Stability and electronic sensitivity of CunM (M = Co, Mn, Pd, Au and V; n = 3–8) nanoclusters towards HCOOH molecule: a computational study

The stability, electronic and magnetic properties of the Cun + 1 and CunM (M = Co, Mn, Pd, Au and V; n = 3–8) nanoclusters were investigated using the PW91PW91/LANL2DZ/-311G(d,p) level of theory. The electronic sensitivity of these clusters towards the formic acid (FA) has also been evaluated. The results obtained show that the doping of the Cun + 1 with Co, Mn, Pd, Au or V atom has strongly altered their electronic properties. The interaction of HCOOH molecule over the CunM clusters exhibits that the most favourable adsorption site for the molecule is the metal atom dopant, and the calculated adsorption energies (E ads) range from −113.4 to −436.0 kJ mol−1, indicating a great chemisorption between both species. The values of ΔH and ΔG of the formed complexes by the adsorption of the HCOOH onto the CunM clusters are found to be negative, indicating that the adsorption process is regarded as exothermic and thermodynamically realisable at room temperature. The results reveal also that the CunV and CunAu clusters have the greatest sensitivity towards the HCOOH molecule in comparison with the other clusters, suggesting that the two clusters could be proposed as high-performance clusters for the detection of HCOOH molecule.


Introduction
Metal nanoclusters have shown exceptional physical properties which differs profoundly from those the bulk metal [1][2][3][4][5].This is why they are widely employed in several fields such as electronics, optical and biomedical science [6][7][8][9][10].Also, they are widely employed as catalysts for energy storage and heterogeneous catalysis [11][12][13][14].The reactivity of the nanoclusters in the catalytic reactions was found strongly influenced by the size of the clusters and their shapes [15,16].The doping of the pure clusters by another atom is effective way to improve their catalytic performances [17,18].
Copper nanoclusters exhibit unique optical and electronic properties due to their small size and the high surface to volume ratio [19].Due to these interesting properties, the copper clusters are largely used as catalysts in several catalytic reactions [20,21].For example, copper clusters have a high catalytic activity in hydrogenation reactions [22][23][24].They showed also considerable catalytic performances in synthesis of methanol [25][26][27].Many studies have demonstrated that the doping of the copper nanoclusters with another transition metal enhances their catalytic activity [28][29][30].As an example, the doping of a single Pd atom at the edge site of the Cu 55 shell can substantially reduce the activation energy of H 2 dissociation, thus the reactivity of the doped clusters in the dissociation of hydrogen is higher than that of the pure copper clusters [28].Also, the doping of gold in the copper clusters makes the resulting binary clusters possess high reactivity in the CO oxidation reaction [29].Generally, the clusters which are doped by another atom are found very active and their catalytic performances were found to be better than those observed for the pure clusters [31][32][33].On other hand, several studies were performed to evaluate the effect of the doping of the transition metal atoms into the copper nanoclusters onto their stability and physical and chemical properties [34][35][36][37].For example, Li et al. [35] performed a systematic investigation on the structural and electronic properties of Cu n + 1 and Cu n Se (n = 1-8) clusters, and their results indicate that the lowest-energy structures of Cu n Se are different than those predicted for the corresponding pure Cu n clusters.By using density functional theory (DFT), Xu et al. [36] investigated the effect of Zr doping in Cu nanoclusters with the icosahedral structure on the catalytic activity of CO 2 hydrogenation to CHO.The obtained results demonstrate that Zr doping on the surface of Cu nanoclusters makes them possess superior catalytic ability for CO 2 reduction to methanol in comparison with that obtained for the copper clusters.The stability, reactivity, and electronic and magnetic properties of the Cu n Mn (n = 2-12) clusters were systematically investigated by Boudjahem et al. [37], and their major findings indicate that the Cu 6 Mn and Cu 9 Mn clusters are found more stable compared to neighbouring clusters.The condensed Fukui function was calculated for each atom in the Cu n Mn clusters, and the results showed that the reactivity of these clusters is mainly localised on the Mn atom.This suggests that the Cu n Mn clusters are considered as effective nanocatalysts which can capture the molecules onto their surface.Recently, we conducted a theoretical study on the copper clusters and their doping with ruthenium atom [38].The results show that the doping of these clusters by the ruthenium atom greatly improves the sensitivity performances of the binary clusters towards the CH 3 OH molecule.Moreover, the complexation process between the CH 3 OH molecule and the Cu n Ru clusters was found to be exothermic and thermodynamically feasible.The adsorption and decomposition mechanism of the formic acid (FA) molecule over the surface of a catalyst has been extensively studied [39][40][41].By using DFT calculations, the adsorption of formic acid over the Zn 12 O 12 cage was studied by Salimi et al. [40], and the results obtained by them indicate that the adsorption process of HCOOH is accompanied by release of energies which vary of 30.84 to 151.08 kJ mol −1 .Moreover, the calculations show that the adsorption of trans-formic acid is found to be much more favourable than the cis-acid.Esrafili et al. [39] have investigate the adsorption and decomposition mechanism of HCOOH over the Al 12 N 12 cluster by using the PBE/DNP level of theory, and the results show that the attachment of the O atom of the carboxyl group over the Al atom of the Al 12 N 12 cluster is energetically favourable than the oxygen atom of the hydroxyl group.Also, the results suggest that the HCOOH molecule was strongly adsorbed on the surface of the cluster with adsorption energies which vary from −120.5 to −568.6 kJ mol −1 .This great interaction between both species alters the electronic structure of the Al 12 N 12 cluster which could be conducted to the change in its electrical conductivity.The adsorption of HCOOH molecule over the metalembedded graphene (MGr) surfaces was investigated by Akça et al. [41] by using DFT calculations.The calculations suggest that the HCOOH molecule preferred to bonded by its oxygen (in the C = O bond) to the MGr surfaces, and the calculated adsorption energies for the HCOOH on CuGr and NiGr surfaces were −88.76 and −81.04 kJ mol −1 , respectively.
In this work, DFT calculations were carried out to explore the stability, electronic and magnetic properties of the Cu n + 1 and Cu n M (M = Co, Mn, and V) clusters and their sensitivity performances towards the HCOOH molecule.This paper was organised as follows: In Section 2, we describe the computational methods used in our calculations.The stability, electronic and magnetic properties of the Cu + 1 and Cu n M clusters and their interaction with the HCOOH molecule are discussed in Section 3. The findings of this study are summarised in Section 4.

