Physisorption Energy Research Articles

Anion Effect in Electrochemical CO2 Reduction: From Spectators to Orchestrators.

The electrochemical CO2 reduction reaction (eCO2RR) offers a pathway to produce valuable chemical fuels from CO2. However, its efficiency in aqueous electrolytes is hindered by the concurrent H2 evolution reaction (HER), which takes place at similar potentials. While the influence of cations on this process has been extensively studied, the influence of anions remains largely unexplored. In this work, we study how eCO2RR selectivity and activity on a gold catalyst are affected by a wide range of inorganic and carboxylate anions. We utilize in situ differential electrochemical mass spectrometry (DEMS) for real-time product monitoring coupled with molecular dynamics (MD) simulations. We show that anions significantly impact eCO2RR kinetics and eCO2RR selectivity. MD simulations reveal a new descriptor─free energy of anion physisorption─where weakly adsorbing anions enable favorable CO2 reduction kinetics, despite the negative charge carried by the electrode surface. By leveraging these fundamental insights, we identify propionate as the most promising anion, achieving nearly 100% Faradaic efficiency while showing high CO production rates that are comparable to those in bicarbonate. These insights underscore the vital role of anion selection in achieving a highly efficient eCO2RR in aqueous electrolytes.

Exploring the interaction of Cu-modified B12N12 nanocages for Favipiravir drug delivery using density functional theory study

Drug delivery has become a pivotal strategy in medical research, aiming for precise delivery near cells while minimizing unwanted effects. In this study, we have used density functional theory (DFT) calculations at the B3LYP/6-311G(d,p) basis set to explore the potential of Cu-modified boron nitride (B12N12) nanocages as smart nanocarriers for delivering the Favipiravir (FAV) drug. This study examined the adsorption energy, electronic features, and thermodynamic properties (ΔG and ΔH) of FAV with B12N12 and Cu-modified B12N12 nanocages, revealing enhanced drug-delivery capacity with notable physisorption and negative adsorption energies. A comprehensive analysis confirmed FAV’s interaction with Cu-modified B12N12 nanocages, involving frontier molecular orbitals, adsorption energy, fractional charge transfer, molecular electrostatic potential (MEP), non-covalent interaction (NCI), and natural bond orbital (NBO) assessments. The analyses of frontier molecular orbitals (FMO), partial density of states (PDOS), and natural bond orbital (NBO) indicate that nanocages act as charge acceptors, while the drug acts as a charge donor during the adsorption process. Among the various Cu-modified B12N12 nanocages studied, Cu-doped CuB11N12 emerged as the most promising candidate for transporting FAV, showcasing notably moderate recovery time (ranging from 29.01 ms to 7.25 s at 298.15 K). Remarkably, the CuB11N12 system exhibited exceptional electronic sensitivity (ΔEgap = 65.38 %) to the FAV drug, surpassing other modified systems. Among the modified cases, the Cu-decorated Cu@b64 and Cu@b66 nanocages showed the most significant decrease in energy levels before and after FAV absorption, reducing from 3.28 eV and 3.33 eV to 1.54 eV and 1.59 eV, respectively. This elucidation may lay the foundation for developing effective drug-delivery systems using nanocages for targeted therapies. In conclusion, this study offers a comprehensive insight into the interaction mechanism between the FAV drug and B12N12, unveiling the potential of Cu-modified B12N12 nanocages as promising candidates for delivering the FAV drug.

Promotional mechanism of nitrogen-doping in activated carbon for formaldehyde removal: Enhanced attractive noncovalent interactions coupled with Cannizzaro-type disproportionation reaction

Inserting nitrogen (N) heteroatoms into the carbonaceous adsorbents has been confirmed to be one of efficient strategies for enhancing HCHO removal. However, the essential promotion mechanisms of specific N-containing groups (such as pyridinic-N, pyrrolic-N, and quaternary-N) remain blurred. Herein, a series of N-doped activated carbons were prepared by annealing the melamine impregnated activated carbons at 600–900 °C and used for HCHO elimination. It manifested that the HCHO elimination performance of samples was remarkably improved after N-doping and their HCHO adsorption capacities were in the order of ACN-600 (16.37 mg/g) > ACN-750 (9.87 mg/g) > ACN-900 (7.28 mg/g) > AC (5.09 mg/g). DFT calculation results revealed that there existed stronger attractive noncovalent interactions between pyrrolic-N doped carbon and HCHO due to the formation of stronger H-bonds. Therefore, the HCHO physisorption energy on pyrrolic-N doped carbon was the highest (−32.83 kJ/mol). Compared with the single physisorption mechanism of previous studies, the in-situ DRIFTS results manifested that the pyridinic-N atom (as a typical strong Lewis base) could trigger the Cannizzaro-type disproportionation reaction, which would transform toxic HCHO into relatively less toxic methanol and formic acid. Benefiting from the dual enhanced mechanisms of attractive noncovalent interactions and Cannizzaro-type disproportionation reaction, the ACN-600 manifested excellent HCHO removal performance. This study not only intrinsically discloses the promotion mechanism of specific N-containing groups on HCHO removal at molecular level but also provides guidelines for rational design and development of carbonaceous materials for effective HCHO elimination.

