Incremental Binding Energies Research Articles

Parity alternation of linear ground-state hydrogenated cationic carbon clusters HC nSi + ( n = 1–10)

Making use of molecular graphics software, we have designed numerous models of HC n Si + ( n = 1–10), and by means of the B3LYP density functional method, performed geometry optimization and calculation on vibrational frequency. The ground-state isomers of HC n Si + ( n = 1–10) are found to be linear with the Si and H atom located at the ends of the C n chain. When n is even, the C n chain is polyacetylene-like whereas when n is odd, the C n chain displays a structure that fades into a cumulenic-like arrangement towards the Si end. According to the results of mass spectrometric investigation available in the literature, the intensities of even- n HC n Si + are more intense than those of odd- n HC n Si +, implying that the former are more stable than the latter. We detect trends of odd/even alternation in electronic configuration, the highest vibrational frequency, ionization potential, incremental binding energy as well as in certain bond length and certain atomic charge of the linear ground-state structures of the HC n Si + ( n = 1–10) clusters. The calculation results reveal that the even- n cationic clusters are more stable than the odd- n ones.

Structures and stabilities of charged cobalt-doped carbon clusters

The structure and properties of the different linear, fan and cyclic isomers of CoC n + and CoC n − ( n = 1–8) clusters have been calculated using the B3LYP method with the 6–311+G(d) basis set. The stability of clusters as a function of the size has been discussed in terms of the incremental binding energies. Linear, fan and cyclic structures of CoC n + clusters show a clear even–odd alternation in stability, n-odd members being more stable than the corresponding n-even ones. An opposite parity effect is found for linear and fan CoC n − clusters, whereas the relative stability of cyclic isomers decrease with n. Linear structures are the most stable CoC n + and CoC n − clusters, with the only exception of CoC 2 +/− and CoC 7 − where the fan and cyclic arrangements are slightly lower in energy. The computed ionization potentials for the three structures show a clear even–odd alternation, with higher values for n-even clusters than for n-odd ones. Electron affinities for CoC n clusters increase along the series.

Geometries and stabilities of ( n + 4)-membered monocyclic C nB 4 ( n = 2–9) clusters

The DFT(B3LYP)/6-311+G(d) method is used to study the geometries, growth feature, and relative stability of 106 lower-energy isomers of monocyclic C n B 4 ( n = 2–9). Vibrational frequency analysis is performed to ensure the optimized isomers are stable at the same level. It is interesting to find that the formation of the lowest-energy isomers of monocyclic C n B 4 ( n = 2–9) is through joining –C m – ( m = 0–2) and –C n – ( n = 0–5) carbon chains by two B–C–B bridges under the constraint of C 2v symmetry (or D 2h symmetry if m = n). The stability of global minimum isomers is discussed based on their binding energies per atom, the incremental binding energy, second order energy difference, vertical ionization energy, vertical electron affinity, and average polarizability.

A density functional study of CoCn (n = 1–8) clusters: Structures and stabilities

AbstractA theoretical study of the different linear, fan and cyclic CoCn (n = 1–8) clusters has been carried out. Predictions for their electronic energies, rotational constants, dipole moments, and harmonic vibrational frequencies have been made using the B3LYP method with the 6‐311+G(d) basis set. Doublet and quartet lowest‐lying states have been found for neutral CoCn clusters. The stability of linear, fan, and cyclic structures as a function of the size of the cluster has been discussed in terms of the incremental binding energies. Only fan structures show a clear even‐odd alternation in stability. The incremental binding energies exhibit small changes along the series in the case of linear isomers, whereas for cyclic ones decrease along the series. It is also found that for the small CoCn clusters in general, the linear‐type structures are more stable than the fan and cyclic ones. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

H2O Nucleation around Au+

First principles electronic structure calculations have been carried out to investigate the ground state geometry, electronic structure, and the binding energy of [Au(H2O)n]+ clusters containing up to 10 H2O molecules. It is shown that the first coordination shell of Au+ contains two H2O molecules forming a H2O-Au+-H2O structure with C2 symmetry. Subsequent H2O molecules bind to the previous H2O molecules forming stable and fairly rigid rings, each composed of 4 H2O molecules, and leading to a dumbbell structure at [Au(H2O)8]+. The 9th and the 10th H2O molecules occupy locations above the Au+ cation mainly bonded to one H2O from each ring, leading to structures where the side rings are partially distorted and forming structures that resemble droplet formation around the Au+ cation. The investigations highlight quantum effects in nucleation at small sizes and provide a microscopic understanding of the observed incremental binding energy deduced from collision induced dissociation that indicates that [Au(H2O)n]+ clusters with 7-10 H2O molecules have comparable binding energy. The charge on the Au+ is shown to migrate to the outside H2O molecules, suggesting an interesting screening phenomenon.