Computational details
We have carried out DFT calculations as implemented in the Gaussian 09 software package [42] to evaluate the structural, electronic and magnetic properties of the copper clusters (Cu n + 1 ) and their interaction with the HCOOH molecule.In order to study the effect of the Co, Mn, Pd, Au or V atom doping over the electronic, magnetic and adsorption properties of the Cu n + 1 clusters, a substitution of a Cu atom in the Cu n + 1 clusters by a Co/Mn/Pd/Au/V atom was realised.The Perdew-Wang (PW91) functional was used in our calculations to estimate the physical and chemical properties of the clusters and their complexes formed by interaction with the HCOOH molecule [43].The LANL2DZ basis set was employed for Cu, Co, Mn, Pd, Au and V atoms [44,45], while the 6-311G(d,p) basis set has been used for the C, O, and H atoms in order to compute the properties of the interaction between the HCOOH molecule and the surface of the clusters [44,45].The Perdew-Wang (PW91) functional was frequently utilised to investigate the relative stability and electronic properties of the binary clusters [46][47][48][49].First, we relaxed a lot of possible initial structures with different electronic states and symmetries in order to search the ground states of the Cu n + 1 (n = 3-8) clusters.After finding the most stable structures of the Cu n + 1 clusters, the configuration of the Cu n M (M = V, Mn, Pd, Au and Co) are obtained by replacing a copper atom by a M atom.The substitution process was carried out on all possible sites of the Cu n + 1 in order to find the most stable structure.The vibrational frequencies are calculated and the values obtained are positive for all the optimised structures, confirming that the configurations do not present any imaginary value, thereby the geometries predicted are considered as the most stable clusters.The most stable clusters are used to estimate their electronic and magnetic properties.The energy gap (E g ) and the total magnetic moment (µ T ) of the clusters were calculated using the following formulas: where E LUMO and E HOMO are respectively the energies of the LUMO and HOMO orbitals respectively.µ(↑) and µ(↓) are respectively the spin-up and spin-down states.
To determine the most stable configurations of the adsorbed HCOOH over the surface of the clusters, the molecule was systematically placed on several sites at the surface of Cu n + 1 , Cu n Co, Cu n Mn, Cu n Pd, Cu n Au and Cu n V clusters, and the optimised complexes were compared.The most stable complexes have been selected according to their high adsorption energies.
The strength of the adsorption energy (E ads ) of the HCOOH molecule over the surface of the Cu n + 1 and Cu n M clusters was computed as follows [50]: The sensitivity performances of the Cu n + 1 and Cu n M (M = Co, Mn, Pd, Au and V) clusters were evaluated towards the HCOOH molecule.The sensitivity (S) was estimated by using the following expression [51]: where E 1 and E 2 are the energy gaps of the cluster and its complex formed by the interaction of the HCOOH with its surface.k and T are the Boltzman's constant (8.62 × 10 −5 eV/K) and temperature in K.

The most stable configurations of the Cu n + 1 and Cu n M (M = V, Co, Pd, Au and Mn) nanoclusters
The most stable configurations of the Cu n + 1 and Cu n M (M = V, Co, Pd, Au and Mn; n = 3-8) nanoclusters have been obtained (see Figures 1 and 2), and their structural, electronic and magnetic properties are reported in Tables 1 and 2. According to Figure 1, the most stable structure of the Cu 4 cluster is a planar rhombus geometry with C 2h symmetry.The addition of a TM atom (TM = V, Mn, Pd, Au or Co) has not changed of the optimised geometry of Cu 4 , and the most stable configuration obtained for the five doped clusters (Cu 3 V, Cu 3 Mn, Cu 3 Pd, Cu 3 Au and Cu 3 Co) is also a planar rhombus (see Figures 1 and 2).The most stable configuration of the Cu 5 cluster is a distorted trigonal bipyramid geometry (C 1 symmetry).The addition of the Mn or Au atom did not change the geometry of Cu 5 , in contrast, the introduction of the V, Pd or Co atom in the Cu 5 cluster completely modified their structure, and the resulting geometry after doping is a square pyramid where the Co/V/Pd atom occupies the vertex position of the pyramid.For the Cu 6 cluster, a pentagonal pyramid configuration was optimised as the ground state geometry.The doping of the Cu 6 by a Mn, Pd, Au or V atom has a strong  effect on its configuration, whereas the replacement of a copper atom in the Cu 6 cluster by a cobalt atom has no influence on its geometry.The most stable geometry obtained for the Cu 5 M (M = Mn, Pd and Au) clusters is an octahedron (C S symmetry) where the metal atom dopant lies at the top of the pyramid, whereas a capped square pyramid geometry is predicted as the ground state for the Cu 5 V cluster.For the Cu 7 cluster, the pentagonal bipyramid configuration with C S symmetry was calculated as the most stable cluster.An identical geometry was obtained for the copper cluster doped by Mn, Pd, Au, V or Co, in which the metal atom dopant is located at the top of the pyramid.The most stable configuration of the Cu 8 cluster is a bicapped octahedron geometry with C 2V symmetry.A similar configuration has also been identified as the most stable geometry for Cu 7 Co, Cu 7 Pd, Cu 7 Au and Cu 7 Mn clusters, while for the Cu 7 V cluster, the most-stable structure obtained is a tricapped trigonal bipyramid geometry with C S symmetry.For the Cu 9 cluster, the bicapped pentagonal bipyramid geometry with C S symmetry was predicted as the most stable geometry.The addition of the Co, Pd, Au or V atom did not alter the geometry of Cu 9 , and the configuration obtained after doping is a bicapped pentagonal bipyramid where the metal atom dopant is located at the vertex of the pyramid.
In contrast to four previous atoms, the Mn atom doping in the Cu 9 cluster was completely changed its geometry, in which the most stable configuration predicted is a tricapped octahedron with C S symmetry.

