MMCC Results

The third source of information on software usage is even smaller, but highly relevant. It is MMCC Results, which is a new, topical newsletter with abstracts of selected articles on molecular modeling.For the two years 1992 and 1993, there were slightly fewer than 2000 articles covered from a wide... 

The third and final source of literature data is MMCC Results. This newsletter covers a broad spectrum of journals, but only a few articles presenting computational chemistry results may be abstracted from each issue of a journal. Articles are apparently selected on the basis of the likely interests of the newsletter s subscribers. 

In contrast to the character string searches that were done on the full articles in the CJACS and CJWILEY databases, a different method of counting was used with MMCC Results. The newsletter usually indicates which of the... 

Of the 2000 articles covered in MMCC Results during 1992 and 1993, one-quarter (496) were cited as mentioning a software vendor. Only 10 vendors received designations in the newsletter. These are shown in Figure 24. The big three vendors, BIOSYM, Tripos, and MSI, each with 150 or more designations. 

Figure 24 Total number of times software vendors have been cited in MMCC Results during 1992 and 1993, the first two years of the newsletter s publication.

Figure 25 Number of times the three most frequently cited software vendors have appeared in MMCC Results in 1992 and in 1993.

How many articles involving computational chemistry are being published each year in all journals In Figure 2 we saw that more than 2000 articles pertaining to computational chemistry were published in CJACS journals in 1993. Based on the articles covered in MMCC Results in 1993, only about 30% of these 2000 published reports appeared in journals of the American Chemical Society. Thus for all journals in toto, it can be roughly estimated that more than 6000 articles were published in 1993 that pertained in some way to computational chemistry. This total is thought to be an upper estimate because papers that mention more than one program would be counted more than once. 

One of the most thorough ways of retrieving data from the literature is through searching databases of full articles. We find, from a detailed analysis of CAS s CJACS database, year-by-year increases in mention of many computational chemistry programs. Because of the sheer size of CJACS (145,001 articles), we expect it to be quite representative of the chemical literature as a whole. In addition, we have shown corroborative data from CAS s CJWILEY database and from the MMCC Results newsletter. 

The purpose of the present paper is to review the most essential elements of the excited-state MMCC theory and various approximate methods that result from it, including the aforementioned CR-EOMCCSD(T) [49,51,52,59] and externally corrected MMCC ]47-50, 52] approaches. In the discussion of approximate methods, we focus on the MMCC corrections to EOMCCSD energies due to triple excitations, since these corrections lead to the most practical computational schemes. Although some of the excited-state MMCC methods have already been described in our earlier reviews [49, 50, 52], it is important that we update our earlier work by the highly promising new developments that have not been mentioned before. For example, since the last review ]52], we have successfully extended the CR-EOMCCSD(T) methods to excited states of radicals and other open-shell systems ]59]. We have also developed a new type of the externally cor-... 

Equation (50) (or its CCSD/EOMCCSD-based analog, Eq. (53)) defines the exact MMCC formalism for ground and excited states. This equation allows us to improve the CC/EOMCC (e.g. CCSD/EOMCCSD) results, in a state-selective manner, by adding the noniterative corrections (in practice, one of the approximate forms of or obtained using the... 

We limit our discussion to the low-order MMCC(myi, ms) schemes with ruA = 2 and niB =, which can be used to correct the results of the CCSD/EOMCCSD calculations for the effects of triple excitations (for the description of the MMCC(2,4) and other higher-order MMCC mA,mB) methods, see Refs. [48-50,52,61-63,72]). The MMCC(2,3) energy expression is as follows [47-52,61-63, 72] ... 

In the specific case of the Cl-corrected MMCC(2,3) approach, very good results are obtained when the wave function in Eq. (67) is replaced by the wave function obtained in the active-space CISDt calculations, which... 

TABLE 2. A comparison of the MMCC(2,3)/CI, MMCC(2,3)/PT, CR-EOMCCSD(T), and CR-EOMCCSD(T) jj, vertical excitation energies of the CH+ ion, as described by the [5s3pld/3slp] basis set of Olsen et al. [103], at the equilibrium geometry, with the exact, full Cl, data and other CC results. ... 

