the extensive I-V_B curves obtained were subjected to statistical analysis using laboratory-developed Python software.

The data for current-gate voltage (I-V_G) curves was derived from conductance-gate voltage curves (G-V_G) using the formula I = G*V. The characterization of conductance-gate voltage curves was performed in hover mode. In this mode, the potential was swept forward and backward within the potential range of –0.4 to 0.5 V, with a scanning speed of 2 V/s. After testing, a large number of G-V_G curves were subjected to statistical analysis using laboratory-developed Python software. Finally, the I-V_G curves were obtained by converting the data using the established formula.

The data for current-gate voltage (I-V_G) curves were derived from conductance-gate voltage curves (G-V_G) using the formula I = G*V. The characterization of conductance-gate voltage curves was performed in hover mode. In this mode, the potential was swept forward and backward within the potential range of −0.4 to 0.5 V, with a scanning speed of 2 V/s. After testing, a large number of G-V_G curves were subjected to statistical analysis using laboratory-developed Python software to finally obtain the I-V_G curves through data conversion.

The method for testing the gate circuit current was as follows: the tip electrode, reference electrode, and counter electrode are immersed in the electrolyte solution, while the tip and substrate electrodes are kept disconnected (Supplementary Figs. 2a and 13). The current measured under these conditions corresponded to the gate circuit current³⁶.

Mimicking synaptic plasticity through a single-molecule device

In our study, we emulated synaptic plasticity by applying designed pulse sequences in a “hover” mode. This approach enabled the application of diverse electrical pulse sequences to emulate synaptic behavior while monitoring corresponding conductance changes. The stability of this hovering operation was verified using the EC-STMBJ setup (Supplementary Fig. 12). We systematically applied individual gate voltage pulses, separate bias pulses, and combined gate-bias voltage pulses to the device in this mode (Supplementary Figs. 16–22). Depending on the specific input sequences, the duration of a single hover session ranged from 200 to 2300 ms.

Handwritten digit recognition simulation

The presented spiking neural network (SNN) incorporates dual-exponential synaptic conductance dynamics^49,50, establishing a biologically interpretable hierarchical processing architecture (Supplementary Fig. 31a). The input layer receives 28 × 28 pixel grayscale images, which undergo temporal encoding through a Poisson spike generator governed by the following stochastic process:

$$s_{ij\left(t\right)}~\mathrm{Bernoulli}\left(x_{ij}\right),\forall t=\left\{1,2,\dots ,T\right\}$$ 1

Where x_ij ϵ [0, 1] denotes normalized pixel intensity values and T = 10 ms specifies the temporal window duration. This encoding mechanism probabilistically transforms spatial luminance information into temporally distributed spike trains, maintaining intensity-proportional firing rates across the input population.

The encoded spatiotemporal spike patterns propagate through a fully-connected network with bifurcated synaptic conductance pathways. The first synaptic layer implements feature projection through dimensional reduction from 784 input channels to 128 latent features:

$$h_{1\left(t\right)}=W_{1s\left(t\right)}+b_1$$ 2

where $W_1{\in \mathrm{R}}^{\left\{128\times 784\right\}}$ represents the trainable weight matrix. Subsequent spike generation is governed by dual-exponential neuronal dynamics.

$$i_{\mathrm{fast}}^t=\alpha i_{\mathrm{fast}}^{t-1}+h_{1\left(t\right)}$$ 3

$$i_{\mathrm{slow}}^t=\beta i_{\mathrm{slow}}^{t-1}+h_{1\left(t\right)}$$ 4

$$v^t=v^{t-1}+\left(i_{\mathrm{fast}}^t-i_{\mathrm{slow}}^t\right)$$ 5

The decay coefficients are defined as:

$$\alpha =\exp \left(-\frac{1}{{\tau }_1}\right)$$ 6

$$\beta =\exp \left(-\frac{1}{{\tau }_2}\right)$$ 7

characterizing fast and slow temporal integration constants. A firing threshold mechanism triggers spike emission when v(t) ≥ θ_th = 1 mV, followed by instantaneous membrane potential reset to baseline.