Relative stability of the Cu n + 1 and Cu n M (M = V, Co, Pd, Au and Mn) clusters
In order to understand the stability of the lowest-energy configurations of the Cu n + 1 and Cu n M (M = V, Co, Pd, Au and Mn) clusters, the binding energies per atom (E b ) and the fragmentation energies ( E f ) are calculated using the following expressions [52,53]: where E(Cu n + 1 ) and E(Cu  in Figure 3.The results of the fragmentation energies ( E f ) have also been displayed in Figure 4.
Regarding The fragmentation energy ( E f ) is an important factor to evaluate the relative stability of the nanoclusters.Also, the values of E f can be closely linked with the relative abundance determined in mass spectroscopy experiments.The results of the fragmentation energy ( E f ) of the most stable configurations of the Cu n + 1 and Cu n M clusters are shown in Figure 4.As depicted in Figure 4, the curve of E f exhibits remarkable peaks at n = 6 and 8 for the Cu n + 1 clusters, implying that the Cu 7 and Cu 9 clusters are relatively more stable than their neighbouring clusters.The introduction of a M atom (M = V, Mn, Co, Pd and Au) in the Cu n + 1 clusters modify the stability of the resulting clusters.For example, the Cu n + 1 clusters which were doped by V and Mn atoms, the most stable clusters predicted are Cu 6 V and Cu 6 Mn as shown in Figure 4.For the Cu n Pd cluster, two peaks were appeared at n = 4 and 6, reflecting that the Cu 4 Pd and Cu 6 Pd clusters are more stable than the other isomers.Unlike to the above clusters, the local maximums were found at n = 5 and 7 for Cu n Co and Cu n Au, respectively, indicating that the Cu 5 Co and Cu 7 Au clusters are chemically stable compared to their corresponding neighbours.