Poisonous effect of carbon bearing species on adsorption of hydrogen on Pd-membrane surfaces

Hydrogen separation through Pd-membrane is one of the most promising technologies to produce pure H2. In this study, for the first time, the adsorption of hydrogen on covered Pd-membranes with both hydrogen and impurity gaseous species (CO, CO2 and CH4) was investigated using density functional theory (DFT). Specifically, the study aims to sample the energy landscape associated with hydrogen-adsorption while varying the structural and compositional degrees of freedom. The relative orientations of adsorbing molecule with respect to the surface of the slab, the crystallographic plane of the slab and various configurations of the adsorbed species have been investigated. In the case of compositional degrees of freedom, adsorption as a function of surface coverage, of hydrogen, is studied. The physisorption of H2 on Pd-surface at different coverages of H-atoms (and without any impurities) has revealed that among the available adsorption sites, top site with horizontally oriented gaseous molecule is energetically the most favorable (−0.343 eV). Among the impurity gaseous species, when investigated for their binding to the Pd-surface and for their effect on the physisorption energies of the H2, CO is found to alter the energetics of the adsorption process, indicating a higher poisoning effect relative to CO2 and CH4. Also, it has the highest adsorption energy (−1.887 eV). Moreover, the study also showed that at higher coverages of H-atoms, the physisorption energies of H2 decrease (−0.063 eV).

Effect of functional groups on VOCs adsorption by activated carbon: DFT study

Volatile organic compounds (VOCs) have attracted increasing attention in the field of environmental control due to their harmful effects on human health and the environment. Activated carbon is promising as an adsorbent for VOCs. The physisorption of six VOCs (methane (CH4), dichloromethane (CH2Cl2), ethylene (C2H4), formaldehyde (HCHO), ethanol (C2H5OH), and toluene (C7H8)) by four activated carbon models (without functional group (NF), with hydroxyl (HD), pyridine (PD), and pyrrole (PR) group, respectively) was studied in combination with their electrostatic potential (ESP). The results show that ESP plays a decisive role in the adsorption of CH4, CH2Cl2, C2H4, HCHO, and C2H5OH, as their adsorption is mainly carried out by H-bonds. The functional group affects the adsorption process by changing the ESP distribution on the activated carbon surface. The orders of the absolute ESP values on the plane and edge of activated carbon are PR>HD>NF>PD and HD>PR>PD>NF, respectively, so that the order of the interaction strength and the physisorption energy are almost the same. Meanwhile, dispersion can enhance adsorption and change the order. For example, the order of CH2Cl2 adsorption at the activated carbon edge is PD>HD>PR>NF. C7H8 is difficult to be adsorbed at the activated carbon edge, but it can be adsorbed on the plane by a π-π stacking interaction whose strength is controlled by the relative molecular mass of activated carbon. This study will guide the design of activated carbon for efficient adsorption of VOCs.

Interfacial Segregation, Structure, and Diffusion ofn-Alkane Mixture Films Adsorbed on Smooth and Rough Gold Surfaces

