Identification of agronomically favorable quantitative trait loci alleles from a dent corn inbred Dan232 using advanced backcross QTL analysis and comparison with the F<Subscript>2:3</Subscript> population in popcorn

Specific traits are an important consideration in plant breeding. In popcorn, inferior agronomic traits could be improved using dent or flint corn backcrossed with popcorn. In this study, we used advanced backcross quantitative trait locus (AB-QTL) analysis to identify trait-improving QTL alleles from a dent maize inbred Dan232, and compared the detection of QTL in the BC₂S₁ population with QTL results using F_2:3 families of the same population. Two hundred and twenty BC₂S₁ families developed from a cross between Dan232 and an elite popcorn inbred N04 were evaluated for nine plant traits in replicated field trials under two environments. Using composite interval mapping (CIM), a total of 28 significant QTL were detected, and of these, 23 (82.14%) had favorable alleles contributed by the dent corn parent Dan232. Nine QTL (32.14%) detected in the BC₂S₁ population were also located in or near the same chromosome intervals in the F_2:3 population. All of the favorable QTL alleles from Dan232 could be used in marker-assisted selection (MAS) to improve the respective plant traits in popcorn breeding. In addition, their near isogenic lines (QTL-NILs) could be obtained through selfing or another 1–2 backcross with N04. Also, N04 improved for the studied plant traits could be developed from the BC₂S₁ families used in this study. This study demonstrated that the AB-QTL method can be applied to identify favorable QTL from dent corn inbred in popcorn breeding and, once identified, the alleles could be used in marker-assisted selection to improve the respective plant traits.     

Advanced backcross QTL analysis in progenies derived from a cross between a German elite winter wheat variety and a synthetic wheat (<Emphasis Type="Italic">Triticum aestivum</Emphasis>L.)

We report here the second advanced backcross quantitative trait locus (AB-QTL) analysis carried out in winter wheat. Seven agronomic traits were studied in a BC₂F₁population derived from a cross between the German winter wheat variety Flair and the synthetic wheat line XX86 developed in Japan. We selected 111 BC₂F₁ lines and genotyped these with 197 microsatellite markers. Field data for seven agronomic traits were collected from corresponding BC₂F₃ families that were grown at up to six locations in Germany. QTL analyses for yield and yield components were performed using single-marker regression and interval mapping. A total of 57 putative QTLs derived from XX86 were detected, of which 24 (42.1%) were found to have a positive effect from the synthetic wheat XX86. These favourable QTLs were mainly associated with thousand-grain weight and grain weight per ear. Many QTLs for correlated traits were mapped in similar chromosomal regions. The AB-QTL data obtained in the present study are discussed and compared with results from previous QTL analyses.     

Mapping QTL for popping expansion volume in popcorn with simple sequence repeat markers

Popping expansion volume is the most important quality trait in popcorn ( Zea mays L.), but its genetics is not well understood. The objectives of this study were to map quantitative trait loci (QTLs) responsible for popping expansion volume in a popcorn x dent corn cross, and to compare the predicted efficiencies of phenotypic selection, marker-based selection, and marker-assisted selection for popping expansion volume. Of 259 simple sequence repeat (SSR) primer pairs screened, 83 pairs were polymorphic between the H123 (dent corn) and AG19 (popcorn) parental inbreds. Popping test data were obtained for 160 S(1) families developed from the [AG19(H123 x AG19)] BC(1) population. The heritability ( h(2)) for popping expansion volume on an S(1) family mean basis was 0.73. The presence of the gametophyte factor Ga1(s) in popcorn complicates the analysis of popcorn x dent corn crosses. But, from a practical perspective, the linkage between a favorable QTL allele and Ga1(s) in popcorn will lead to selection for the favorable QTL allele. Four QTLs, on chromosomes 1S, 3S, 5S and 5L, jointly explained 45% of the phenotypic variation. Marker-based selection for popping expansion volume would require less time and work than phenotypic selection. But due to the high h(2) of popping expansion volume, marker-based selection was predicted to be only 92% as efficient as phenotypic selection. Marker-assisted selection, which comprises index selection on phenotypic and marker scores, was predicted to be 106% as efficient as phenotypic selection. Overall, our results suggest that phenotypic selection will remain the preferred method for selection in popcorn x dent corn crosses.     