Electronic and magnetic properties of the Cu n + 1 and Cu n M (M = V, Co, Pd, Au and Mn) clusters
The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is a significant criterion that reflects the chemical reactivity of the clusters.A large E g suggests high stability of the clusters, and a little E g indicates a higher reactivity of the cluster.The HOMO-LUMO energy gap (E g ) of the Cu n + 1 and Cu n M (M = V, Co, Pd, Au and Mn) clusters were estimated and the results obtained are reported in Table 2.The energy gaps of the Cu n + 1 clusters are in the range of 0.31 to 1.75 eV, indicating a semiconductor behaviour with moderate energy gap (E g ≤ 1.75 eV).The results indicate also that after the introduction of the Co, Mn, Pd, Au or V atom in the Cu n + 1 clusters, the energy gap of the binary clusters which contain an odd number of copper atoms (n = 3, 5 and 7) was greatly decreased, suggesting an increase in their chemical reactivity.On other hand, the Cu n M (M = V, Co and Mn) clusters which contain an even number of copper atoms, their energy gaps are significantly increased (see Table 2), except for the Cu 6 V cluster where its E g was slightly reduced (0.32 eV).This indicates that the addition of V/Co/Mn atom greatly improves the catalytic performances of the binary clusters which contains an odd number of copper atoms.Meanwhile, the stability of the binary clusters having an even atom has been sharply enhanced.The results obtained demonstrate that when the Cu n + 1 clusters were doped by the Pd/Au atom, their energy gaps were greatly decreased, with the exception of the Cu 4 Au where its E g was slightly increased, suggesting that the reactivity of the copper clusters was strongly improved after doping.When the copper atom in the Cu n + 1 clusters was replaced by TM atom (Co, V, Pd, Au or Mn), the charge transfer between the metal atom dopant and the other part of the cluster takes place.The charge on the metal dopant in the clusters was calculated and the values estimated are reported in Table 2.The charge on the V, Co and Mn atoms are found to be positive, which indicates that the charge transfer occurs from the metal dopant to the copper atoms in the binary clusters.On the contrary, the charge on the Pd/Au atom was found negative, implying that the charge was transferred from the copper atoms to the Pd/Au dopant.Furthermore, the positive charge onto the metal atom dopant in the clusters makes it a preferred adsorption site for molecules having an electron donor-character, whereas the negative charge on the metal dopant makes it a preferred adsorption site for molecules having an electron acceptor-character.
The ionisation potential (VIP) and electronic affinity (VEA) are significant quantities that define the ability to lose and gain an electron, respectively.The calculated VIP and VEA of the lowest-energy Cu n + 1 and Cu n M (M = V, Co, Pd, Au and Mn) clusters were summarised in Table 2.The two electronic quantities (VIP and VEA) have been calculated using the following expressions [54]: where E 0 represents the total energy of the neutral cluster in its ground state.E C and E A represent the total energies of the cationic and anionic clusters, respectively, with the identical configuration as the neutral cluster.According to Table 2, it was noticed that the introduction of a metal atom such as V, Co, Pd, Au or Mn into the Cu n + 1 clusters had a slight effect on the VIP and VEA values.The calculated values of VIP for Cu n + 1 and Cu n M clusters are in the range of 6.23-8.66eV and 5.09-7.68eV, respectively.And, the values of VEA for Cu n + 1 and Cu n M clusters range from 1.21 to 1.87 eV, and 0.34 to 2.97 eV, respectively.The comparison between the VIP and VEA values of all clusters exhibit that the VEA values are very lower than those of the VIP, indicating that the clusters can easily receive electrons.
The dipole moment of the Cu n + 1 clusters were evaluated and the results obtained show that the β values of the pure clusters are very small (0-0.75D), and their doping with V, Co, Pd, Mn or Au atom has no effect on their polarisability (see Table 2).The magnetic properties of the clusters were also estimated, and the total magnetic moment per atom (µ T ) of each cluster is represented in Table 2.As it was mentioned in Table 2, the Cu n + 1 clusters with an even number of copper atoms are nonmagnetic, while the clusters with an odd number of copper atoms in the clusters show a little magnetic moment (0.11-0.20 µ B /atom).The replacement of a copper atom in the Cu n + 1 clusters by a transition metal atom (Co, V, Pd, Au or Mn) considerably improves their magnetism.The comparison between the TM-doped Cu n + 1 clusters indicates that the Cu n Mn and Cu n V clusters have the highest magnetic moments compared to those calculated for the other clusters, in which the values of µ T for the Cu n Mn and Cu n V clusters vary from 0.50 to 1.50 µ B /atom (Table 2).The greatest magnetic moment was found for the Cu 3 Mn cluster (1.50 µ B /atom).To obtain more information on the magnetic properties of the clusters, NBO analysis, the density of states (DOS) and the partial density of states (PDOS) of the doped clusters were calculated and analysed.The curves for the Cu 4 M (M = V, Co, Mn, Pd and Au) clusters as representative samples are shown in Figure S1.The Fermi level (E F ) is represented in figures by dashed line.The results show that the total magnetic moment of the doped clusters is mostly localised on the metal atom dopant for the Cu 4 V, Cu 4 Co and Cu 4 Mn clusters, but for the other clusters (Cu 4 Pd and Cu 4 Au), the contribution of the metal atoms dopants to the total magnetic moment is less important compared with the atoms dopants above (V, Mn and Co).For example, the contribution of the Co atom to the total magnetic moment of the Cu 4 Co cluster is 80.3%, while the contribution of the Pd atom in the Cu 4 Pd cluster is only 23.4%.Based on the PDOS analysis of the clusters (see Figure S1), the results indicate that the µ T is localised on the d orbital of the atoms dopants for the Cu 4 V, Cu 4 Co and Cu 4 Mn clusters, and the contribution of s and p orbitals is very small.Similar results were observed for the Rh n Os and Cu n Mn clusters [55,56].For the other two clusters (Cu 4 Pd and Cu 4 Au), the contribution of d orbitals of the clusters are less important than the s and p orbitals.The same conclusions were obtained for the other clusters.

Adsorption of the HCOOH molecule over the Cu n + 1 clusters
First, we studied the interaction of the HCOOH molecule with the surface of the Cu n + 1 clusters in order to evaluate their adsorptive properties.The most stable configurations of the complexes formed by the fixation of the HCOOH molecule onto the surface of the clusters are represented in Figure S2 and their electronic and thermodynamic parameters are summarised in Table S1.As shown in Table S1, Gibbs energy change ( G) of the complexation of the Cu n + 1 clusters with an even number of copper atoms (n + 1 = 5, 7 and 9) and the HCOOH molecule is positive ( G > 0), implying that the formation of these complexes is thermodynamically not feasible at room temperature.From a thermodynamic point of view, only the clusters with an odd number of copper atoms (Cu 5 , Cu 7 and Cu 9 ) that can react easily with the HCOOH molecule to form the HCOOH-Cu n + 1 complexes (n = 4, 6 and 8) ( G < 0).The adsorption energies for these three complexes were calculated and reported in the same table above.The estimated E ads range from −136.2 to −245.6 kJ mol −1 , indicating that the interaction between both species is considered as a chemisorption process.This great adsorption was confirmed by the shortest interaction distances (2.02-2.07Å).The effect of the adsorbed HCOOH onto the electronic properties of the Cu n + 1 clusters has also been evaluated, and the results obtained show a considerable change in their E g after adsorption process.For example, the energy gap of the Cu 5 cluster was decreased from 0.31 eV to 0.05 eV when the HCOOH molecule was fixed over its surface, thereby a reduction of 84% in its energy gap.During the complexation phenomena, it was observed that there is a low charge transfer from HCOOH to clusters (+0.02 to +0.10 e).In addition to charge transfer, the adsorption of the molecule on the clusters substantially increases their dipole moments, and the values predicted are in the range of 6.74 to 7.83 D. The results indicate also that the three clusters are very sensitive to the HCOOH molecule, so they can easily react with the HCOOH molecule to form the complexes at room temperature.This is consistent with the thermodynamic parameters which were calculated above.As it is very difficult to control the size of the copper clusters prepared experimentally, thus, we cannot obtain the desired size of clusters that can easily interact with the HCOOH molecule to form the complexes as indicated by the results of thermodynamics, so it is not practical to use Cu n + 1 clusters as detectors of the HCOOH molecule.

