| (1) By counterpoise-corrected optimization method, the sixantiaromatic ring π multi-hydrogen bond structures with diversiform shapesfor (H2O)n-C4H4 (n = 1,2) have been obtained at the MP2/aug-cc-pVDZ level.At the CCSD(T)/aug-cc-pVDZ level, the interaction energy obtained mainlydepends on the numbers of H2O and fold numbers of π multi-hydrogen bond.The interaction energy order is -2.342 (1(a) with π mono-hydrogen) < -2.777(1(b) with π bi-hydrogen) << -4.683 (2(a) with π bi-hydrogen) < -4.734 (2(b)with π tri-hydrogen) < -4.782 (2(c) with π tri-hydrogen) < -5.009 kcal/mol (2(d)with π tetra-hydrogen bond). Strangely, why the interaction energy of the πbi-hydrogen bond in 1 (b) is close to that of the π mono-hydrogen bond in 1(a)(their difference is only 15.7%)? The reason is that a π-type H-bond (as anaccompanying interaction) between two lone pairs of the O atom and a nearpair of H atoms of C4H4 exists with shoulder by shoulder in the 1(a), 2(a), 2(b)and 2(c) and contributes to the interaction energy. Another accompanyinginteraction, repulsive interaction between π H-bond (using the H atom(s) ofH2O) and near pair of H atoms of C4H4 also is found. For the structures andinteraction energies, the π-type H-bond produces four effects: bending thestrong π H-bond, attracting the pair of H atoms of C4H4 to deviate from C4ring plane, showing the interaction energy contribution, and bringing the largerelectron correlation contribution. The repulsive interaction also produces foureffects: pushing the pair of H atoms of C4H4 to deviate from its ring plane,elongating distance of the π H-bond, promoting the forming of π-type H-bond,and slightly influencing the interaction energy. In present paper, one C=C bondwith two H2O (over and below the ring plane) forms π H-bond link in twoways: strong-weak π H-bond link and strong-strong π H-bond link. Thestability contribution of the former is more favorable than the latter. One H2Oforms π H-bond with C4H4 in two ways. One strong π H-bond part (over orbelow the ring plane) always is accompanied by another H-bond part. Theaccompanying part is either weak π H-bond or π-type H-bond.(2) In order to explore the coordination number (around the cation)dependence of the nonlinear optical (NLO) properties in alkalides, this paperstudies the structures and large NLO responses of model alkalides,Li(NH3)nNa (n=1-4). At the MP2/aug-cc-pVDZ level, the structuralcharacteristic is determined as that the Li-Na distance increases (from 3.030 ?to 4.646 ?) with the increasing of the number of NH3 (n from 1 to 4). Resultsshow that Li(NH3)nNa (n=1-4) have considerably large firsthyperpolarizabilities (β0). Especially, a prominent coordination numberdependence of the β0 value is found as: β0 = 13669 (n=1) < 26840 (n=2) <39764 (n=3) < 77921 au (n=4) at the MP2 level. With the same coordinationnumber (four N atoms) of Li+ cation, the β0 value (77921 au) of this "small"inorganic molecule Li(NH3)nNa is over five times larger than that of the "big"organic molecule Li@Calix[4]pyrrole-Na (14772 au). This indicates that theβ0 value is strongly related to the flexibility of the complexant. Obviously, theflexibility of (NH3)4 is much greater than that of the cup-like shapeCalix[4]pyrrole. This work suggests that two important factors should be takeninto account to enhance the first hyperpolarizability of alkalide, i.e., thecoordination number around the cation and the flexibility of the complexant.(3) Complexant shape effect on the first hyperpolarizability (β0) ofalkalide system, Li+(NH3)4M-(M= Li, Na and K), is explored. As determinedat the MP2/6-311++G level, Li+(NH3)4M-(M= Li, Na and K) haveconsiderably large β0 value due to excess electrons from the chemical dopingand charge-transfer. Compared to the alkalide systems Li+(calix[4]pyrrole)M-,the complexant shape effect in Li+(NH3)4M-is detected. The β0 values ofLi+(NH3)4M-with "smaller" inorganic Td symmetry (NH3)4 complexant areover four times larger than those of Li+(calix[4]pyrrole)M-with "bigger"organic C4V symmetry calix[4]pyrrole complexant. The ratios of β0 valuesbetween Li+(NH3)4M-and Li+(calix[4]pyrrole)M-are 6.57 (M=Li), 6.55(M=Na) and 5.17 (M=K), respectively. In the Li+(NH3)4M-systems, it is foundthat the alkali anion atomic number monotonously depends upon the NBOcharge and oscillator strength. The order of the NBO charges of alkali anion(M-) is -0.667 (M=Li) > -0.644 (M=Na) > -0.514 (M=K), whereas the order ofthe oscillator strengths in crucial transition is 0.351 (M=Li) < 0.360 (M=Na) <0.467 (M=K). This indicates the complexant shape effects are strong andconsequently the β0 values of Li+(NH3)4M-are found as: β0 = 70295 (M=Li) <96780 (M=Na) < 185805 au (M=K). This work reveals that an importantfactor should be taken into account to enhance the first hyperpolarizability ofalkalide from special chemical doping, i.e., using high symmetry complexant.
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