The secondary synaptic layer performs categorical projection through dimensionality reduction from 128 hidden features to ten output classes:

$$h_{2\left(t\right)}=W_{2s_{1\left(t\right)}}+b_2$$ 8

Where$W_2{\in \mathrm{R}}^{\left\{10\times 128\right\}}$ denotes the class-specific weight matrix. The final classification probabilities emerge through temporal integration of output spikes:

$$p_c=\left(\frac{1}{T}\right){\mathrm{\Sigma }}_{\left\{t=1\right\}}^T{s}_2^{c\left(t\right)}$$ 9

This architecture leverages dual-exponential differentiation mechanisms for temporal filtering, where the antagonistic interaction between fast (τ₃) and slow (τ₄) currents enhances spatiotemporal pattern discrimination. Network parameters are optimized via spatiotemporal backpropagation through time (BPTT) algorithm, supervised by cross-entropy loss minimization:

$$L=-{\sum }_{c=0}^9{y}_c\log \left(p_c\right)$$ 10

Through the proposed biologically plausible training paradigm, the model achieves progressive optimization of the objective function, attaining a final training loss of L_train = 1.626 (Supplementary Fig. 31b). This minimization process demonstrates strict adherence to neuromorphic learning principles, exhibiting a smooth convergence trajectory, stable parameter updates, and effective gradient propagation. The optimized network achieves peak classification accuracies of 97.4% on the validation set (Supplementary Fig. 31c) and 96.9% on the hold-out test set (Supplementary Fig. 31d), demonstrating a minimal 0.5% performance deviation indicative of robust generalization.

Dynamic calculation

The force-field molecular dynamics (MD) simulations were performed using the Materials Studio package (Acelrys Software)⁵¹. The interatomic interactions were described by the condensed-phase-optimized molecular potentials for atomistic simulation studies (COMPASS) force field, and the electrostatic energy was calculated by the Ewald & Group summation method. The Ewald & Group summation method has an Ewald accuracy of 10⁻⁵ kcal·mol⁻¹ when used for calculating electrostatic potential energy. The periodic boundary conditions were set in all three directions. The electrostatic interactions were computed using Ewald methods. The velocity Verlet algorithm was used to integrate Newton’s equations of motion with a time step of 1 fs. A cutoff radius of 18.5 Å was assumed for the Lennard-Jones interaction potential calculation. The simulated temperature was controlled by a Nosé thermostat.

The self-molecular diffusivities were obtained from equilibrium MD simulations. The size of the box is 45.0 × 45.0 × 45.0 ų, which contains 600 PC, 10 TBA⁺ and 10 PF₆⁻ molecules. The box was first optimized by geometry optimization using the force field. Then, the NpT ensemble, i.e., the numbers of particles (N), pressure (p), and temperature (T) are kept as constants, were performed for 100 ps in 100,000 steps for systems after the systems are equilibrated at 298 K. After equilibrium under the NpT ensemble, dynamics processes in the NVT ensemble, i.e., the numbers of particles (N), volume (V) and temperature (T) are kept as constants, were performed for 200 ps in 200,000 steps for systems after the systems are equilibrated at 298 K. The mean square displacement (MSD) of ions is shown in Supplementary Fig. 32. The slope of MSD as a function of time was used to determine the self-diffusivity following the Einstein relation.

$$\mathrm{MSD}\left(\mathrm{\tau }\right)=2nD\mathrm{\tau }+b$$ 11

where MSD is the mean squared displacement, n is the dimension of framework (n = 3 for 3D frameworks), D is the diffusion coefficient, τ is the time, and b is the thermal factor arising from atomic vibrations.

The ion migration under the external electric field were obtained from nonequilibrium MD simulations. The size of the box is 26.1 × 90.4 × 31.3 ų, which contains 340 PC, 4 TBA⁺, 4 PF₆⁻, and 2 molecules linked by the Au tip and Au substrate. The box was first optimized by geometry optimization using the force field. Then the NVT ensemble were performed for 200 ps in 200,000 steps for systems after the systems are equilibrated at 298 K. The external electric field (E_x = +0.28 V/Å and E_y = +0.28 V/Å) was applied under NVT ensemble, the NVT ensemble were performed for 200 ps in 200,000 steps. The ionic mobility of TBA⁺ is defined by the ratio between the distance between the molecular lock and TBA⁺ to simulation time (200 ps). The ionic mobility of PF₆⁻ is defined by the ratio between the distance between the molecular lock and PF₆⁻ to simulation time (arriving at the bottom of the molecular lock, the start time of the platform in Supplementary Fig. 34).