The compositional, structural, and diffusional properties of equal-weight mixtures of liquid n-hexane and n-hexadecane films supported on atomically smooth and rough gold surfaces are explored with the use of temperature-controlled, canonical, molecular dynamics simulations at 315 K. Preferential adsorption of n-hexadecane molecules is found in the region next to the solid surface. The selective molecular segregation effect is much stronger at the smooth Au(111) surface, where it is accompanied by pronounced layering exhibited in the density profile of the adsorbed film normal to the surface, which shows the formation of two well-defined interfacial liquid layers. For both the smooth and rough solid surfaces, in the region of the first layer located about 5 Å from the solid surface, the alkane molecules order with their axis oriented parallel to the adsorbing surface, thus maximizing the attractive physisorption energy. The orientational ordering is accompanied by the formation of ordered domains in the first liquid-film layer, with the molecules in each domain lying parallel to each other. The interfacial domain ordering is frustrated in the alkane mixture film adsorbed on the rough surface. Reduced diffusive motion is found for molecules located near the solid surfaces. However, in the region of the first adsorbed layer of the liquid film adsorbed on the smooth surface, the rate of diffusion, particularly of the hexane molecules, is larger than at the rough surface. It is found that the smaller, hexane, molecules diffuse through channels at the boundaries between the ordered domains formed by the hexadecane molecules. For the rough surface case, where the domain ordering is frustrated, such interdomain boundary channels do not form and consequently the domain boundary-assisted diffusion of the smaller molecules is not operative there, resulting in a smaller diffusion rate.

Does boron or nitrogen substitution affect hydrogen physisorption on open carbon surfaces?

Incorporation of heteroatoms in carbon materials is commonly expected to influence their physical or chemical properties. However, contrary to previous results for methane adsorption, no technologically significant effect was identified for the hydrogen physisorption energies (measured 4.1-4.6 kJ mol-1 and calculated qst = -ΔHads = 4.1 ± 0.7 kJ mol-1 using a comprehensive set of levels of theory) as a function of B- and N-substitution of a mid-plane C-site on open carbon surfaces.

Molecular simulation for physisorption characteristics of O2 in low-rank coals

In this paper, systematic research of the physisorption characteristics of oxygen in low-rank coals had been carried out using the Grand Canonical Monte Carlo (GCMC) and the Density Functional Theory (DFT) methods based on the assumption of no chemisorption. Firstly, the surface molecular structure parameters of five different low-rank coals were determined, the coal molecules and their unit cells structure were constructed; Secondly, Oxygen physisorption behaviour in coal molecular unit cells was simulated based on the GCMC and the Molecular Dynamics (MD) method; Finally, the physisorption parameters for oxygen physisorption at each adsorption site were simulated based on the DFT. The results show that the microporous structure of coal molecules is positively correlated with the total physisorption amount of oxygen and has an effect on the physisorption heat; oxygen is gathered around aliphatic hydrocarbons, the mutual distances of methyl and methylene to oxygen were 3.57 Å and 3.81 Å, respectively; the adsorption capacity of the low-rank coal molecules is effected by aromatic, oxygenated aliphatic hydrocarbons, and the degree of condensation of polycyclic aromatic hydrocarbons, the physisorption energy of the aromatic ring, hydroxyl and ether bonds to oxygen were −3.4790 kcal/mol, −2.9933 kcal/mol and −2.9663 kcal/mol respectively. This research will enable us to better understand the physisorption mechanism of oxygen in low-rank coals.

Superior sensing performance of two-dimensional ruthenium carbide (2D-RuC) in detection of NO, NO2 and NH3 gas molecules

In this work, for the first time, we report the enhanced adsorption of nitrogen-containing gas (NCG) molecules such as NO, NO2 and NH3 on two-dimensional ruthenium carbide (2D-RuC). Density functional theory calculations are performed to analyze the electronic properties, charge transfer, work function, recovery time and sensitivity. The computed physisorption energies for NO, NO2 and NH3 molecules are −1.718 eV, −1.480 eV and −0.895 eV respectively. Electronic property analysis reveals that 2D-RuC exhibits metallic character in the presence of adsorbed molecules, which is suitable for a good sensing performance. From the Bader charge analysis, we found that significant amount of charge is transferred from NO (0.210 e) and NO2 (0.413 e) molecules to the 2D-RuC sheet; whereas, charge transfer from the surface to the NH3 molecule is observed (−0.195 e). We also noticed significant changes in the work function of 2D-RuC after the adsorption of NCGs which indicates the high sensitivity and selectivity of this 2D material. The computed temperature-dependent desorption time of the NH3 molecule from the 2D-RuC sheet is much shorter (in the order of seconds) than other molecules. The results indicate that 2D-RuC is an excellent material for the design of reusable NH3 sensor devices.

