Fast and Accurate Calculation of the UV–Vis Spectrum with the Modified Local Excitation Approximation

The local excitation approximation (LEA), a method for the calculation of electronic excitations localized in a specific region of a molecule, has been modified with new approaches to enhance the accuracy of the original method. The primary concept behind LEA involves isolating the region of interest as a submolecule from the full molecule using a localization method, followed by calculating electronic excitations solely within this submolecule. In this study, we examined approaches that improve the accuracy in describing the region of interest, particularly its molecular orbital energies. Additionally, the localization method was extended with a new projection technique to accelerate calculations. These approaches were studied in time-dependent density functional theory (TDDFT) calculations applied to four testing systems with a chromophore as the region of interest: two basic linear molecules, acrolein surrounded by 24 water molecules, and a model of a green fluorescent protein. For all studied systems, the results of TDDFT calculations combined with LEA exhibited near-zero error when groups of atoms adjacent to the chromophore were explicitly included in the submolecule. This was achieved with at least a quadratic speedup of the calculation time as a function of the submolecule size

Fast and Accurate Calculation of the UV–Vis Spectrum with the Modified Local Excitation Approximation

The local excitation approximation (LEA), a method for the calculation of electronic excitations localized in a specific region of a molecule, has been modified with new approaches to enhance the accuracy of the original method. The primary concept behind LEA involves isolating the region of interest as a submolecule from the full molecule using a localization method, followed by calculating electronic excitations solely within this submolecule. In this study, we examined approaches that improve the accuracy in describing the region of interest, particularly its molecular orbital energies. Additionally, the localization method was extended with a new projection technique to accelerate calculations. These approaches were studied in time-dependent density functional theory (TDDFT) calculations applied to four testing systems with a chromophore as the region of interest: two basic linear molecules, acrolein surrounded by 24 water molecules, and a model of a green fluorescent protein. For all studied systems, the results of TDDFT calculations combined with LEA exhibited near-zero error when groups of atoms adjacent to the chromophore were explicitly included in the submolecule. This was achieved with at least a quadratic speedup of the calculation time as a function of the submolecule size

Substituent Effects on Menshutkin-Type Reactions in the Gas Phase and Solutions: Theoretical Approach from the Orbital Interaction View

In this study, we developed a method to interpret the mechanism of acceleration for Menshutkin-type reactions in solutions theoretically, from the orbital interaction view, utilizing the through-space/bond (TS/TB) interaction analysis in the polarizable continuum model (PCM). Different method levels were tested to determine the substituent effects on the reactions of NH₃ attacking para-substituted benzyl bromide. The geometrical structures and Mulliken charge distributions were analyzed to elucidate the substituent effects on the S_N2 reaction center. The results of Mulliken charge analysis showed that the para-substituted benzyl group (−C₆H₄Y) received negative charge through the reaction process, and both electron-donating and electron-withdrawing substituents Y made −C₆H₄Y groups receive greater charges. Solvent effects on the structures of transition states (T-S(s)) were significant. The structures of T-S(s) were found to be exhibiting longer bond lengths in solutions, especially in polar solvents such as water. Our TS/TB-PCM analysis method can predict the substituent effects in solutions by evaluating contributions from orbital interactions in question. The orbital interaction analysis results revealed that the key orbital interactions for stabilizing the T-S(s) of the systems with substituents Y = NH₂ and NO₂ in water were <i>n</i>(NH₂)−π*­(ph) (ph = phenyl) and π­(ph)−π*­(NO₂) interactions, respectively. Stronger interactions between π*­(ph) and σ*­(C_α-Br) occurred because of the <i>n</i>(NH₂)−π*­(ph) and π­(ph)−π*­(NO₂) interactions that resulted when para-substituents −NH₂ and −NO₂, respectively, were added to the system. These stronger π*­(ph)−σ*­(C_α-Br) interactions stabilized the transition state and enabled the Br leaving group to leave more easily

Bimetallic Clusters Pt₆Au: Geometric and Electronic Structures within Density Functional Theory