Structures and properties of the tin-doped carbon clusters [formula omitted

A systemic density functional theory study of the tin-doped carbon clusters SnC n / SnC n + / SnC n - ( n = 1 – 10 ) has been carried out using B3LYP method with TZP+ basis set. For each species, the electronic states, relative energies and geometries of various isomers are reported. Except for smaller SnC 2 and the largest SnC 10 / SnC 10 + , the Sn-terminated linear or quasi-linear isomer is the most stable structure for SnC n / SnC n + / SnC n - clusters. The electronic ground state is alternate between 3Σ (for n-odd member) and 1Σ (for the n-even member) for linear SnC n and invariably 2Π for linear SnC n + and SnC n - , except for SnC/SnC +/SnC −, SnC 2 / SnC 2 + , SnC 4 + , SnC 6 + and SnC 10 / SnC 10 + . The incremental binding energy diagrams show that strong even–odd alternations in the cluster stability exist for both neutral SnC n and anionic SnC n - , with their n-even members being much more stable than the corresponding odd n − 1 and n + 1 ones, while for cationic SnC n + , the alternation effect is less pronounced. These parity effects also reflect in the ionization potential and electron affinity curves. By comparing with the fragmentation energies accompanying various channels, the most favorable dissociation channel for each kind of the SnC n / SnC n + / SnC n - clusters are given. All these results are very similar to those obtained previously for the PbC n / PbC n + / PbC n - clusters.

Aqueous Microsolvation of Mercury Halide Species†

The effects of aqueous solvation on the thermochemistry of reactions between mercury and small halogen molecules has been investigated by the microsolvation approach using ab initio and density functional theory (DFT) calculations. The structures, vibrational frequencies, and binding energies of 1, 2, and 3 water molecules with mercury-halide (HgBr2, HgBrCl, HgCl2, HgBr, and HgCl) and related mercury and halogen species (Br2, BrCl, Cl2, Cl, Hg, and Br) have been computed with second order Møller-Plesset perturbation theory (MP2) and the B3LYP density functional method. Accurate incremental water binding energies have been obtained at the complete basis set (CBS) limit using sequences of correlation consistent basis sets, including higher order correlation effects estimated from coupled cluster calculations. The resulting energetics were used to calculate the influence of water molecules on the thermochemistry of a number of reactions between mercury and small halogen-containing molecules. In general, the presence of water favors the formation of oxidized mercury halide species.

Application of the Computationally Efficient Self-Consistent-Charge Density-Functional Tight-Binding Method to Magnesium-Containing Molecules

The geometric properties, ionization potentials, heats of formation, incremental binding energies, and protonation energies for up to 75 magnesium-containing compounds have been studied using the self-consistent-charge density-functional tight-binding method (SCC-DFTB), the complete-basis set (CBS-QB3) method, traditional B3LYP density-functional theory, and a number of modern semiempirical methods such as Austin Model 1 (AM1), modified neglect of diatomic overlap without and with inclusion of d functions (MNDO, MNDO/d), and the Parametric Method 3 (PM3) and its modification (PM5). The test set contains some widely varying chemical motifs including ionic or covalent, closed-shell or radical compounds, and many biologically relevant complexes. Geometric data are compared to experiment, if available, and otherwise to previous high-level ab initio calculations or the present B3LYP results. SCC-DFTB is found to predict bond lengths to high accuracy, with the root-mean-square (RMS) error being less than half that found for the other semiempirical methods. However, SCC-DFTB performs very poorly for absolute heats of formation, giving an RMS error of 29 kcal mol(-1), but for this property B3LYP and the other semiempirical methods also yield poor but useful results with errors of 12-22 kcal mol(-1). Nevertheless, SCC-DFTB does provide useful results for biologically relevant chemical-process energies such as protonation energies (RMS error 10 kcal mol(-1), with the range 6-19 kcal mol(-1) found for the other semiempirical methods) and ligation energies (RMS error 9 kcal mol(-1), less than the errors of 12-23 kcal mol(-1) found for the other semiempirical methods). SCC-DFTB is shown to provide a computationally expedient means of calculating properties of magnesium compounds, providing results with at most double the inaccuracy of the high-quality but dramatically more-expensive B3LYP method.