Insight on açaí seed biomass economy and waste cooking oil: Eco-sorbent castor oil-based

The reuse of açaí seeds is an organic approach for valorizing biomass, encouraging the public policies of circular economy, which reduces the human impact on the production chain processes. This research proposes an alternative for açaí seed as a filler in castor oil-based polyurethane, obtaining eco-sorbent to evaluate the sorption capacity for another impactful food industry by-product: waste cooking oil (WCO). Eco-sorbents were obtained with castor oil based-polyol and isocyanate (MDI) by mass mixing equal to 1:1 (OH:NCO), reinforced with açaí seed residue (5–20 wt%). The samples were characterized by techniques scanning electron microscopy (SEM), optical microscopy (OM), apparent density, contact angle, infrared spectroscopy (FTIR), and thermogravimetric analysis (TGA). Sorption capacity and efficiency were evaluated as a function of the fiber content, with tests performed in times of 30–180 s in two systems: oil and oil/water. The results showed that the eco-sorbents had a hydrophobic nature (θ > 98.3°) and macroporous morphology (pore size from 152 to 119 μm), which allowed the adsorption of residual cooking oil by the porous structure. The kinetics study showed that the sample with greater fiber content (15% wt.) reached the equilibrium in a short time compared to the neat PU for the oil system, with a sorption capacity of 9.50 g g−1 in the first 30 s. For the oil/water system, an opposite behavior could be observed, with a sorption capacity of 9.98 g g−1 in the 150 s equilibrium time. The Langmuir isotherm model presented a maximum adsorption capacity of 10.42 g g−1. However, the Freundlich isotherm model had a better fit to the experimental data with R2 (0.97) and lower chi-square (0.159), showing favorable adsorption (n = 1.496). Thus, it was proved that the weak interactions (connection H) and the binding energy of the predominant physisorption for the oil/water system. Thus, developed eco-sorbents are an excellent option for the sorption of WCO.

A molecular dynamics study on the interfacial properties of millerite

The present study aims at developing force field parameters for describing the millerite structure and subsequently for investigation of its interfacial properties under varying conditions within the framework of molecular dynamics simulations. The first set of calculations were performed to obtain the required force field parameters, validated through reproduction of the bulk properties. This was followed by estimation of the surface energy and evaluation of the collector physisorption onto the non-polar (100) and (110) surfaces. Collector molecules exhibited higher affinity towards the former, with the branched alkyl chain favoring the interactions with either of the surfaces. Further simulations were conducted to examine the changes in the contact angle of the intrinsically hydrophilic (110) surface upon oxidization. Observations through transition from the neutral surface fully covered by elemental sulfur to a charge-bearing surface containing sulfur and polysulfides were compared against the theoretical predictions made by the Lippmann equation, and the discrepancies were attributed to the significance of line tension at the atomic scale. Finally, propensity of collector molecules towards the positively and negatively charged (110) surface was examined in the absence and presence of excess calcium hydroxide. In both cases, the collector-surface interactions were impeded in the strong alkaline solution.

Atomic layer deposition of Al2O3 and HfO2 for high power laser application

Atomic layer deposition has promising application in optical coatings because of the self-terminating feature. An ideally self-terminating ALD process is based on the saturate chemi-sorption and complete purging of the desorbed precursor molecules. The kinetics of adsorption and desorption are analyzed, providing instruction for the development of ALD process. The exposure length is related to the partial pressure and molecule mass, while the purging length is dependent on the physi-sorption potential energy and substrate temperature. The GPC versus pulse length of ALD Al2O3 and HfO2 are measured. With a set of properly selected parameters, film layers with distinctive self-terminating feature are obtained. A coating consisting of several nanolaminates is analyzed with TEM to study the ALD film structure. An anti-reflection coating is deposited, controlling the film thickness by counting the cycles. The laser resistance of the ALD Al2O3 film, HfO2 film and anti-reflection coating is studied. The results certify the analysis and indicate a promising application in developing a self-terminating ALD process for a new material on a new plant.

Dioxygen Binding to all 3d, 4d, and 5d Transition Metals from Coupled-Cluster Theory.

Understanding how transition metals bind and activate dioxygen (O2 ) is limited by experimental and theoretical uncertainties, making accurate quantum mechanical descriptors of interest. Here we report coupled-cluster CCSD(T) energies with large basis sets and vibrational and relativistic corrections for 160 3d, 4d, and 5d metal-O2 systems. We define four reaction energies (120 in total for the 30 metals) that quantify O-O activation and reveal linear relationships between metal-oxygen and O-O binding energies. The CCSD(T) data can be combined with thermochemical cycles to estimate chemisorption and physisorption energies for each metal from metal oxide embedding energies, in good correlation with atomization enthalpies (R2 =0.75). Spin-geometry variations can break the linearities, of interest to circumventing the Sabatier principle. Pt, Pd, Co, and Fe form a distinct group with the weakest O2 binding. R2 up to 0.84 between surface adsorption energies and our energies for MO2 systems indicate relevance also to real catalytic systems.