Adsorption of the HCOOH molecule over the Cu n M (M = Co, Mn, Pd, Au and V) clusters
The purpose in this section is to investigate the adsorption of the HCOOH molecule over the surface of the Cu n M (M = Co, Mn, Pd, Au and V; n = 3-8) clusters.To find the most stable complexes which have been formed by the interaction of the HCOOH molecule and the surface of the clusters, the HCOOH is placed over the surface of the clusters with different orientations and several positions.Upon full optimisations, the most stable configurations of the complexes were presented in Figures 5-9, and their electronic and adsorption properties are mentioned in Table 3.

Adsorption of the HCOOH molecule over the Cu n Co clusters
In this section, the interaction between the HCOOH molecule and the Cu n Co clusters was examined.The most stable configurations of the HCOOH-Cu n Co complexes which were obtained are depicted in Figure 5, and their electronic and adsorption properties are summarised in Table 3.As can be seen from this figure, the preferred adsorption site for the HCOOH molecule     This small interaction distance between the HCOOH molecule and the Cu n Co clusters is caused by the great interaction between the metal atom dopant in the clusters and the O atom of the HCOOH molecule, which is consistent with the above finding.It was also observed that the interaction of the HCOOH with the surface of the clusters does not have a significant effect on the Cu-Cu and Cu-Co bond distances in the clusters, thereby these clusters will not be deformed after the adsorption process (Table S2).This finding is also valid for the interaction of the HCOOH molecule with the surface of the other clusters which were studied below.The charge of the adsorbed molecule in each complex has been computed and the values predicted indicate that the charge transfer occurs from the HCOOH molecule to the surface of the Cu n Co clusters.The charge transferred between both species varies between +0.03 and +0.12 e.The changes in enthalpy ( H) and changes in Gibbs free energy ( G) of the HCOOH-Cu n Co complexes were calculated, and the results obtained are listed in Table 3  complexes were found in the range of 2.92 and 6.47 Debye.This raise in β was assigned to the charge transfer between the clusters and the HCOOH molecule.On the other hand, the interaction of HCOOH with Cu n Co clusters produces a profound change in their energy gaps (except for the Cu 5 Co cluster where the variation in E g is less than 1%), which leads to sharp decrease in the electrical conductivity of the clusters.The sensitivity (S) of the clusters towards the HCOOH molecule was calculated and the values estimated from Equation (3) indicate that the Cu n Co clusters have good sensitivity for the detection of the HCOOH molecule, except for the Cu 5 Co cluster where its sensitivity is only 17.7%.

Adsorption of the HCOOH molecule over the Cu n Mn clusters
In the same way as above, several configurations of adsorbed HCOOH molecule over Cu n Mn clusters were examined.After optimisations, the most stable HCOOH-Cu n Mn complexes were obtained and represented in Figure 6, and their electronic and adsorption properties are summarised in Table 3.As it was observed in this figure, the HCOOH molecule prefers to adsorb on the Mn atom rather than the copper atoms in the Cu n Mn clusters.In this case, the Mn atom in the clusters is considered as the most favourable adsorption site in which it can easily capture the HCOOH molecule by forming a strong M-O bond.The Mn-O bond length in the optimised complexes varies between 1.83 and 1.94 Å.This short adsorption distance between the adsorbate and the adsorbent signifies that the interaction between both species is a great chemisorption with E ads which vary of −260.8 to −339.6 kJ mol −1 .NBO analysis reveals that the electronic charge is transferred from HCOOH to Cu n Mn clusters as shown in Table 3.The amount of charge which was transferred from HCOOH to the Cu n Mn clusters varies from +0.05 to +0.28 e.The calculations exhibited that the changes in enthalpy ( H) of the HCOOH-Cu n Mn complexes were found to be in the range of −264.1 to −286.6 kJ mol −1 , confirming a strong chemisorption.Furthermore, the complexation process between the HCOOH molecule and the Cu n Mn clusters is considered as an exothermic phenomenon.The calculated values of G for all formed complexes are negative, implying a spontaneous chemisorption of HCOOH molecule over the surface of the clusters.The electric dipole moments of these systems were also determined as reported in Table 3, and the results suggest that the adsorption of HCOOH onto the Cu n Mn clusters has a significant effect on their dipole moments.The dipole moment increases from 2.67 in FA-Cu 5 Mn complex to 7.21 D in FA-Cu 4 Mn complex.
Compared with the E g values of the Cu n Mn clusters, the energy gaps of the HCOOH-Cu n Mn complexes are considerably changed upon the adsorption process, and the values estimated range from 0.19 to 0.95 eV.For example, the energy gap of the Cu 3 Mn cluster increases from 0.38 eV to 0.95 eV when the HCOOH molecule is fixed on its surface by the adsorption process.Therefore, an increase of 153% in E g of the cluster after chemisorption.This implies that the electronic properties of the Cu n Mn clusters are very sensitive to the presence of the HCOOH molecule over their surface.
The sensitivity performances of the clusters to the HCOOH molecule were evaluated, and the calculated values for the Cu 6 Mn and Cu 7 Mn clusters are 32% and 44% (see Table 3), respectively, verifying a low sensitivity to the HCOOH molecule.On the contrary, the other clusters have high sensitivity (97.9-666 × 10 4 %) to the adsorbed molecule, thereby the detection of the HCOOH molecule is very easy by these clusters.