Within density functional theory at the general gradient approximation for exchange and correlation (BPW91) and the relativistic 19-electron Los Alamos National Laboratory effective core pseudopotentials and basis sets (3s3p2d), the geometric and electronic structures of Pt6Au bimetallic clusters have been studied in detail in comparison with Pt7. A total of 38 conformations for Pt6Au are located. The most stable conformation for Pt6Au is a sextet with an edge- and face-capped trigonal bipyramid, in which the Au atom caps an edge of the trigonal bipyramid. Pt6Au, in general, prefers a three-dimensional geometry and high spin electronic state with multireference character. The electronic impact of the doping of Au in Pt clusters on the overall chemical activity of the doped bimetallic cluster is not as significant as that of the doping of Pt in Au clusters; however, the doping of Au lowers the chemical activity, thus enhancing the chemoselectivity in the gas phase, of PtAu bimetallic clusters

Binary Clusters AuPt and Au₆Pt: Structure and Reactivity within Density Functional Theory

Within density functional theory with the general gradient approximation for the exchange and correlation, the bimetallic clusters AuPt and Au6Pt have been studied for their structure and reactivity. The bond strength of AuPt lies between those of Au2 and Pt2, and it is closer to that of Au2. The Pt atom is the reactive center in both AuPt and AuPt+ according to electronic structure analysis. AuPt+ is more stable than AuPt. Au6Pt prefers electronic states with low multiplicity. The most stable conformation of Au6Pt is a singlet and has quasi-planar hexagonal frame with Pt lying at the hexagonal center. The doping of Pt in Au cluster enhances the chemical regioselectivity of the Au cluster. The Pt atom essentially serves as electron donor and the Au atoms bonded to the Pt atom acts as electron acceptor in Au6Pt. The lowest triplet of edge-capped rhombus Au6Pt clusters is readily accessible with very small singlet−triplet energy gap (0.32 eV). O2 prefers to adsorb on Au and CO prefers to adsorb on Pt. O2 and CO have stronger adsorption on AuPt than they do on Au6Pt. CO has a much stronger adsorption on AuPt bimetallic cluster than O2 does. The adsorption of CO on Pt modifies the geometry of AuPt bimetallic clusters

Nonlinear Optical Properties of Alkalides Li⁺(calix[4]pyrrole)M^- (M = Li, Na, and K): Alkali Anion Atomic Number Dependence

A new type of alkalide compound, Li+(calix[4]pyrrole)M- (M = Li, Na, and K), is presented in theory, which may be stable at room temperature. It has been shown by our calculations that the first hyperpolarizability (β) is considerably large by means of the density functional theory method. The β values are determined at the B3LYP/6-311++G level (for the alkali atoms the 6-311++G(3df) basis set is employed) as 8.9 × 103, 1.0 × 104, and 2.4 × 104 au for M = Li, Na, and K, respectively. These β values are much larger than that of electride Li+(calix[4]pyrrole)e- (β = 7.3 × 103 au) by a factor of 1.2 to 3.4. Comparing to the cryptand calix[4]pyrrole, the β values of Li+(calix[4]pyrrole)M- are enhanced by 20−60 times. It is revealed, for the first time, that the β value of alkalide compounds depends on the atomic number of the alkali anion, and it can be enhanced by choosing the akali anions with larger atomic numbers. The alkali anion in the alkalide compound decreases the transition energy and also increases the oscillator strength of the main transition, consequently the β value is enhanced. This study proposes such a novel way to synthesize and design new NLO materials by using the alkali atom with a larger atomic number to create an anion in alkalide compounds

Lithium Salt Electride with an Excess Electron PairA Class of Nonlinear Optical Molecules for Extraordinary First Hyperpolarizability