Physi-Sorption of H2 on Pure and Boron–Doped Graphene Monolayers: A Dispersion–Corrected DFT Study

High-surface-area carbons are of interest as potential candidates to store H2 for fuel–cell power applications. Earlier work has been ambiguous and inconclusive on the effect of boron doping on H2 binding energy. Here, we describe a systematic dispersion–corrected density functional theory study to evaluate the effect of boron doping. We observe some enhancement in H2 binding, due to the presence of a defect, such as terminal hydrogen or distortion from planarity, introduced by the inclusion of boron into a graphene ring, which creates hydrogen adsorption sites with slightly increased binding energy. The increase is from −5 kJ/mol H2 for the pure carbon matrix to −7 kJ/mol H2 for the boron–doped system with the boron content of ~7%. The H2 binding sites have little direct interaction with boron. However, the largest enhancement in physi-sorption energy is seen for systems, where H2 is confined between layers at a distance of about 7 Å, where the H2 binding nearly doubles to −11 kJ/mol H2. These findings suggest that interplanar nanoconfinement might be more effective in enhancing H2 binding. Smaller coronene model is shown to be beneficial for understanding the dependence of interaction energy on the structural configurations and preferential H2 binding sites.

Exploring the air stability of PdSe2 via electrical transport measurements and defect calculations

In this work we investigate the effects of ambient exposure on CVD grown PdSe2 and correlate density functional theory calculations of various physisorption and chemisorption binding energies and band structures to the observed changes in the electrical transport. Pristine PdSe2 is n-type due to intrinsic selenium vacancies, but shows increased p-type conduction and decreased n-type conduction as a function of ambient aging during which various aging mechanisms appear to be operative. Short term aging (<160 h) is ascribed to an activated chemisorption of molecular O2 at selenium vacancies; first-principles calculations suggest a ~0.85 eV activation energy and adsorption geometries with binding energies varying between 1.3–1.6 eV, in agreement with experimental results. Importantly, this chemisorption is reversible with a low temperature anneal. At long term aging (>430 h), there is a total suppression of n-type conduction, which is attributed to a dissociative adsorption/reaction of the O2 molecules to atomic O and subsequent PdO2 formation. XPS confirms the presence of PdO2 in long term aged flakes. At these extended aging times, the low temperature anneal restores low n-type conduction and suppresses p-type conduction due to the low thermal stability of PdO2 which, in agreement with XPS measurements, sublimates during the anneal. Thus PdSe2 devices can be processed into device architectures in standard laboratory environments if atmospheric exposure times are limited to on the order of 1 week.

Effect of N-doping on NO2 adsorption and reduction over activated carbon: An experimental and computational study

Due to high adsorption capacity, NO2 adsorption using activated carbon has become a potential denitration technology. A correlation between N-doping and NO2 adsorption process on activated carbon is pointed out by previous studies but lacks a clear explanation. The main objective of this work is to clarify the influencing mechanism of N-doping on NO2 adsorption and reduction over activated carbon. N-doped activated carbons were synthesized by melamine impregnation followed by calcination and tested as NO2 adsorbents. Experimental results showed that AC600 with highest N content possessed highest NO2 adsorption capacity and lowest NO release percentage. NO2 adsorption on activated carbon is a complex process, including NO2 adsorption, NO2 reduction to NO, and NO release. Density functional theory calculations results showed that N-doping affected all steps mentioned above. Firstly, N-doping increased NO2 physisorption energies, meaning that NO2 was easier to be adsorbed. Thus, NO2 adsorption capacities increased with the increase of N content experimentally. Secondly, N-doping increased the energy barrier of the rate-determining step of NO2 reduction. Thus, the reduction of NO2 to NO was harder. Thirdly, N-doping increased NO desorption energies, implying that the release of generated NO was harder. The inhibition of NO2 reduction and NO desorption results in the decrease of NO release percentage due to N-doping jointly. This work elucidates the influencing mechanism of N-doping on NO2 adsorption and NO2 reduction on theoretical level, which fills up the research gap and guides the design of activated carbon for efficient NO2 adsorption.

