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We examine the impact of the intrinsic molecular reorganization energy on switching in two-state quantum-dot cellular automata (QCA) cells. Switching a bit involves an electron transferring between charge centers within the molecule. This in turn causes the other atoms in the molecule to rearrange their positions in response. We capture this in a model that treats the electron motion quantum-mechanically, but the motion of nuclei semiclassically. This results in a non-linear Hamiltonian for the electron system. Interaction with a thermal environment is included by solving the Lindblad equation for the time-dependent density matrix. The calculated response of a molecule to the local electric field shows hysteresis during switching when the sweep direction is reversed. The relaxation of neighboring nuclei increases localization of the electron, which provides an intrinsic source of enhanced bistability and single-molecule memory. This comes at the cost of increased power dissipation., Comment: 14 pages, 17 figures

A series of experiments and electronic structure calculations were performed to identify metastable 1,1′-ferrocenedicarboxylic acid supramolecular structures formed during solution deposition in a vacuum on a Au(111) substrate, as well as to observe their evolution into more stable species under mild annealing conditions. Electrospray ionization mass spectrometry measurments were performed to determine which species are likely to be present in the rapidly evaporating droplet, and these experiments found that a hexamer can exist in solution during deposition, albeit as a metastable species. The molecular clusters present after solution deposition were observed and analyzed using ultrahigh-vacuum scanning tunneling microscopy, and the initial monolayer contains four basic classes of structures: ordered dimer domains, tilted dimer rows, square tetramers, and rectangular chiral hexamers. Electronic structure calculations indicate that the chiral hexamers consist of a central dimer surrounded by four molecules...

We examine the energy dissipated by a two-state quantum system during a switching operation when interacting with a thermal environment. For an isolated system, the excess energy decreases exponentially with switching time. For classically damped systems, the energy dissipation decreases linearly with switching time. We model the quantum system coupled to a thermal environment using a Lindblad equation for the density matrix. For rapid switching, the exponential quantum adiabaticity holds. For slow enough switching, the damping from the bath yields linear dissipation, as in the classical limit. Between these two limits, when the switching time is comparable to the characteristic energy transfer time to the thermal bath, there is an inverted region when dissipation increases with longer switching times. Consequences for the design of molecular quantum-dot cellular automata are discussed.

For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum operator entropy, which is the Shannon entropy of the probability distribution for the eigenvalues of a Hermitian operator. These entropies characterize the missing information about a particular observable inherent in the quantum state itself. The von Neumann entropy is the quantum operator entropy for the case when the operator is the density matrix. We examine pure state unitary evolution in a simple model system comprised of a set of highly-interconnected topologically disordered states and a time-independent Hamiltonian. An initially confined state is subject to free expansion into available states. The time development is completely reversible with no loss of quantum information and no course graining is applied. The positional entropy increases in time in a way that is consistent with both the classical statistical mechanical entropy and the second law., Comment: 10 pages, 10 figures

The Landauer Principle connects the information theoretic notion of entropy to the physics of statistical mechanics. When a physical system performs a logical operation that erases or loses information, without a copy being preserved, it must transfer a minimum amount of heat, \(k_B T \log (2)\), to the environment. How can there be such a connection between the abstract idea of information and the concrete physical reality of heat? To address this question, we adopt the Jaynes approach of grounding statistical mechanics in the Shannon notion of entropy. Probability is a quantification of incomplete information. Entropy should not be conceived in terms of disorder, but rather as a measure on a probability distribution that characterizes the amount of missing information the distribution represents. The thermodynamic entropy is a special case of the Shannon entropy applied to a physical system in equilibrium with a heat bath so that its average energy is fixed. The thermal probability distribution is obtained by maximizing the Shannon entropy, subject to the physical constraints of the problem. It is then possible to naturally extend this description to include a physical memory device, which must be in a nonequilibrium long-lived metastable state. We can then explicitly demonstrate how the requirement for a fundamental minimum energy dissipation is tied to erasure of an unknown bit. Both classical and quantum cases are considered. We show that the classical thermodynamic entropy is in some situations best matched in quantum mechanics, not by the von Neumann entropy, but by a perhaps less familiar quantity—the quantum entropy of outcomes. The case of free expansion of an ideal quantum gas is examined in this context.

