Structures and Stabilities of Carbon Chain Clusters Influenced by Atomic Antimony

The C-C bond lengths of the linear magnetic neutral CnSb, CnSb+ cations and CnSb− anions are within 1.255–1.336 Å, which is typical for cumulene structures with moderately strong double-bonds. In this report, we found that the adiabatic ionization energy (IE) of CnSb decreased with n. When comparing the IE~n relationship of CnSb with that of pure Cn, we found that the latter exhibited a stair-step pattern (n ≥ 6), but the IE~n relationship of CnSb chains took the shape of a flat curve. The IEs of CnSb were lower than those of corresponding pure carbon chains. Different from pure carbon chains, the adiabatic electron affinity of CnSb does not exhibit a parity effect. There is an even-odd alternation for the incremental binding energies of the open chain CnSb (for n = 1–16) and CnSb+ (n = 1–10, when n > 10, the incremental binding energies of odd (n) chain of CnSb+ are larger than adjacent clusters). The difference in the incremental binding energies between the even and odd chains of both CnSb and pure Cn diminishes with the increase in n. The incremental binding energies for CnSb- anions do not exhibit a parity effect. For carbon chain clusters, the most favorable binding site of atomic antimony is the terminal carbon of the carbon cluster because the terminal carbon with a large spin density bonds in an unsaturated way. The C-Sb bond is a double bond with Wiberg bond index (WBI) between 1.41 and 2.13, which is obviously stronger for a carbon chain cluster with odd-number carbon atoms. The WBI of all C-C bonds was determined to be between 1.63 and 2.01, indicating the cumulene character of the carbon chain. Generally, the alteration of WBI and, in particular, the carbon chain cluster is consistent with the bond length alteration. However, the shorter C-C distance did not indicate a larger WBI. Rather than relying on the empirical comparison of bond distance, the WBI is a meaningful quantitative indicator for predicting the bonding strength in the carbon chain

Strong Designated Verifier Signature Scheme with Undeniability and Strong Unforgeability in the Standard Model

Strong designated verifier signature can provide an efficient way to protect the identity privacy of the signer and the integrity of the data transmitted over the public channel. These characteristics make it very useful in outsourcing computing, electronic voting, electronic bidding, electronic auction and other fields. However, most strong designated verifier signature schemes are unable to identify the real signature generator when the signer and the designated verifier dispute a signature. In addition, the existing strong designated verifier signature schemes in the standard model rarely satisfy strong unforgeability, and thus cannot prevent the attacker from forging a valid signature on any previously signed message. Therefore, designing a strong designated verifier signature scheme without random oracles that satisfies strong unforgeability and undeniability is very attractive in both practice and theory. Motivated by these concerns, we design the first undeniable strong designated verifier signature scheme without random oracles, in which the arbiter can independently perform the judgment procedure to prove whether a controversial signature is generated by the signer or the designated verifier. Under standard assumptions, the scheme is proved to be strongly unforgeable in standard model. Furthermore, it not only achieves non-transferability and privacy of the signer’s identity but also satisfies the undeniable property of traditional digital signature schemes. Performance analysis results show that the length of the signer’s private key, the designated verifier’s private key and signature length are 40 bits, 40 bits and 384 bits, respectively. Compared with he related schemes, the proposed scheme has higher performance in signature length, private key size and computational overhead. Finally, we show how to apply it to implement outsourcing computation in cloud computing

Structures and Stabilities of Carbon Chain Clusters Influenced by Atomic Antimony

The C-C bond lengths of the linear magnetic neutral CnSb, CnSb+ cations and CnSb− anions are within 1.255–1.336 Å, which is typical for cumulene structures with moderately strong double-bonds. In this report, we found that the adiabatic ionization energy (IE) of CnSb decreased with n. When comparing the IE~n relationship of CnSb with that of pure Cn, we found that the latter exhibited a stair-step pattern (n ≥ 6), but the IE~n relationship of CnSb chains took the shape of a flat curve. The IEs of CnSb were lower than those of corresponding pure carbon chains. Different from pure carbon chains, the adiabatic electron affinity of CnSb does not exhibit a parity effect. There is an even-odd alternation for the incremental binding energies of the open chain CnSb (for n = 1–16) and CnSb+ (n = 1–10, when n > 10, the incremental binding energies of odd (n) chain of CnSb+ are larger than adjacent clusters). The difference in the incremental binding energies between the even and odd chains of both CnSb and pure Cn diminishes with the increase in n. The incremental binding energies for CnSb− anions do not exhibit a parity effect. For carbon chain clusters, the most favorable binding site of atomic antimony is the terminal carbon of the carbon cluster because the terminal carbon with a large spin density bonds in an unsaturated way. The C-Sb bond is a double bond with Wiberg bond index (WBI) between 1.41 and 2.13, which is obviously stronger for a carbon chain cluster with odd-number carbon atoms. The WBI of all C-C bonds was determined to be between 1.63 and 2.01, indicating the cumulene character of the carbon chain. Generally, the alteration of WBI and, in particular, the carbon chain cluster is consistent with the bond length alteration. However, the shorter C-C distance did not indicate a larger WBI. Rather than relying on the empirical comparison of bond distance, the WBI is a meaningful quantitative indicator for predicting the bonding strength in the carbon chain

Structures and Stabilities of Carbon Chain Clusters Influenced by Atomic Antimony

The C-C bond lengths of the linear magnetic neutral CnSb, CnSb+ cations and CnSb− anions are within 1.255–1.336 Å, which is typical for cumulene structures with moderately strong double-bonds. In this report, we found that the adiabatic ionization energy (IE) of CnSb decreased with n. When comparing the IE~n relationship of CnSb with that of pure Cn, we found that the latter exhibited a stair-step pattern (n ≥ 6), but the IE~n relationship of CnSb chains took the shape of a flat curve. The IEs of CnSb were lower than those of corresponding pure carbon chains. Different from pure carbon chains, the adiabatic electron affinity of CnSb does not exhibit a parity effect. There is an even-odd alternation for the incremental binding energies of the open chain CnSb (for n = 1–16) and CnSb+ (n = 1–10, when n > 10, the incremental binding energies of odd (n) chain of CnSb+ are larger than adjacent clusters). The difference in the incremental binding energies between the even and odd chains of both CnSb and pure Cn diminishes with the increase in n. The incremental binding energies for CnSb− anions do not exhibit a parity effect. For carbon chain clusters, the most favorable binding site of atomic antimony is the terminal carbon of the carbon cluster because the terminal carbon with a large spin density bonds in an unsaturated way. The C-Sb bond is a double bond with Wiberg bond index (WBI) between 1.41 and 2.13, which is obviously stronger for a carbon chain cluster with odd-number carbon atoms. The WBI of all C-C bonds was determined to be between 1.63 and 2.01, indicating the cumulene character of the carbon chain. Generally, the alteration of WBI and, in particular, the carbon chain cluster is consistent with the bond length alteration. However, the shorter C-C distance did not indicate a larger WBI. Rather than relying on the empirical comparison of bond distance, the WBI is a meaningful quantitative indicator for predicting the bonding strength in the carbon chain