QTL consistency and meta-analysis for grain yield components in three generations in maize

Grain yield is the most important and complex trait in maize. In this study, a total of 258 F₉ recombinant inbred lines (RIL), derived from a cross between dent corn inbred Dan232 and popcorn inbred N04, were evaluated for eight grain yield components under four environments. Quantitative trait loci (QTL) and their epistatic interactions were detected for all traits under each environment and in combined analysis. Meta-analysis was used to integrate genetic maps and detected QTL across three generations (RIL, F_2:3 and BC₂F₂) derived from the same cross. In total, 103 QTL, 42 pairs of epistatic interactions and 16 meta-QTL (mQTL) were detected. Twelve out of 13 QTL with contributions (R ²) over 15% were consistently detected in 3–4 environments (or in combined analysis) and integrated in mQTL. Only q100GW-7-1 was detected in all four environments and in combined analysis. 100qGW-1-1 had the largest R ² (19.3–24.6%) in three environments and in combined analysis. In contrast, 35 QTL for 6 grain yield components were detected in the BC₂F₂ and F_2:3 generations, no common QTL across three generations were located in the same marker intervals. Only 100 grain weight (100GW) QTL on chromosome 5 were located in adjacent marker intervals. Four common QTL were detected across the RIL and F_2:3 generations, and two between the RIL and BC₂F₂ generations. Each of five important mQTL (mQTL7-1, mQTL10-2, mQTL4-1, mQTL5-1 and mQTL1-3) included 7–12 QTL associated with 2–6 traits. In conclusion, we found evidence of strong influence of genetic structure and environment on QTL detection, high consistency of major QTL across environments and generations, and remarkable QTL co-location for grain yield components. Fine mapping for five major QTL (q100GW-1-1, q100GW-7-1, qGWP-4-1, qERN-4-1 and qKR-4-1) and construction of single chromosome segment lines for genetic regions of five mQTL merit further studies and could be put into use in marker-assisted breeding.     

Theory for identification of marker locus-QTL associations in population by line crosses

The objective of this paper is to present genetic theory demonstrating the conditions under which it should be possible to identify molecular marker-quantitative trait locus (QTL) associations in crosses of random-mating populations to inbreds. Using as an example the cross of a corn (Zea mays L.) population to an inbred, the expected disequilibrium for testcross and per se performance of F₂, F₃, BC₁ (to the inbred) and recombinant inbred generations was derived for cases where a marker allele is linked to an unfavorable QTL allele in the inbred and where the marker allele is linked to a favorable QTL allele in the inbred. Disequilibrium in segregating generations was shown to be a function of disequilibrium in the parent population, the frequency of marker and QTL alleles in the parent population, and the recombination distance between the marker and the QTL. To maximize the opportunity to identify a favorable QTL the following procedures are suggested:

QTL Analysis of Popping Fold and the Consistency of QTLs Under Two Environments in Popcorn

Popping fold (PF) is the most important quality trait in popcorn. In this study, a total of 259 F_2:3 families, derived from the cross between a dent corn inbred Dan232 and a popcorn inbred N04, were evaluated for their popping folds in replicated experiments under two environments. Of 613 simple sequence repeat (SSR) primer pairs screened, 183 pairs were selected to construct a genetic linkage map with the genetic distance of 1 762.2 cM (centimorgan) and on average 9.63 cM every marker. Quantative trait loci (QTL) were identified, and their genetic effects were estimated using CIM (composite interval mapping) method. The interactions among QTLs detected were calculated using MIM (multiple interval mapping) method. In all, 22 QTLs were detected, and only 5 of them were common under two environments. Contribution to phenotypic variation of a single QTL varied from 3.07% to 12.84%, and total contributions of all QTLs under two environments were 66.46% and 51.90%, respectively. Three QTLs (qPF-6-1, qPF-8-1 and qPF-1-3) with more than 10% contributions were observed. The additive effects were larger than dominant effects for most QTLs. The amount of QTLs showing additive, partially dominant, dominant and over-dominant effects were 4, 5, 0, 2 in spring sowing and 2, 5, 2, 2 in summer sowing, respectively. There were only 2.60% pairs of QTLs or maker intervals expressing AA, DA or DD interactions.     