Power dissipation is one of the most important factors limiting the development of integrated circuits. In this chapter, we will explore the limits of energy dissipation in computation with experiments and circuit designs. Our experiments show that there is no fundamental limit on energy that must be dissipated to perform computation as long as information is preserved, in agreement with the Landauer principle. The erasure of information leads to a loss of bit energy with an ultimate lower limit of kBT ln2, sometimes incorrectly referred to as the “Landauer limit for energy dissipation in computation.” We present an experiment where a dissipation of 0.005 kBT which is far below the limit of kBT ln2 occurs in reversible adiabatic bit manipulation, and experimentally demonstrate that dissipation of the full bit energy occurs if information is erased. To exploit the advantages of quasi-adiabatic reversible computation, we discuss adiabatic logic systems, and present the design of a microprocessor based upon adiabatic logic. Due to their inherent leakage current, field-effect transistors have limitations in adiabatic implementations. We discuss possible devices that have a better match to adiabatic systems. Finally, we present experiments making direct measurement of the heat generated in logical operations.

The preparation of 7-Fc(+) -8-Fc-7,8-nido-[C2 B9 H10 ](-) (Fc(+) FcC2 B9 (-) ) demonstrates the successful incorporation of a carborane cage as an internal counteranion bridging between ferrocene and ferrocenium units. This neutral mixed-valence Fe(II) /Fe(III) complex overcomes the proximal electronic bias imposed by external counterions, a practical limitation in the use of molecular switches. A combination of UV/Vis-NIR spectroscopic and TD-DFT computational studies indicate that electron transfer within Fc(+) FcC2 B9 (-) is achieved through a bridge-mediated mechanism. This electronic framework therefore provides the possibility of an all-neutral null state, a key requirement for the implementation of quantum-dot cellular automata (QCA) molecular computing. The adhesion, ordering, and characterization of Fc(+) FcC2 B9 (-) on Au(111) has been observed by scanning tunneling microscopy.

Monolayers of indole-2-carboxylic acid and indole-3-carboxylic acid on gold are studied using ultrahigh-vacuum scanning tunneling microscopy. Both molecules form symmetric, cyclic, hydrogen-bonded pentamers, a structure that is stabilized by the presence of a weak hydrogen-bond donor (NH or CH) adjacent to the carboxylic acid on the five-membered ring. In addition to pentamers, indole-2-carboxylic acid forms hexamers and catemer chains, while indole-3-carboxylic acid monolayers are generally disordered. Density functional theory calculations show that pentamers and hexamers have stability comparable to dimers or short catemers. The coexistence of all of these structures likely arises from the nonequilibrium conditions present in solution during pulse deposition of the monolayer.

Mixed-valence complexes are potential candidates for the molecular quantum-dot cellular automata (QCA) approach, which encodes binary information using the configuration of localized and mobile charges. In the Robin–Day classification of mixed-valence complexes, charge localization/delocalization is determined by the ratio of the nuclear reorganization energy and the electron transfer (ET) matrix element. We point out that the driving force for charge localization in molecular QCA is the Coulomb interaction between neighboring molecules rather than nuclear relaxation. This suggests a different criterion for the relevant charge localization, one based on the ET matrix element and the driving bias of a neighboring molecule.

We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale. We consider a system consisting of two qubits, each realized by an electron in a double quantum dot, which are initially in an entangled Bell state. The qubits are widely separated and each interacts with its own environment. The environment for each is modeled by surrounding double quantum dots placed at random positions with random orientations. We calculate the unitary evolution of the joint system and environment. The global state remains pure throughout. We examine the time dependence of the expectation value of the bipartite Clauser-Horne-Shimony-Holt (CHSH) and Brukner-Paunkovi\'c-Rudolph-Vedral (BPRV) Bell operators and explore the emergence of correlations consistent with local realism. Though the details of this transition depend on the specific environmental geometry, we show how the results can be mapped on to a universal behavior with appropriate scaling. We determine the relevant disentanglement times based on realistic physical parameters for molecular double-dots., Comment: 14 pages, 3 figures

Heat generation limits the performance of state-of-the-art integrated circuits, originating from the wasteful static CMOS operating principle. Near-term solutions like adiabatic charging for energy recovery and limiting friction-type heat sources provide considerable improvement. However, these methods do not address the ultimate thermodynamic necessity to expel energy related to information loss in the computing process. In emerging beyond-CMOS technologies, this bit erasure heat alone can overwhelm the cooling capacity and set the limits of the computing performance. Therefore, logical information loss is becoming an important factor for digital circuit design, and tools have to be developed for analysis and optimization. This article presents a framework for estimating the amount of information loss in complex logic circuits, demonstrating the method by modeling the irreversible bit erasures in a standard binary adder structure. Binary addition is one of the most often used and highly optimized digital designs, and we estimate the erasure bounds for components on various levels of design abstraction, showing that the actual logic gate implementations have orders of magnitude higher loss than the addition operation itself would require. The method and the results can be used to optimize circuits for a higher degree of logical reversibility and energy conservation.