Figure 2. Potential energy curves for the CH+ ion (energies in hartree and the C-H distance in bohr see Refs. [44,47] for the EOMCCSD and MMCC(2,3)/CI data see Refs. [45,103] for the full Cl data). The results include the ground state and the two lowest excited states of the symmetry (the full Cl curves are indicated by the dotted lines and other results are represented by ), the lowest two fl states (the full Cl curves are indicated by the dashed-dotted lines and other results are represented by 0)> the lowest state (the fuU Cl curve is indicated by the dashed hne and other results are indicated by A), (a) A comparison of the EOMCCSD and full Cl results, (b) A comparison of the CISDt and full Cl results, (c) A comparison of the MMCC(2,3)/CI and fuU Cl results. 

As shown in Table 2, the inexpensive MMCC(2,3)/CI approach is capable of providing the results of full EOMCCSDT quality. Indeed, the errors in the vertical excitation energies for the 2 S+, 1 A, 2 A, and 2 states of CH+ that have large double excitation components, obtained with the noniterative MMCC(2,3)/CI approximation, are 0.006-0.105 eV. This should be compared to the 0.327-0.924 eV errors in the EOMCCSD results, the 0.219-0.318 eV errors obtained with the CC3 method, and the 0.504-0.882 eV errors obtained with the CISDt approach used to construct wave functions T ) for the MMCC(2,3)/CI calculations [47,48]. For the remaining states shown in Table 2 (the third and fourth states and the lowest-energy state), the errors in the CISDt-corrected MMCC(2,3) results, relative to full Cl, are 0.000-0.015 eV. Again, the only standard EOMCC method that can compete with the MMCC(2,3)/CI approach is the expensive full EOMCCSDT approximation. 

In the specific case of the MMCC(2,3)/PT approximation, we go one step further and, after rewriting each I l p), Eq. (89), in the form of the Cl expansion relative to the reference determinant ) used in the CCSD and EOMCCSD calculations whose results we want to improve. 

As shown in Table 2, the inexpensive MMCC(2,3)/PT approach is capable of providing the results which are practically as good as the excellent MMCC(2,3)/CI results. In the case of the 2 S+ and 1 states, which have a strong double excitation character, causing the EOMCCSD approach to fail, the MMCC(2,3)/PT corrections to CCSD/EOMCCSD energies produce the results of the EOMCCSDT quality, reducing the 0.560 and 0.924 eV errors in the EOMCCSD results to 0.102 and 0.090 eV, respectively. For these two states, the errors relative to full Cl obtained with the noniterative MMCC(2,3)/PT approach are 2-3 times smaller than the errors obtained with the much more expensive and iterative CC3 method. For states such as 2 n, which have a partially biexcited character, and for states dominated by single excitations (3 1 11), the MMCC(2,3)/PT results are as... 

The CR-EOMCCSD(T) sf method is currently under development, so that we cannot show too many examples of the actual applications yet. However, we have already tested the CR-EOMCCSD(T) approach using the electronic excitations in the CH+ ion as an example. The CR-EOMCCSD(T)j > results for the three lowest-energy excited states of the symmetry and two lowest-energy states of the H and symmetries, obtained at the equilibrium geometry Rc-h = Re = 2.13713 bohr and the same [5s3pld/3slp] basis set of Ref. [103] as used in the MMCC(2,3)/CI, MMCC(2,3)/PT, and CR-EOMCCSD(T) calculations discussed in Section 3.1, are shown in Table 2. As one can see, the CR-EOMCCSD(T) 5f approach is as effective in improving the EOMCCSD results as the CR-EOMCCSD(T) method analyzed in Section 3.1.2. This is particularly true for the 2 1 A, and 2 A states that are dominated by double exci-... 

EOMCCSD energies, is very encouraging. However, we have to perform a larger number of calculations to see if CR-EOMCCSD(T) offers the same level of consistency in applications involving singly and doubly excited states as other MMCC approximations. The results of our findings will be reported elsewhere [79]. 

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