利用三倍体胚乳遗传模型定位玉米籽粒淀粉含量QTL

在两种环境条件下种植以普通玉米自交系丹232和爆裂玉米自交系N04为亲本构建的259个F2:3家系群体, 采用SSR标记构建了包含183个标记的玉米遗传连锁图谱, 覆盖玉米基因组1 762.2 cM, 标记间平均距离为9.6 cM。利用三倍体胚乳遗传模型和区间作图方法对籽粒淀粉含量进行了QTL定位和遗传效应分析, 春、夏播条件下共检测到10个QTL, 春播条件下检测到的QTL在夏播均被检测到, 分别位于第1、3、4、5、7染色体上,可解释淀粉的表型总变异分别为36.84%和72.65%, 单个QTL解释表型变异介于4.74%~11.26%。在检测到的 QTL中, 有2个QTL的遗传作用方式在春播均表现为超显性, 而夏播分别为加性和部分显性; 其他2个为加性, 1个为部分显性, 5个为超显性。3个QTL的增效基因来自丹232, 其余QTL的增效基因均来自N04。     

爆裂玉米胚乳数量性状的遗传研究

采用三倍体胚乳种子遗传模型及其分析方法,研究了4个爆裂玉米膨爆特性的胚乳直接效应、母体效应和细胞质效应。结果表明,百粒重、膨化体积的遗传同时由3套遗传体系所控制,百粒重的细胞质、膨化体积的母体和细胞质遗传率较高。爆花率和膨化倍数受胚乳和母体2套遗传体系的影响,且遗传率相近。爆花率和膨化倍数的直接和母体杂种优势均为负值。要组配出优良爆裂玉米杂交种,必须首先选育出膨爆特性突出的自交系,同时还要注意不同自交系的恰当组配。在6个供试自交系中,必须首先选育出膨爆特性突出的自交系,同时还要注意不同自交系的恰当组配。在6个供试自交系中,P3,P4适宜用作母本,P5则适宜作父本。     

Influence of dent corn genetic backgrounds on QTL detection for plant-height traits and their relationships in high-oil maize

QTL mapping for plant-height traits has not been hitherto reported in high-oil maize. A high-oil maize inbred ‘GY220’ was crossed with two dent maize inbreds (‘8984’ and ‘8622’) to generate two connected F_2:3 populations. Four plant-height traits were evaluated in 284 and 265 F_2:3 families. Single-trait QTL mapping and multiple-trait joint QTL mapping was used to detect QTLs for the traits and the genetic relationship between plant height (PH) and two other plant-height traits. A total of 28 QTLs and 12 pairs of digenic interactions among detected QTLs for four traits were detected in the two F_2:3 families. Only one marker was shared between the two populations. Joint analysis of PH with ear height (EH) and PH with top height (TH) detected 32 additional QTLs. Our results showed that QTL detection for PH was dependent on the genetic background of dent corn inbreds. Multiple-trait joint QTL analysis could increase the number of detected QTLs.     

AB-QTL analysis in winter wheat: I. Synthetic hexaploid wheat (<Emphasis Type="Italic">T. turgidum</Emphasis> ssp. <Emphasis Type="Italic">dicoccoides </Emphasis> × <Emphasis Type="Italic">T. tauschii</Emphasis>) as a source of favourable alleles for milling and baking quality traits

The advanced backcross QTL (AB-QTL) strategy was utilised to locate quantitative trait loci (QTLs) for baking quality traits in two BC₂F₃ populations of winter wheat. The backcrosses are derived from two German winter wheat cultivars, Batis and Zentos, and two synthetic, hexaploid wheat accessions, Syn022 and Syn086. The synthetics originate from hybridisations of wild emmer (T. turgidum spp. dicoccoides) and T. tauschii, rather than from durum wheat and T. tauschii and thus allowed for the first time to test for exotic QTL effects on wheat genomes A and B in addition to genome D. The investigated quality traits comprised hectolitre weight, grain hardness, flour yield Type 550, falling number, grain protein content, sedimentation volume and baking volume. One hundred and forty-nine SSR markers were applied to genotype a total of 400 BC₂F₃ lines. For QTL detection, a mixed-model ANOVA was conducted, including the effects DNA marker, BC₂F₃ line, environment and marker × environment interaction. Overall 38 QTLs significant for a marker main effect were detected. The exotic allele improved trait performance at 14 QTLs (36.8%), while the elite genotype contributed the favourable effect at 24 QTLs (63.2%). The favourable exotic alleles were mainly associated with grain protein content, though the greatest improvement of trait performance due to the exotic alleles was achieved for the traits falling number and sedimentation volume. At the QTL on chromosome 4B the exotic allele increased the falling number by 19.6% and at the QTL on chromosome 6D the exotic allele led to an increase of the sedimentation volume by 21.7%. The results indicate that synthetic wheat derived from wild emmer × T. tauschii carries favourable QTL alleles for baking quality traits, which might be useful for breeding improved wheat varieties by marker-assisted selection.     