Self-assembled monolayers of ferrocenecarboxylic acid (FcCOOH) contain two fundamental units, both stabilized by intermolecular hydrogen bonding: dimers and cyclic five-membered catemers. At surface coverages below a full monolayer, however, there is a significantly more varied structure that includes double-row clusters containing two to twelve FcCOOH molecules. Statistical analysis shows a distribution of cluster sizes that is sharply peaked compared to a binomial distribution. This rules out simple nucleation-and-growth mechanisms of cluster formation, and strongly suggests that clusters are formed in solution and collapse into rows when deposited on the Au(111) surface.

Molecular quantum-dot cellular automata (QCA) paradigm is a promising approach to molecular electronics. QCA cells can be implemented using mixed-valence compounds. However, the existence of counterions can perturb the local electric field and thus is detrimental to information encoding and processing. Here we examine the feasibility of using charge neutral, zwitterionic mixed-valence complex as QCA cells in which the positive and negative charges are found at different yet fixed locations within the molecule and therefore counterion effects are more predictable and controllable. A double-dot model molecule based on the derivative of the 1-carba- closo -decaborate monoanion [ closo -1-CB 9 H 10 ] − is investigated using computational chemistry techniques. The model molecule demonstrates bistability and switchability.

This paper examines adiabatic logic for computation, and presents a design for a MIPS processor implemented in CMOS. Adiabatic reversible logic was examined in the 1980s and 1990s but in that era power dissipation was a secondary concern, and the trade-off of reduced computational speed for reduced power was deemed unacceptable. Now, power dissipation and the associated heat are the major obstacles limiting progress in integrated circuits, particularly processors. In modern processors trading performance for reduced power dissipation is already done using techniques such as multi-core and dark silicon, so adiabatic logic may now be an attractive approach. To evaluate the adiabatic approach, this paper uses the figure of merit of the product of switching energy, delay time, and area (EDA). Using this figure of merit, adiabatic logic is shown to be advantageous when additional constraints are considered, such as maximum allowed power density. As a proof of concept circuit, a simplified MIPS microprocessor was designed using adiabatic logic based on split-rail charge recovery logic and Bennett clocking. New design and verification tools were developed using structural Verilog and extensions of ModelSim to provide needed capabilities are not available in commercial packages. The design is implemented using a standard cell design.

The two fundamental limitations of the present computing paradigm are power dissipation from transistor switching and the architectural von Neumann bottleneck that segregates processing from memory. We examine a cellular architecture which radically intermixes memory and processing, and which is based on a transistor-less approach to representing binary information using the arrangement of charge within the molecule. Representing bits by molecular configuration, rather than a current switch, yields the limits of functional density and low power dissipation. Matching a new computational element to a new architectural framework could enable general purpose computing to evolve along a new roadmap.

Molecular quantum-dot cellular automata is a computing paradigm in which digital information is encoded by the charge configuration of a mixed-valence molecule. General-purpose computing can be achieved by arranging these compounds on a substrate and exploiting intermolecular Coulombic coupling. The operation of such a device relies on nonequilibrium electron transfer (ET), whereby the time-varying electric field of one molecule induces an ET event in a neighboring molecule. The magnitude of the electric fields can be quite large because of close spatial proximity, and the induced ET rate is a measure of the nonequilibrium response of the molecule. We calculate the electric-field-driven ET rate for a model mixed-valence compound. The mixed-valence molecule is regarded as a two-state electronic system coupled to a molecular vibrational mode, which is, in turn, coupled to a thermal environment. Both the electronic and vibrational degrees-of-freedom are treated quantum mechanically, and the dissipative vibrational-bath interaction is modeled with the Lindblad equation. This approach captures both tunneling and nonadiabatic dynamics. Relationships between microscopic molecular properties and the driven ET rate are explored for two time-dependent applied fields: an abruptly switched field and a linearly ramped field. In both cases, the driven ET rate is only weakly temperature dependent. When the model is applied using parameters appropriate to a specific mixed-valence molecule, diferrocenylacetylene, terahertz-range ET transfer rates are predicted.