Parity alternation of linear ground-state C nS 2− ( n = 6–18) clusters

Making use of the software of molecular graphics, we designed many patterns of C n S 2− ( n = 6–18) models. We carried out geometry optimization and calculation on vibrational frequency by means of the B3LYP density functional method. The most probable ground-state isomers of C n S 2− ( n = 6–18) are linear with the sulfur atom located at one end of the C n chain. When n is even, the isomer is polyacetylene-like. The C n S 2− ( n = 6–18) with even number of carbon atoms are more stable than those with odd number, matching the peak pattern observed in studies of mass spectrometry. The trend of odd/even alternation is also detected in certain bond length, atomic charge, electronic configuration, the highest vibrational frequency, energy difference, electron detachment energy, and incremental binding energy of the most probable ground-state isomers.

Structure and Stability of Small ZnCn Clusters.

A theoretical study of the small ZnCn (n = 1-8) clusters has been carried out at the B3LYP/6-311+G(d) level. Different molecular properties for open-chain and cyclic species have been calculated. The computed properties include electronic energies, vibrational frequencies, dipole moments, and rotational constants for individual species. In addition, the relative stability of the different clusters is also discussed in terms of the incremental binding energy. In the case of open-chain clusters, the lowest-lying states correspond to triplet states with the exception of ZnC2, whereas the electronic ground state is found to be a singlet state for cyclic clusters. The incremental binding energy graph shows a smooth even-odd parity effect in the incremental binding energy, n-even species being, in general, more stable than the adjacent odd-numbered ones. It was also found that the first members in the series, excepting ZnC2, prefer open-chain structures, whereas when n ≥ 6 cyclic ground states are favored.

Structures and stabilities of non-linear VC n+/− ( n = 1–8) clusters

A theoretical study of the different fan and cyclic isomers of VC n +/− ( n = 2–8) clusters has been carried out. Predictions for different molecular properties, such as electronic energies, harmonic vibrational frequencies or rotational constants, have been made using the B3LYP method with different basis set including effective core potentials, ECPs. In general, fan and cyclic structures have been predicted to prefer triplet ground states. The stability of fan and cyclic clusters as a function of the size has been discussed in terms of the incremental binding energies. For cationic systems a clear even–odd alternation in stability is found, n-even clusters being more stable than n-odd ones. This parity effect is also found for the first members of the fan isomers of VC n −, whereas for cyclic VC n − structures the stability decreases along the series. It is also found that VC n + systems with n < 5 prefer fan structures over linear ones, whereas for n = 5–7 the open-chain isomers are the most stable and for n = 8 cluster the cyclic structure is the most stable. Anionic vanadium-doped carbon clusters with n ≤ 5 prefer fan structures, whereas for n > 5 n-even clusters prefer open-chain structures and for VC 7 − the cyclic structure is the most stable.

Parity Alternation of Ground-State Pn- and Pn+ (n = 3−15) Phosphorus Clusters

The ground-state structures of neutral, cationic, and anionic phosphorus clusters P(n), P(n)(+), and P(n)(-) (n = 3-15) have been calculated using the B3LYP/6-311+G* density functional method. The P(n)(+) and P(n)(-) (n = 3-15) clusters with odd n were found to be more stable than those with even n, and we provide a satisfactory explanation for such trends based on concepts of energy difference, ionization potential, electron affinity, and incremental binding energy. The result of odd/even alternations is in good accord with the relative intensities of cationic and anionic phosphorus clusters observed in mass spectrometric studies.