Verification and fine mapping of <Emphasis Type="Italic">qGW1.05</Emphasis>, a major QTL for grain weight in maize (<Emphasis Type="Italic">Zea mays</Emphasis> L.)

Grain weight, one of the important factors to determine corn yield, is a typical quantitative inheritance trait. However, the molecular genetic basis of grain weight still remains limited. In our previous researches, a major QTL associated with grain weight, qGW1.05, has been identified between SSR markers umc1601 and umc1754 at bin locus 1.05–1.06 in maize. Here, its genetic and environmental stabiliteis were verified using a BC₃F₂ population to identify the effect of qGW1.05 on grain weight. Further, qGW1.05-NILs were obtained by MAS successfully. Via a large BC₆F₂ segregation population, together with polymorphic microsatellite markers developed between the parents to screen the genotype of the recombinant plants, qGW1.05 was positioned to a 1.11 Mb genome interval. Furthermore, the progenies of 15 recombinants were tested to confirm the effect of qGW1.05 on grain weight. Combining collinearity among cereal crops and genome annotation, the several candidate genes taking part in grain development were identified in the qGW1.05 region. In this study, qGW1.05 was limited to a 1.11 Mb region on chromosome 1, which established the foundation for understanding the molecular basis underlying kernel development and improving grain weight through MAS using the tightly flanking molecular markers in maize.     

QTL mapping for test weight by using F<Subscript><Emphasis Type="Bold">2:3</Emphasis></Subscript> population in maize

Test weight is an important trait in maize breeding. Understanding the genetic mechanism of test weight is important for effective selection of maize test weight improvement. In this study, quantitative trait loci (QTL) for maize test weight were identified. In the years 2007 and 2008, a F_2:3 population along with the parents Chang7-2 and Zheng58 were planted in Zhengzhou, People’s Republic of China. Significant genotypic variation for maize test weight was observed in both years. Based on the genetic map containing 180 polymorphic SSR markers with an average linkage distance of 11.0 cM, QTL for maize test weight were analysed by mixed-model composite interval mapping. Five QTL, including four QTL with only additive effects, were identified on chromosomes 1, 2, 3, 4 and 5, and together explained 25.2% of the phenotypic variation. Seven pairs of epistatic interactions were also detected, involving 11 loci distributed on chromosomes 1, 2, 3, 4, 5 and 7, respectively, which totally contributed 18.2% of the phenotypic variation. However, no significant QTL × environment (Q×E) interaction and epistasis × environment interaction effects were detected. The results showed that besides the additive QTL, epistatic interactions also formed an important genetic basis for test weight in maize.     

Mapping quantitative trait loci for yield components and morphological traits in an advanced backcross population between Oryza grandiglumis and the O. sativa japonica cultivar Hwaseongbyeo

Introgression has been achieved from wild species Oryza grandiglumis (2n=48, CCDD, Acc. No. 101154) into O. sativa subsp. japonica cv. Hwaseongbyeo as a recurrent parent. An advanced introgression (backcross) line, HG101, produced from a single plant from BC₅F₃ families resembled Hwaseongbyeo, but it showed differences from Hwaseongbyeo in several traits, including days to heading and culm length. To detect the introgressions, 450 microsatellite markers of known chromosomal position were used for the parental survey. Of the 450 markers, 51 (11.3%) detected O. grandiglumis segments in HG101. To characterize the effects of alien genes introgressed into HG101, an F_2:3 population (150 families) from the cross Hwaseongbyeo/HG101 was developed and evaluated for 13 agronomic traits. Several lines outperformed Hwaseongbyeo in several traits, including days to heading. Genotypes were determined for 150 F₂ plants using simple sequence repeat markers. Qualitative trait locus (QTL) analysis was carried out to determine the relationship between marker genotype and the traits evaluated. A total of 39 QTL and 1 gene conferring resistance to blast isolate were identified using single-point analysis. Phenotypic variation associated with each QTL ranged from 4.2 to 30.5%. For 18 (46.2%) of the QTL identified in this study, the O. grandiglumis-derived alleles contributed a desirable agronomic effect despite the overall undesirable characteristics of the wild phenotype. Favorable wild alleles were detected for days to heading, spikelets per panicle, and grain shape traits. Grain shape QTL for grain weight, thickness, and width identified in the F_2:3 lines were further confirmed based on the F₄ progeny test. The confirmed locus, tgw2 for grain weight is of particular interest because of its independence from undesirable height and maturity. Several QTL controlling amylose content and grain traits have not been detected in the previous QTL studies between Oryza cultivars, indicating potentially novel alleles from O. grandiglumis. The QTL detected in this study could be a rich source of natural genetic variation underlying the evolution and breeding of rice.     