International audience; The molecule {Cp*(dppe)Fe(C C-)}(3)(1,3,5-C6H3) (Fe3) was adsorbed on a single-crystal gold surface and studied using ultrahigh-vacuum scanning tunneling microscopy (STM). Both the singly oxidized Fe3(+) and doubly oxidized Fe3(2+) are mixed-valence ions, and localization of the charge at specific metal centers was observed as the appearance of pronounced asymmetry in STM images. Switching the tip sample bias voltage demonstrates that this asymmetry is electronic in nature. The nature of intramolecular structure and the degree of asymmetry produced in STM images varies according to the state of the scanning tip. Constrained density functional theory was used to simulate STM images for the neutral molecule and for both mixed-valence species, and simulated images agreed closely with observed results. In particular, changing the number of molecular electronic states contributing to contrast in the STM image produced a good match to the variation in structures measured experimentally.

Quantum-dot cellular automata is a novel paradigm for computing at the nanoscale. Cells are the basic computing element in quantum-dot cellular automata and function as structured charge containers rather than as current switches. Computing with quantum-dot cellular automata is enabled by quantum-mechanical tunneling and Coulomb interactions. The use of molecules as cells to realize quantum-dot cellular automata may make possible nanometer-scale devices and ultra-high device densities without excessive heat dissipation. Molecular quantum-dot cellular automata can be clocked using an external electric field. A time-varying clock can be used to drive data flow through layouts of cells. Together, the clock and the device layout define a computational architecture where data flows through the circuitry in the form of bit packets. Here we analyze the energetics of QCA bit packets. We find a heuristic model based on cell-cell interactions works well. Bit packet energies in general scale with the packet length. It may, however, be possible to design a cell geometry so that the energy is packet-length independent. Fan-out and fan-in can be understood as investing energy from the clock in the signal, and then returning the energy back to the clock.

Quantum-dot cellular automata (QCA) is a low-power, non-von-Neumann, general- purpose paradigm for classical computing using transistor-free logic. Here, classical bits are encoded on the charge configuration of individual computing primitives known as &ldquo, cells.&rdquo, A cell is a system of quantum dots with a few mobile charges. Device switching occurs through quantum mechanical inter-dot charge tunneling, and devices are interconnected via the electrostatic field. QCA devices are implemented using arrays of QCA cells. A molecular implementation of QCA may support THz-scale clocking or better at room temperature. Molecular QCA may be clocked using an applied electric field, known as a clocking field. A time-varying clocking field may be established using an array of conductors. The clocking field determines the flow of data and calculations. Various arrangements of clocking conductors are laid out, and the resulting electric field is simulated. It is shown that that control of molecular QCA can enable feedback loops, memories, planar circuit crossings, and versatile circuit grids that support feedback and memory, as well as data flow in any of the ordinal grid directions. Logic, interconnect and memory now become indistinguishable, and the von Neumann bottleneck is avoided.

{Cp*(dppe)Fe(C≡C-)}(2)(1,3-C(6)H(4)) is studied both as a neutral molecule, Fe(II)-Fe(II), and as a mixed-valence complex, Fe(II)-Fe(III). Scanning tunneling microscopy (STM) is used to image these species at 77 K under ultrahigh-vacuum conditions. The neutral molecule Fe(II)-Fe(II) has a symmetric, "dumbbell" appearance in STM images, while the mixed-valence complex Fe(II)-Fe(III) demonstrates an asymmetric, bright-dim double-dot structure. This asymmetry results from localization of the electron to one of the iron-ligand centers, a result which is confirmed through comparison to theoretical STM images calculated using constrained density-functional theory (CDFT). The observation of charge localization in mixed-valence complexes outside of the solution environment opens up new avenues for the control and patterning of charge on surfaces, with potential applications in smart materials and molecular electronic devices.

In the molecular quantum-dot cellular automata (QCA) paradigm clocking wires are used to produce an electric field which is perpendicular to the device plane of surface-bound molecules and is sinusoidally modulated in space and time. This clocking field guides the data flow through the molecular QCA array. Power is dissipated in clocking wires due to the non-zero resistance of the conductors. We analyze quantitatively the amount of power dissipated in the clocking wires and find that in the relevant parameter range it is fairly small. Dissipation in the molecular devices themselves will likely dominate the energy budget.