A density functional study of the structures and energies of C nN 5− ( n = 1–13) clusters

We designed numerous models of C n N 5 − ( n = 1–13) using molecular graphics software. Geometry optimization and calculation of vibration frequency were carried out by means of the B3LYP density functional approach. After comparison of structure stability, we found that the ground-state structure of CN 5 − shows a N 4CN chain configuration whereas those of C n N 5 − ( n = 2–13) contain a planar pentagonal ring compose of nitrogen and carbon atoms when n ≤ 8, and of carbon atoms only when 9 ≤ n. For odd- n ground-state isomers with 1 < n ≤ 9, one carbon atom of the ring is bonded to a nitrogen atom and the other carbon atom(s) are bonded to a cyano (–CN) group. When n is even and with 2 ≤ n ≤ 10, all the carbon atom(s) within the ring are bonded to a cyano group. When n = 11–13, one of the carbon atoms of the ring is bonded to a straight NC 2–, NC 3– and NC 4– chain, respectively, while the other carbon atoms of the ring are each bonded to a cyano group. The NC 2– and NC 4– chains show cumulenic-like structures whereas the NC 3– chain shows polyacetylene-like structure. According to total energies, the C n N 5 − with even n are more stable than those with odd n, matching the peak patterns observed in the mass spectra of C n N 5 −. The trend of such odd/even alternation can be explained based on concepts of bonding characters, energy differences, electron affinities, and incremental binding energies.

Structure of small TiC n clusters: A theoretical study

A theoretical study of the TiC n ( n = 1–8) clusters has been carried out at the B3LYP/6-311+G(d) level. Molecular properties for three different isomers, namely linear, cyclic, and fan species, have been determined. The fan isomers, where the titanium atom is essentially side-bonded to the entire C n unit, are predicted to be more stable than both linear and cyclic isomers. Only for the largest studied species, TiC 8, the cyclic isomer is located lower in energy. An even–odd parity effect in the incremental binding energies is observed for the three isomers, n-even species being in general more stable for linear and fan isomers, whereas for the cyclic species n-odd clusters are favoured. A topological analysis of the electronic charge density shows that all cyclic isomers correspond to true monocyclic rings, whereas for the fan species a variety of different connectivities has been observed.

메탄올과 에탄올의 K+착물에 대한 Ab Initio 연구

K+(C2H5OH)n, (n=1~5) 착물에 대한 구조와 결합에너지에 대하여 MP2/full gen 6d와 MP2/6-311G**의 방법으로 계산하였다. n이 증가함에 따라 착물의 형태는 선형, 삼각형, 정사면체, 삼각이중피라밋 형태를 갖는 것으로 나타났고 K+-O의 길이는 용매 분자수가 증가함에 따라 증가하고 ∠K+OC도 증가하며 ∠K+OH는 n이 증가함에 따라 감소함을 보였다. 결합에너지는 n이 증가함에 따라 증가하나 순차적으로 증가하는 폭은 n이 커질수록 감소함을 볼 수 있었고 이는 용매분자간의 상호작용이 많은 영향을 주고 있는 것으로 나타났다. Ab initio calculations of the structure and the binding energies of K+(C2H5OH)n, (n=1~5) complexes were carried out with MP2/ full gen 6d and MP2/ 6-311G** methods. The stable structures of the complexes with n=2 to 5 were linear, trigonal, tetrahedral and trigonal bipyramid respectively. The binding energies of complexes were increased with the number of ligands, but the incremental binding energies were decreased. These results agreed well with the results of K+ complexes with other solvents.

Experimental and Theoretical Studies on Carbon−Nitrogen Clusters C2nN7-

C(2n)N7(-) cluster ions are produced by laser ablating on the K(3)[Fe(CN)6] sample. DFT calculations have been performed for these cluster anions. Various isomeric structures of these clusters are optimized and their energies are compared to find the most stable isomers. The most stable structure for C8N7(-) is similar to that of adenine by theoretical calculation, which is in agreement with the collision-induced dissociation (CID) experimental results. With the increasing even numbers of C atoms from 8 to 16, the N atoms in the double-ring structure are gradually substituted by C atoms from the six-membered ring to the five-membered ring. All these C(2n)N7(-) (n = 3-9) clusters exhibit planar aromatic characters. The energy difference and incremental binding energy analyses show that C(2n)N7(-) (n = 4-8) clusters are more stable than C6N7(-) and C18N7(-), which are consistent with the observed mass spectrum.