Identification of QTLs for Yield and Associated Traits in F₂ Population of Rice

Identification of quantitative trait loci (QTLs) controlling yield and yield-related traits in rice was performed in the F₂ mapping population derived from parental rice genotypes DHMAS and K343. A total of 30 QTLs governing nine different traits were identified using the composite interval mapping (CIM) method. Four QTLs were mapped for number of tillers per plant on chromosomes 1 (2 QTLs), 2 and 3; three QTLs for panicle number per plant on chromosomes 1 (2 QTLs) and 3; four QTLs for plant height on chromosomes 2, 4, 5 and 6; one QTL for spikelet density on chromosome 5; four QTLs for spikelet fertility percentage (SFP) on chromosomes 2, 3 and 5 (2 QTLs); two QTLs for grain length on chromosomes 1 and 8; three QTLs for grain width on chromosomes1, 3 and 8; three QTLs for 1000-grain weight (TGW) on chromosomes 1, 4 and 8 and six QTLs for yield per plant (YPP) on chromosomes 2 (3 QTLs), 4, 6 and 8. Most of the QTLs were detected on chromosome 2, so further studies on chromosome 2 could help unlock some new chapters of QTL for this cross of rice variety. Identified QTLs elucidating high phenotypic variance can be used for marker-assisted selection (MAS) breeding. Further, the exploitation of information regarding molecular markers tightly linked to QTLs governing these traits will facilitate future crop improvement strategies in rice.     

Bayesian QTL mapping using genome-wide SSR markers and segregating population derived from a cross of two commercial F<Subscript>1</Subscript> hybrids of tomato

Key message

Using newly developed euchromatin-derived genomic SSR markers and a flexible Bayesian mapping method, 13 significant agricultural QTLs were identified in a segregating population derived from a four-way cross of tomato.

Abstract

So far, many QTL mapping studies in tomato have been performed for progeny obtained from crosses between two genetically distant parents, e.g., domesticated tomatoes and wild relatives. However, QTL information of quantitative traits related to yield (e.g., flower or fruit number, and total or average weight of fruits) in such intercross populations would be of limited use for breeding commercial tomato cultivars because individuals in the populations have specific genetic backgrounds underlying extremely different phenotypes between the parents such as large fruit in domesticated tomatoes and small fruit in wild relatives, which may not be reflective of the genetic variation in tomato breeding populations. In this study, we constructed F₂ population derived from a cross between two commercial F₁ cultivars in tomato to extract QTL information practical for tomato breeding. This cross corresponded to a four-way cross, because the four parental lines of the two F₁ cultivars were considered to be the founders. We developed 2510 new expressed sequence tag (EST)-based (euchromatin-derived) genomic SSR markers and selected 262 markers from these new SSR markers and publicly available SSR markers to construct a linkage map. QTL analysis for ten agricultural traits of tomato was performed based on the phenotypes and marker genotypes of F₂ plants using a flexible Bayesian method. As results, 13 QTL regions were detected for six traits by the Bayesian method developed in this study.

     

Molecular cloning,sequence and expression analysis of <Emphasis Type="Italic">ZmArf2</Emphasis>, a maize ADP-ribosylation factor

A full-length cDNA encoding a maize GTP-binding protein of the ADP-ribosylation factor family was cloned by suppression subtractive hybridization and an in silico cloning approach. The cDNA was 938 bp in length and contained a complete ORF of 612 bp, which encodes a protein of 203 amino acid residues. Its deduced amino acids sequence had an 83% identity with that of a GTP-binding protein in rice. The gene was designated ZmArf2. The ZmArf2 gene consists of G1, G2, G3, G4 and G5 boxes, and Switch I and Switch II regions. Eight nucleotides differed and five amino acids changed between the popcorn inbred N04 and the dent corn inbred Dan232. One changed amino acid was in the G1 box. RT-PCR analysis showed that ZmArf2 expression increased in the early stages of endosperm development and was not tissue-specific.     