High energy-density multi-form thermochemical energy storage based on multi-step sorption processes

A novel multi-form thermochemical energy storage method is proposed for high energy-density thermal energy storage based on multi-step sorption processes. The proposed multi-form thermochemical energy storage combines the physisorption energy storage of a porous matrix, the chemisorption energy storage of a salt hydrate, and the absorption energy storage of the salt solution. High-performance composite sorbent of MgCl2@zeolite was prepared to demonstrate the feasibility of the proposed multi-form thermochemical energy storage. The water uptake contributions of physisorption, chemisorption and absorption of the composite sorbent were measured by a “three-step” hydration method. The multi-step desorption processes measured by TG at an extremely slow heating rate shows the apparent decrease of decomposition temperature of MgCl2 hydrates in zeolite matrix. The maximum sorption capacity of the MgCl2@zeolite composite sorbent without solution leakage is as high as 0.55 g/g and its gravimetric and volumetric thermal energy densities reach 1368 kJ/kg and 308 kWh/m3 respectively with charging temperature of 200 °C. This gravimetric energy density is about 2.26 times higher than that of pure zeolite 13X. The experimental results verified that the proposed multi-form thermochemical energy storage is an effective method to improve sorption capacity and to achieve high energy-density thermal storage.

A thermodynamic correction to the theory of competitive chemisorption of ions at surface sites with nonelectrostatic physisorption.

We resolve a thermodynamic inconsistency in previous theoretical descriptions of the free energy of chemisorption (charge regulation) under conditions where nonelectrostatic physisorption is included, as applied to surface forces and particle-particle interactions. We clarify the role of nonelectrostatic ion physisorption energies and show that a term previously thought to represent physisorbed ion concentrations (activities) should instead be interpreted as a "partial ion activity" based solely on the electrostatic physisorption energy and bulk concentration, or alternatively on the nonelectrostatic physisorption energy and surface concentration. Second, the chemisorption energy must be understood as the change in chemical potential after subtracting the electrostatic energy, not subtracting the physisorption energy. Consequently, a previously reported specific ion nonelectrostatic physisorption contribution to the chemisorption free energy is annulled. We also report a correction to the calculation of surface charge. The distinction in "partial ion activity" evaluated from bulk concentration or from surface concentration opens a way to study nonequilibrium forces where chemisorption is in equilibrium with physisorbed ions but not in equilibrium with bulk ions, e.g., by a jump in ion concentrations.

A theoretical approach of the ethanol adsorption on Au(100), Au(110) and Au(111) surfaces

The adsorption of ethanol on Au(100), Au(110) and Au(111) surfaces was studied using electronic structure calculations under the scheme of the density functional theory (DFT) with van der Waals corrections, vdW-DF2 and PBE functionals, using numerical atomic orbitals (NAO) basis set implemented in the SIESTA code and plane-waves basis set in the CASTEP code. The lowest physisorption energies using the plane-wave basis set in neutral media were observed at the TOP position in all the surfaces, with values in between −53.35 kJ.mol−1 and −61.80 kJ.mol−1. Structurally, the method based on linear combination of atomic orbitals (LCAO) using NAO as basis set gives the best result respect to the ideal bulk. However, the relaxation of the slab is better defined by the plane-wave scheme. Band structure has shown no change in the sp-like bands and the 5d occupied bands with and without the ethanol molecule adsorbed. However, a slight variation was obtained in the unoccupied bands due to the interaction with the lone pair of electrons from the oxygen (non-bonding orbitals).

Van der Waals Correction to the Physisorption of Graphene on Metal Surfaces

Adsorption is a scientifically and technologically important interfacial phenomenon, which however presents challenges to conventional density functional theory (DFT) due to the long-range van der Waals (vdW) interactions. We have developed a model of long-range vdW correction for physisorption of graphene (G) on metals with the Lifshitz–Zaremba–Kohn second-order perturbation theory, by incorporating dipole- and quadrupole-surface interactions and screening effects. The physisorption energies calculated by the model between graphene and eight metal surfaces (Al, Ni, Co, Pd, Pt, Cu, Ag, and Au), and the adsorption energies for the same G/metal structures from self-consistent DFT PBE (Perdew–Burke–Ernzerhof) calculations, are obtained in a range of distances between G and the metal surfaces. The sum of these two parts is the total adsorption energy as a function of the distance, from which the equilibrium distance and the binding energy are determined simultaneously. The results show high accuracy, with the...