Adsorption of the HCOOH molecule over the Cu n V clusters
The sensitivity performances of the Cu n V (n = 3-8) clusters towards the HCOOH molecule have also been studied.After full optimisations, the most stable complexes which were obtained with their structural and electronic parameters are reported in Figure 7 and Table 3.The interaction distances between the formic acid (FA) molecule and the surface of the Cu n V clusters vary between 1.80 and 2.03 Å, implying that these short distances between both species suggest that the interaction of the HCOOH molecule with the surface of the Cu n V clusters was regarded as a strong chemisorption.The calculated adsorption energies (E ads ) are found between −327.8 and −417.2 kJ mol −1 , confirming a great chemisorption between these two species.NBO analysis show that there is a transfer of charge from Cu n V clusters to the HCOOH molecule, and the amount of charge transferred (q CT ) ranges from −0.13 e in the HCOOH-Cu 8 V complex to −0.45 e in the HCOOH-Cu 5 V complex (Table 3).The thermodynamic parameters such as enthalpy change ( H) and Gibbs freeenergy change ( G) for the complexation phenomena were also calculated and the predicted values are summarised in Table 3.As it was presented in this table, the values of H and G are found to be more negative, indicating that the complexation process between the cluster and the HCOOH molecule is exothermic and thermodynamically realisable.In other words, the formation of the complexes by the interaction of the HCOOH molecule with the Cu n V clusters is feasible and can be easily realised at room temperature.The analysis of the results also suggests that the interaction between the HCOOH molecule and the Cu n V clusters causes great influence on the electric dipole moments of the clusters.The dipole moments of the clusters were increased when the HCOOH is chemisorbed onto their surface (Table 3).The results show also that the energy gap of the Cu n V clusters was highly modified by the fixation of the HCOOH molecule over the metal-site dopant in the clusters, which improves the sensitivity performances of the Cu n V clusters.The calculated E g of the complexes are between 0.45 and 0.88 eV.The calculations show that the Cu n V clusters have high sensitivity to the HCOOH molecule, in which the obtained values of the sensitivity ranges from 291.2 to 810 × 10 4 %, indicating that all the clusters can easily detect the molecule when it approaches to their surface.In comparison with the other clusters, the sensitivity of the Cu n V clusters to the HCOOH molecule is greater than that obtained for the other types of the clusters, therefore, they can detect the HCOOH molecule more easily, which makes them promising sensors for the detection of the HCOOH molecule.

Adsorption of the HCOOH molecule over the Cu n Pd and Cu n Au clusters
The adsorption of the HCOOH onto the Cu n Pd and Cu n Au clusters was also evaluated, and the results obtained including the optimised complexes, structural parameters and electronic and adsorptive properties are reported in Figures 8 and 9 and Table 3.As can be seen from Figures 8 and 9, the preferred binding site for the O atom of the HCOOH molecule is the Pd/Au atom, except for the Cu 8 Au cluster, where the O atom prefers to chemisorb on the Cu atom.The calculated E ads are in the range of −193.3 to −436.0 kJ mol −1 , reflecting a great chemisorption between the two species.The interaction distance between both species in the obtained complexes varies from 2.12 to 2.89 Å.The interaction of the HCOOH molecule with the surface of the clusters leads to a charge transfer between both species (q CT ), which varies between +0.08 and +0.16 e.The positive charge on the HCOOH molecule indicates that the electronic charge is transferred from HCOOH molecule to clusters.The H and G of the HCOOH-Cu n Pd and HCOOH-Cu n Au complexes have been computed, and the values estimated are summarised in Table 3.The H of the complexes are found to be negative, implying that the formation of the complexes from the adsorption of the HCOOH over the surface of the clusters is regarded as exothermic process.The large H values obtained are −413.7 and −430.8 kJ mol −1 for the HCOOH-Cu 6 Pd and HCOOH-Cu 5 Au complexes, respectively, reflecting that the interaction between the molecule and the surface of the clusters is very strong.This finding is very consistent with the value of the adsorption energy of the HCOOH-Cu 6 Pd and HCOOH-Cu 5 Au complexes (−436.0kJ mol −1 ).The G values of all formed complexes are negative, confirming that the complexation process between both species can be carried out spontaneously at room temperature.The results show also that the adsorption process can significantly change the electronic properties (see Table 3).For example, the dipole moment (β) was greatly increased when the HCOOH molecule is fixed on the surface of the clusters.The energy gap of the clusters was also strongly modified upon adsorption process, with the exception of the Cu 3 Pd, Cu 8 Pd, Cu 7 Au and Cu 8 Au clusters, where the change in E g is little.For example, the variation in E g ( E g ) for the Cu 5 Pd cluster is 59%, while the calculated E g for the Cu 3 Pd cluster does not exceed 3%.This change in energy gap for the majority of the clusters after the adsorption process conducts to a sharp variation in their electrical conductivity