A new lithium salt electride with an excess electron pair is designed, for the first time, by means of doping two sodium atoms into the lithium salt of pyridazine. For this series of electride molecules, the structures with all real frequencies and the static first hyperpolarizability (β0) are obtained at the second-order Møller−Plesset theory (MP2). Pyridazine H4C4N2 becomes the lithium salt of pyridazine Li−H3C4N2 as one H atom is substituted by Li. The lithium salt effect on hyperpolarizability is observed as the β0 value is increased by about 170 times from 5 to 859 au. For the electride effect, an electride H4C4N2···Na2 formed by doping two Na atoms into pyridazine, the β0 value is increased by about 3000 times from 5 to 1.5 × 104 au. Furthermore, combining these two effects, that is, lithium salt effect and electride effect, more significant increase in β0 is expected. A new lithium salt electride Li−H3C4N2···Na2 is thus designed by doping two Na atoms into Li−H3C4N2. It is found that the new lithium salt electride, Li−H3C4N2···Na2, has a very large β0 value (1.412 × 106 au). The β0 value is 2.8 × 105 times larger than that of H4C4N2, 1644 times larger than that of Li−H3C4N2, and still 93 times larger than that of the electride H4C4N2···Na2. This extraordinary β0 value is a new record and comes from its small transition energy and large difference in the dipole moments between the ground state and the excited state. The frequency-dependent β is also obtained, and it shows almost the same trends as H4C4N2 ≪ Li−H3C4N2 ≪ H4C4N2···Na2 ≪ Li−H3C4N2···Na2. This work proposes a new idea to design potential candidate molecules with high-performance NLO properties

Structures and Large NLO Responses of New Electrides: Li-Doped Fluorocarbon Chain

An alkali-metal-doped effect on the nonlinear optical (NLO) property in new electrides is studied. The electrides are formed by doping alkali atom Li into a fluorocarbon chain H−(CF2−CH2)3−H. Six stable structures of the Lin−H−(CF2−CH2)3−H (n = 1, 2) complexes with all real frequencies are obtained at the MP2/6-31+G (d) level. Among these six structures, the largest first static hyperpolarizabilities (β0) are found to be 76 978 au, which is much larger than the β0 value of 112 au for H−(CF2−CH2)3−H. Clearly, the Li-atom-doped effect on the first hyperpolarizability is dramatic. Three interesting relationships between the structure and β0 value have been observed. (1) For the one-Li-atom-doped systems as well as for the structures with two opposite Li atoms, the shorter the distance between the Li atom and difluoromethyl group, the larger the β0 value. (2) The β0 values of the two-Li-atom-doped chains are much larger than those of the one-Li-atom-doped systems, except for the case of cis-AB where the Li−Li distance (2.847 Å) is close to the bond length of the Li2 molecule (2.672 Å). (3) For the two-Li-atom-doped chains, the β0 value increases as the Li−Li distance increases. These relationships between the structure and β0 value may be beneficial to experimentalists for designing electrides with large NLO responses by using the alkali-metal-doped effect

Structures and Considerable Static First Hyperpolarizabilities: New Organic Alkalides (M⁺@<i>n</i>⁶adz)M‘^- (M, M‘ = Li, Na, K; <i>n</i> = 2, 3) with Cation Inside and Anion Outside of the Cage Complexants

Eighteen structures of new organic alkalides (M+@n6adz)M‘- (M, M‘ = Li, Na, K; n = 2, 3) with the alkali-metal cation M+ lying near the center of the adz cage and the alkali-metal anion M‘- located outside are obtained with all real frequencies. They exhibit very large static first hyperpolarizabilities (β0) up to 3.2 × 105 au, which exceeds the record value of β0 = 1.7 × 105 au for nonlinear optical compounds [Chem.Eur. J. 1997, 3, 1091]. All potassides (M+@n6adz)K- (M = Li, Na, K; n = 2, 3) have considerably large β0 values (1.6 × 105−3.2 × 105 au) much larger than the β0 value (3.6 × 104 au) of the previously designed cuplike alkalide Li+(calix[4]pyrrole)K- [J. Am. Chem. Soc. 2006, 128, 1072]. This shows that the 26adz and 36adz cage complexants are preferable to cuplike calix[4]pyrrole complexant in enhancing the first hyperpolarizability. The effect of cage size of the complexant on the first hyperpolarizability is also presented here:  in most cases, the smaller cage complexant corresponds to the larger β0 value. Moreover, the crucial role by the alkali-metal anion in the large first hyperpolarizability of these alkalides is revealed. These results may provide new means for designing high-performance nonlinear optical materials