To support the accuracy of our theoretical simulations, we conducted NMR pulsed gradient experiments (Supplementary Fig. 33). Theoretical calculations indicated that PF₆⁻ anions diffuse faster than TBA⁺ cations in PC solution. Therefore, we used NMR pulsed gradient experiments to measure the diffusion coefficients of both anions and cations in the same solution⁵². The NMR results showed that the diffusion coefficient for PF₆⁻ is 4.850 × 10⁻¹⁰ m²/s, while for TBA⁺ is 3.048 × 10⁻¹⁰ m²/s. Theoretically, the diffusion coefficient for PF₆⁻ is 4.740 × 10⁻¹⁰ m²/s, while for TBA⁺ is 3.830 × 10⁻¹⁰ m²/s. These experimental results align well with the theoretical simulation values, providing strong support for the accuracy of the kinetic simulations.

To elucidate the nature of interactions between MeO-TBT and the ammonium cation, we constructed models representing the interaction of MeO-TBT with ammonium cations, optimizing them to obtain the lowest energy configurations. To clarify the changes in conductance of MeO-TBT during the coupling and decoupling processes with ammonium cations, we conducted transmission spectra calculations on the states of MeO-TBT, MeO-TBT coupled with one ammonium cation, and MeO-TBT coupled with two ammonium cations.

Thermodynamic calculation

The individual molecular structures, including MeO-TBT, PF₆⁻, and N(CH₃)₄⁺, were constructed and optimized with Gaussian 09 software under B3LYP functionals and 6-311 G**basis set (Supplementary Fig. 35)³⁶. To explore the interaction between MeO-TBT and positively charged ions, the N(CH₃)₄⁺ ions were placed at a distance of 5 Å from the S–O interaction for structural optimization, and a 20 a.u. electric field was applied in the y-direction to simulate the experimental gate electric field. This optimization process was conducted under identical functionals and basis set with DFT-D3 dispersion correction. We then used the fully relaxed structures for the single point energy determination and calculated under m062x functionals and 6-311 + G** with applied electric field and frequency calculation.

Transmission calculation

To construct the single-molecule devices, the gold electrodes were constructed with 9 × 9 × 6 gold atoms and anchors with the target molecule, with the pyramid-shaped gold atoms at the top. The single-molecule devices were constructed with Quantum ATK U-2022.12 software and optimized with PBE-GGA functional and Double-ζ Polarized (DZP) basis set (Double-ζ, DZ for gold atoms). The k-point was set as 4 × 4 × 150. To calculate the transmission spectrum, the nonequilibrium Green Function and Landauer formula. The current flow through the molecular junction is defined as:

$$I=\left(2\frac{e}{h}\right){\int }_{-\infty }^{\infty }\mathrm{d}ET\left(E\right)\left[f_{\mathrm{left}}\left(E\right)-f_{\mathrm{right}}\left(E\right)\right]$$ 12

where e is the electronic charge, h is Planck’s constant and T(E) is the transmission coefficient for electrons passing from one electrode to another.

Author contributions

W. Hong, D. Zhang, and J. Liu supervised the project. W. Hong, D. Zhang, J. Liu, and H. Zhang conceived the concept and designed the experiments. H. Zhang synthesized the test molecules with the support by W. Shang and L. Chen; H. Zhang performed the measurements with the support by Y. Jiang; H. Zhang conducted the data analysis with the support by J. Wu, B. Zhang, W. Xu, C. Yan, Z. Li, T. Zeng, X. Li, J. Bai, J. Li, Z. Xiao, J. Shi, Y. Zhang, and G. Zhang; J. Ye and M. Gao conducted the theoretical calculations with the help of Y. Zhou; W. Hong, D. Zhang, J. Liu, and H. Zhang prepared the manuscript with input from other authors.

Peer review

Peer review information

Nature Communications thanks Yong Yan and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The relevant data used in this study are available in the figshare database under accession code 10.6084/m9.figshare.31528837. The Supplementary Movie 1 used in this study are available in the figshare database under accession code 10.6084/m9.figshare.31534159.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-71127-2.