Comparison between the adsorptive properties of the Cu n Co, Cu n Mn, Cu n Pd, Cu n Au and Cu n V clusters towards the HCOOH molecule
In order to compare the adsorption properties for the five clusters (Cu n Co, Cu n V, Cu n Pd, Cu n Au and Cu n Mn), we have plotted the E ads , d M−O , H, and G as function of the number of the copper atoms, and the results are shown in Figure 10.From this figure, we clearly see that the values of the E ads , H, and G for the majority of the Cu n V clusters during their complexation with the HCOOH molecule show higher exothermicity and more spontaneity in comparison with the values obtained for the other clusters.These results indicate that the complexation of the Cu n V clusters with the HCOOH molecule is carried out more easily at ambient temperature (T = 298 K) than the other types of the complexes.The highest values of the E ads (−417.2kJ mol −1 ), H (−411.2 kJ mol −1 ), and G (−363.4 kJ mol −1 ) were obtained for the Cu 5 V cluster, suggesting that this cluster is more reactive towards HCOOH molecule than their neighbouring clusters.In addition to the Cu n V clusters that can easily form the complexes with the HCOOH molecule, the results obtained indicate also that the Cu 5 Au and Cu 6 Pd clusters are also able to readily form of the stable complexes with HCOOH at ambient temperature (see Figure 10).The results suggest also that the shortest adsorption distances were observed for the complexes formed by the interaction of the HCOOH molecule with the surface of the Cu n V clusters, indicating a strong chemisorption between both species.This result is in excellent agreement with the values calculated of E ads , H, and G for the HCOOH-Cu n V complexes.The sensitivity of the five clusters towards the HCOOH molecule was calculated and the values predicted were reported in Table 3.As can be seen from this table, the Cu n V and Cu n Au clusters have the greatest sensitivity compared to the other three clusters (Cu n Co, Cu n Pd and Cu n Mn), implying that the Cu n V and Cu n Au clusters can easily detect the HCOOH molecule when it approaches to their surface, thereby they can be employed as effective sensors for the detection of HCOOH molecule.Also, the other clusters (Cu n Co, Cu n Pd and Cu n Mn) have high sensitivity performances (with the exception of the Cu 5 Co, Cu 6 Mn, Cu 7 Mn, Cu 3 Pd and Cu 8 Pd clusters) but are less important than those obtained for the Cu n V and Cu n Au clusters.On the basis of the results presented above, the Cu n + 1 clusters which are doped by V or Au atom possess high sensitivity towards the HCOOH molecule in comparison with those which were doped by Mn, Co or Pd atom.

Conclusions
In summary, DFT calculations using the Perdew-Wang (PW91) functional with LandL2DZ/6-311G (d,p) basis sets were performed to investigate the stability, electronic and magnetic properties of the Cu n + 1 and Cu n M (M = Co, Mn, Pd, Au and V; n = 3-8) clusters and their interaction with the HCOOH molecule.The findings of this study are summarised below: (1) Based on the fragmentation energies and the binding energies, the results exhibit that the Cu 6 , Cu 8 , Cu 5 Co, Cu 6 Mn, Cu 6 V, Cu 4 Pd, Cu 6 Pd and Cu 7 Au clusters are found to be more stable than the other clusters.Therefore, they are less reactive than their neighbouring clusters.(2) When a copper atom in the Cu n + 1 clusters was replaced by another atom such as Co, Mn or V, their energy gaps are strongly modified, and the results indicate that the E g of the clusters with an odd number of copper atoms were reduced, therefore, their chemical reactivity was greatly improved.In contrast, the E g of the clusters with an even of copper atoms were increased upon doping, suggesting that these clusters possess great stability compared the Cu n + 1 clusters.Therefore, the chemical reactivity of these clusters was significantly reduced after doping.

Figure 1 .
Figure 1.The most stable structures of Cu n + 1 and Cu n M (M = Co and Mn; n = 3-8) clusters.

Figure 2 .
Figure 2. The most stable structures of Cu n M (M = V, Pd and Au; n = 3-8) clusters.

Figure 3 .
Figure 3. Size dependence of the binding energies per atom (E b ) for the Cu n + 1 and Cu n M clusters.

Figure 4 .
Figure 4. Size dependence of the fragmentation energies ( E f ) for the Cu n + 1 and Cu n M clusters.

Figure 3 ,
the binding energies per atom of the Cu n + 1 and Cu n M clusters increase monotonically with the cluster size (except for the Cu 7 Pd cluster where there is a slight decrease in its E b compared to the Cu 7 Pd cluster), suggesting that the energy of the Cu n + 1 and Cu n M clusters increases continuously during the growth process.In addition, the E b values obtained for the pure Cu n + 1 clusters are larger than those of the Cu n M (M = V, Co, and Mn) clusters, indicating that the doping of copper clusters with M atoms (M = Co, Mn and V) significantly reduces the stability of pure copper clusters.On the other hand, E b of the Cu n + 1 clusters increases with the doping of Pd and Au atoms in the Cu n + 1 clusters, implying a great improvement in the stability of the binary clusters.In other words, the chemical reactivity of the Cu n M clusters can be enhanced when the Mn, Co or V atom was incorporated in the Cu n + 1 clusters, while the introduction of the Pd or Au atom into the Cu n + 1 clusters reduces their chemical reactivity.

Figure 5 .
Figure 5.The most stable configurations of the HCOOH-Cu n Co complexes.

Figure 6 .
Figure 6.The most stable configurations of the HCOOH-Cu n Mn complexes.