Connected populations for detecting quantitative trait loci and testing for epistasis: an application in maize

Quantitative trait loci (QTL) detection experiments have often been restricted to large biallelic populations. Use of connected multiparental crosses has been proposed to increase the genetic variability addressed and to test for epistatic interactions between QTL and the genetic background. We present here the results of a QTL detection performed on six connected F₂ populations of 150 F_2:3 families each, derived from four maize inbreds and evaluated for three traits of agronomic interest. The QTL detection was carried out by composite interval mapping on each population separately, then on the global design either by taking into account the connections between populations or not. Epistatic interactions between loci and with the genetic background were tested. Taking into account the connections between populations increased the number of QTL detected and the accuracy of QTL position estimates. We detected many epistatic interactions, particularly for grain yield QTL (R ² increase of 9.6%). Use of connections for the QTL detection also allowed a global ranking of alleles at each QTL. Allelic relationships and epistasis both contribute to the lack of consistency for QTL positions observed among populations, in addition to the limited power of the tests. The potential benefit of assembling favorable alleles by marker-assisted selection are discussed.     

Identification of Hordeum spontaneum QTL alleles improving field performance of barley grown under rainfed conditions

Advanced backcross QTL (AB-QTL) analysis was deployed to identify allelic variation in wild barley (Hordeum vulgare ssp. spontaneum) of value in the improvement of grain yield and other agronomically important traits in barley (Hordeum vulgare ssp. vulgare) grown under conditions of water deficit in Mediterranean countries. A population of 123 double haploid (DH) lines obtained from BC₁F₂ plants derived from a cross between Barke (European two-row cultivar) and HOR11508 (wild barley accession) were tested in replicated field trials, under varying conditions of water availability in Italy, Morocco and Tunisia, for seven quantitative traits. Significant QTL effects at one (P 0.001) or more trial sites (P 0.01) were identified for all traits. At 42 (52%) of the 80 putative QTLs identified, the allele increasing a “traits' value” was contributed by H. spontaneum. For example, though the majority (67%) of QTL alleles increasing grain yield were contributed by H. vulgare, H. spontaneum contributed the alleles increasing grain yield at six regions on chromosomes 2H, 3H, 5H and 7H. Among them, two QTLs (associated to Bmac0093 on chromosome 2H and to Bmac0684 on chromosome 5H) were identified in all three locations and had the highest additive effects. The present study shows the validity of deploying AB-QTL analysis for identifying favourable QTL alleles from wild germplasm and indicates its potential as an enhancement strategy for the genetic improvement of cultivars better adapted to drought-prone environments.     

The encapsulated lithium effect on the first hyperpolarizability of C<Subscript>60</Subscript>Cl<Subscript>2</Subscript> and C<Subscript>60</Subscript>F<Subscript>2</Subscript>

In this paper, we report a study on the structure and first hyperpolarizability of C₆₀Cl₂ and C₆₀F₂. The calculation results show that the first hyperpolarizabilities of C₆₀Cl₂ and C₆₀F₂ were 172 au and 249 au, respectively. Compared with the fullerenes, the first hyperpolarizability of C₆₀Cl₂ increased from 0 au to 172 au, while the first hyperpolarizability of C₆₀F₂ increased from 0 au to 249 au. In order to further increase the first hyperpolarizability of C₆₀Cl₂ and C₆₀F₂, Li@C₆₀Cl₂ and Li@C₆₀F₂ were obtained by introducing a lithium atom to C₆₀Cl₂ and C₆₀F₂. The first hyperpolarizabilities of Li@C₆₀Cl₂ and Li@C₆₀F₂ were 2589 au and 985 au, representing a 15-fold and 3.9-fold increase, respectively, over those of C₆₀Cl₂ and C₆₀F₂. The transition energies of four molecules (C₆₀Cl₂, Li@C₆₀Cl₂, C₆₀F₂, Li@C₆₀F₂) were calculated, and were found to be 0.17866 au, 0.05229 au, 0.18385 au, and 0.05212 au, respectively. A two-level model explains why the first hyperpolarizability increases for Li@C₆₀Cl₂ and Li@C₆₀F₂.