The computational paradigm known as quantum-dot cellular automata (QCA) encodes binary information in the charge configuration of Coulomb-coupled quantum-dot cells. Functioning QCA devices made of metal-dot cells have been fabricated and measured. We focus here on the issue of robustness in the presence of disorder and thermal fluctuations. We examine the performance of a semi-infinite QCA shift register as a function of both clock period and temperature. The existence of power gain in QCA cells acts to restore signal levels even in situations where high speed operation and high temperature operation threaten signal stability. Random variations in capacitance values can also be tolerated.

We examine power dissipation in different clocking schemes for molecular quantum-dot cellular automata (QCA) circuits. 'Landauer clocking' involves the adiabatic transition of a molecular cell from the null state to an active state carrying data. Cell layout creates devices which allow data in cells to interact and thereby perform useful computation. We perform direct solutions of the equation of motion for the system in contact with the thermal environment and see that Landauer's Principle applies: one must dissipate an energy of at least k(B)T per bit only when the information is erased. The ideas of Bennett can be applied to keep copies of the bit information by echoing inputs to outputs, thus embedding any logically irreversible circuit in a logically reversible circuit, at the cost of added circuit complexity. A promising alternative which we term 'Bennett clocking' requires only altering the timing of the clocking signals so that bit information is simply held in place by the clock until a computational block is complete, then erased in the reverse order of computation. This approach results in ultralow power dissipation without additional circuit complexity. These results offer a concrete example in which to consider recent claims regarding the fundamental limits of binary logic scaling.

Quantum-dot cellular automata (QCA) is a scheme for molecular electronics in which information is transmitted and processed through electrostatic interactions between charges in an array of quantum dots. QCA wires, majority gates, clocked cell operation, and (recently) true power gain between QCA cells has been demonstrated in a metal-dot prototype system at cryogenic temperatures. Molecular QCA offers very high device densities, low power dissipation, and ways to directly integrate sensors with QCA logic and memory elements. A group of faculty at Notre Dame has been working to implement QCA at the size scale of molecules, where room-temperature operation is theoretically predicted. This paper reviews QCA theory and the experimental measurements in metal-dot QCA systems, and describes progress toward making QCA molecules and working out surface attachment chemistry compatible with QCA operation.

trans-[(H(2)NCH(2)CH(2)C triple bond N)(dppe)(2)Ru(C triple bond C)(6)Ru(dppe)(2)(N triple bond CCH(2)CH(2)NH(2))][PF(6)](2), 2[PF(6)](2), a derivative of trans-[Cl(dppe)(2)Ru(C triple bond C)(6)Ru(dppe)(2)Cl] functionalized for binding to a silicon substrate, has been prepared and characterized spectroscopically, electrochemically, and with a solid state, single-crystal structure determination. Covalent binding via reaction of one amine group to a boron-doped, smooth Si-Cl substrate is verified by XPS measurements and surface electrochemistry. Vertical orientation is demonstrated by film thickness measurements. Synthesis of the 2[PF(6)](3) mixed-valence complex on the surface is established by electrochemical techniques. Measurement of the ac capacitance of the film at 1 MHz as a function of voltage across the film with a pulse-counter pulse technique demonstrates controlled electric field generation of the two stable mixed-valence forms differing in the spatial location of one electron, that is, switching. As compared to [trans-Ru(dppm)(2)(C triple bond CFc)(NCCH(2)CH(2)NH(2))][PF(6)][Cl], 1[PF(6)][Cl], the magnitude of the capacitance signal per complex observed on switching is shown to increase with increasing distance between the metal centers. Additional experiments on 1[X][Cl] show that the potential for switching 1[X][Cl] increases in the order [X](-) = [SO(3)CF(3)](-) < [PF(6)](-) < [Cl](-). A simple electrostatic model suggests that the smaller is the counterion, the greater is the perturbation of the metal sites and the larger is the barrier for switching.

Interaction between single electrons in coupled quantum dots is used to perform binary logic operations in Quantum-dot Cellular Automata (QCA). Clocked control over tunneling is necessary to achieve power gain and minimize power dissipation in QCA. The high temperature limit for clocked operation is set by the ability of the cells to store binary information when the input signal is removed (so-called ‘locked mode’). We present an experimental investigation of the temperature dependence of the locked mode in metal-dot based clocked QCA device. The experimental results are in very good agreement with the orthodox Coulomb blockade theory for thermally activated electron escape mechanism.