Figure 7 .
Figure 7.The most stable configurations of the HCOOH-Cu n V complexes.

Figure 8 .
Figure 8.The most stable configurations of the HCOOH-Cu n Pd complexes.

Figure 9 .
Figure 9.The most stable configurations of the HCOOH-Cu n Au complexes.
. The H of the complexes ranges from −108.5 to −341.4 kJ mol −1 , indicating that the adsorption process between the HCOOH molecule and the Cu n Co clusters is considered as an exothermic phenomenon.The highest enthalpy changes ( H) were predicted for the HCOOH-Cu 3 Co complex (−341.4kJ mol −1 ), suggesting great adsorption between the O atom of HCOOH and the Co atom of the cluster.This result is in excellent agreement with the value calculated of E ads for the HCOOH-Cu 3 Co complex (−348.8kJ mol −1 ).For all formed complexes upon the interaction between the two species, the calculated values of G are negative, implying a spontaneous chemisorption of HCOOH molecule over the surface of the clusters.The results also indicate that the interaction between the HCOOH molecule and the Cu n Co clusters has a significant impact on the dipole moments of the clusters.The dipole moment (β) was greatly augmented after the chemisorption of HCOOH onto the Cu n Co clusters, and the β values of the HCOOH-Cu n Co . The sensitivity of the Cu n Pd and Cu n Au clusters towards the HCOOH molecule was calculated and the values estimated from Equation (3) indicate that the Cu n Pd and Cu n Pd clusters have good sensitivity for the detection of the HCOOH molecule, except for the Cu 3 Pd and Cu 8 Pd clusters where their sensitivity does not exceed 22%.A comparison between the sensibility values obtained for the two types of clusters suggests that the Cu n Au clusters present a high sensitivity to the HCOOH molecule in comparison with the Cu n Pd clusters.

Figure 10 .
Figure 10.The variation of (a) d M−O , (b) E ads , (c) H, and (d) G versus the number of the Cu n M (M = Co, Mn, V, Pd and Au) clusters atoms.
The substitution of a Co or Au atom by a Cu atom in the copper clusters conducts to decreases in the energy gap, except for the Cu 8 Pd and Cu 4 Au clusters where their E g were slightly increased.So, the binary clusters present high reactivity in comparison with the Cu n + 1 clusters.(3) The adsorption properties of the Cu n M (M = Co, Mn, Pd, Au and V) clusters towards the HCOOH molecule have also been evaluated, and the obtained results exhibit that the most favourable adsorption site for the HCOOH molecule is the metal atom dopant.And, the interaction between both species forms a strong binding between the O atom of the HCOOH molecule and the metal atom dopant of the clusters.The calculated values of the adsorption energies (E ad ) range from −113.4 to −436.0 kJ mol −1 , suggesting a chemisorption process.The values of H and G of the complexation process are found to be negative, reflecting that the adsorption between the HCOOH molecule and the Cu n M clusters is considered as an exothermic reaction and spontaneous phenomenon.NBO analysis reveals that the charge was transferred from the HCOOH molecule to the Cu n Co, Cu n Pd, Cu n Au and Cu n Mn clusters, where the amount of charge varies between +0.03 and +0.28 e.On the contrary, when the HCOOH-Cu n V complexes are formed, the charge transfer occurs from the Cu n V clusters to the HCOOH molecule, and the amounts of charge transferred between both species during the complexation process vary of −0.13 to −0.45 e. (4) The interaction of the molecule with the surface of the Cu n M (M = Co, Mn, Pd, Au and V) clusters was studied in order to evaluate their sensitivity performances.The results obtained reveal that the Cu n V and Cu n Au clusters have the highest sensitivity to the HCOOH molecule in comparison with the other clusters (Cu n Co, Cu n Pd and Cu n Mn).The results show also that the Cu n Co, Cu n Pd and Cu n Mn clusters possess an acceptable sensitivity towards the HCOOH molecule (except for the Cu 5 Co, Cu 6 Mn, Cu 7 Mn, Cu 3 Pd and Cu 8 Pd clusters where their sensitivity was found to be low), but it is less important than that obtained for the Cu n V and Cu n Au clusters.Therefore, the Cu n V and Cu n Au clusters could be promising candidates to be efficient nanosensors for the detection of the HCOOH molecule.
CONTACTMouhssin Boulbazine mohcene24@gmail.comThe Division of Research in Educational Technologies, National Institute for Research in Education, BP 193, Industrial Zone, Oued Romane El Achour, Alger 16104, Algeria Supplemental data for this article can be accessed online at https://doi.org/10.1080/00268976.2023.2237615.

Table 1 .
Spin Co, Mn, Pd, Au or V atom, E HCOOH−CunM and E HCOOH−Cun + 1 are the total energies of the HCOOH-Cu n M and HCOOH-Cu n + 1 respectively.E Cun + 1 and E CunM are the total energies of the Cu n + 1 and Cu n M clusters respectively.E HCOOH is the total energy of the HCOOH molecule.E BSSE is the energy of the basis set superposition error (BSSE).

Table 2 .
The charge on metal atom dopant (q M ), energy gap (E

Table 3 .
The interaction distance (d M−O ), charge transfer (q CT ), energy gap (E g ), sensitivity (S), adsorption energy (E ads ), change in enthalpy ( H ads ), change in Gibbs free-energy ( G ads ), and dipole moment (β) for the HCOOH-Cu n M complexes.The sensitivity of the clusters towards the HCOOH molecule is calculated at room temperature (298 K). *