Parity alternation in the linear ground-state beryllium-doped carbon clusters BeC n− ( n = 1–8)

Making use of molecular graphics software, we designed numerous models of BeC n − ( n = 1–8). Geometry optimization and calculation on vibration frequency were carried out by the B3LYP density functional method. After comparison of structure stability, we found that the ground-state isomers of BeC n − ( n = 1–8) are linear with the beryllium atom located at one end of the C n chain, except that the linear BeC 5 − isomer is slightly higher in energy than the planar cyclic BeC 5 − isomer. When n is even, the C n chain of BeC n − ( n = 1–8) is polyacetylene-like whereas when at odd n, the carbon chain is cumulene-like. The BeC n − ( n = 1–8) with even n are found to be more stable than those with odd n, and the result is in good accord with the relative intensities of BeC n − ( n = 1–8) observed in mass spectrometric studies. In this paper, we provide satisfactory explanation for such trend of even/odd alternation based on concepts of bonding nature, electronic configuration, electron affinity, incremental binding energy, and dissociation channels.

Ionization potential and electron affinity of VC n ( n=1–8) open-chain clusters: A theoretical study

A DFT theoretical study of the VC n + , and VC n − ( n=1–8) open-chain clusters has been carried out using the B3LYP method. Results for several molecular properties which could help in their possible experimental characterization, such as equilibrium geometries, electronic energies, dipole moments, and vibrational frequencies are provided. For the VC n + open-chain clusters the lowest-lying states correspond to triplet states for n-odd members, whereas for n-even species the ground state is found to be a quintet one. In the case of VC n − species the electronic ground state is found to be a quintet for odd n and a triplet for even n. From the incremental binding energies we can deduce an even–odd parity effect, with n-odd clusters being more stable than n-even ones in the cationic clusters, whereas in the anionic system this effect is reversed. The ionization potentials and electron affinities of VC n linear clusters also exhibit a clear parity alternation trend, with n-even clusters having higher values than n-odd ones.

Small Carbon Clusters Doped with Vanadium Metal: A Density Functional Study of VCn (n = 1-8).

A theoretical study of the different isomers of neutral VCn (n = 1-8) clusters has been carried out. Predictions for their electronic energies, rotational constants, dipole moments, and vibrational frequencies have been made using the B3LYP method with different basis sets. For linear and cyclic VCn clusters, the lowest-lying states correspond to quartet states, with the only exception being VC, which has a (2)Δ ground state. In the fan-type structures, the electronic ground state is found to be a quartet state for even n values, whereas for odd n values, the ground state is a doublet for VC3 and VC5 and a quartet for VC7. From the incremental binding energies, we can deduce an even-odd parity effect, with n-even clusters being more stable than n-odd ones in the linear and fan clusters. It was also found that neutral VCn clusters with n ≤ 6 prefer fan structures over linear and cyclic isomers, whereas cyclic ground states are predicted for the clusters with n > 6.

A Density Functional Study on Beryllium-Doped Carbon Dianion Clusters CnBe2- (n = 4−14)

Making use of the software of molecular graphics, we designed numerous models of C(n)()Be(2-) (n = 4-14). We carried out geometry optimization and calculation on vibration frequency by means of the B3LYP density functional method. After comparison of structure stability, we found that the ground-state isomers of C(n)()Be(2-) (n = 4-14) are linear with the beryllium atom located inside the C(n)() chain. When a side carbon chain is with an even number of carbon atoms, it is polyacetylene-like, whereas when a side chain is with an odd number of carbon atoms, it is cumulene-like. The C(n)Be(2-) (n = 4-14) clusters with an even number of carbon atoms are more stable than that with an odd number of carbon atoms, matching the peak pattern observed in accelerator mass spectrometry (AMS) and Coulomb Explosion Imaging (CEI) investigations of C(n)()Be(2-) (n = 4-14). The trend of such odd/even alternation is explained based on concepts of bonding characteristics, electronic configuration, electron detachment, and incremental binding energy.