Although not as accurate by themselves as STOs, combinations of many Gaussians can attain the accuracy of hydrogen-like orbitals.

Although the resulting energy eigenfunctions ( the orbitals ) are not necessarily isotropic themselves, their dependence on the angular coordinates follows completely generally from this isotropy of the underlying potential: the eigenstates of the Hamiltonian ( that is, the energy eigenstates ) can be chosen as simultaneous eigenstates of the angular momentum operator.

Although Richard Feynman noted that a simplistic interpretation of the relativistic Dirac equation runs into problems with electron orbitals at Z > 1 / α = 137, suggesting that neutral atoms cannot exist beyond untriseptium, and that a periodic table of elements based on electron orbitals therefore breaks down at this point, a more rigorous analysis calculates the limit to be Z ≈ 173, but also that this limit would not actually spell the end of the periodic table.

Although in MO theory some molecular orbitals may hold electrons that are more localized between specific pairs of molecular atoms, other orbitals may hold electrons that are spread more uniformly over the molecule.

Although he questions the extent and nature of the alleged revival of religion and the alleged increase in conformity, and thinks that `` hedonistic '' present-time orientation does not have the meaning usually attributed to it, he does conclude that Americans increasingly enjoy leisure without guilt, do not stress achievement so much as formerly, are more accepting of group harmony as a goal, more tolerant of diversity and aware of other cultures.

Although the false glamour surrounding bourbon or other whisky commercials is possibly no more fatuous than the pseudo-sophistication with which TV soft-drinks are downed or toothpaste applied, there is a sad difference between enticing a viewer into sipping Oopsie-Cola and gulling him into downing bourbon.

Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.

Although today's trucks are as fast as passenger cars, a truck driver has to be a sensible person and guard against hogging the road.

Although they are forbidden to sit with the customers, the dancers are sometimes proffered drinks, and most of them can bolt one down in mid-shimmy.

Although there are many sound reasons for adopting uniform and coordinated fiscal years in Rhode Island, there are also certain difficulties encountered.

Although the site may not contain the features themselves, there are often opportunities to include them as additional interest to the site.

Although the play does show a certain structural amateurishness ( there are eleven acts varying in length from twenty-five seconds to an hour and a half ), the statement it makes concerning the ceaseless yearning and searching of youth is profound and worthy of our attention.

Although there is no question but that the process of washing fabrics involves a number of phenomena which are related together in an extremely complicated way and that these phenomena and their interrelations are not well understood at the present, this section attempts to present briefly an up-to-date picture of the physical chemistry of washing either fabrics or hard surfaces.

Although the standard deviation values on which spread of the lines is based are relatively larger for those centers which begin to ossify early ( Table 1 ), there are considerable differences in this value between centers having the closely timed Onsets.

Although in both emotions sympathetic symptoms are present, different autonomic-somatic patterns underlie aggression and anxiety, respectively, as indicated by the rate of the excretion of the catecholamines, the state of the muscle tone, and the Mecholyl test.

Although we are still far from a complete understanding of these problems, as a first approximation, it is suggested that alterations in the hypothalamic balance with consequent changes in the hypothalamic-cortical discharges account for major changes in behavior seen in various moods and states of emotions in man and beast under physiological circumstances, in experimental and clinical neurosis, and as the result of psychopharmacological agents.

Although the inner functions of religion are not of direct significance in social organization, they have important indirect consequences.

Although the Brandywine population is still predominantly rural, `` there are indications of a consistent and a statistically significant trend away from the older and relatively isolated rural communities.

Although science has given us more effective materials, preparations from anise, castorbean, colchicum, nux vomica, mustard, fennel, and stramonium are familiar to many for the relief of human ailments.

Although the Administration's program cut crop acreage to the lowest point since 1934, farmers, with the help of extra fertilizer and good weather, are getting such high yields per acre that many are being forced to buy new harvesting machines.

Although progress has been made in America's system of libraries it still falls short of what is required if we are to maintain the standards that are needed for an informed America.

Although the theological forms of the past continue to exist in a way they do not in a more secularized situation, the striking thing is the rapidity with which they are being reduced to a marginal existence.

Although there are landscapes in the show ( one of the strongest is a vista of `` Gloucester Harbor '' in 1915 ), the human element was the compelling factor in Sloan's art.

Although this kind of wholesale objection came at first from some men who were not technically Puritans, still, once the Puritans gained power, they climaxed the affair by passing the infamous ordinance of 1642 which decreed that all `` public stage-plays shall cease and be forborne ''.

Although the wood has been changed to coal, much of it still retains its original cell structure.

`` Although it is not the best of which he is capable '', said Shelley as he closed the book, `` it is still poetry of a high order ''.

Although Andrena is gregarious, so that we may find hundreds and hundreds of burrows together, we must still call it a solitary bee.

Although still aware of a great light and glow of warmth in the Book, I stood outside shivering in the cold.

Although he still didn't speak to anyone, he grew fond of saying, `` The future lies in Asia '', when the opportunity arose, and when he graduated from high school his parents sent him to New York to give him a foundation, they said, for his life in Asian studies.

Although blind students have benefited from talking calculators, the abacus is still very often taught to these students in early grades, both in public schools and state schools for the blind.

Although they are often considered to be weeds in gardens, this viewpoint is not always necessary, as most of them die when the soil temperature warms up again in early to late spring when other plants are still dormant and have not yet leafed out.

Although much of Inge's principles, above, still apply to the New Agrarianism, the affiliation with a particular religion and patriarchal tendency have subsided to some degree.

Although the sign still exists, the " of " has now been replaced by the URL of their website.

Although this classification was widely accepted, further infrageneric classification was ( and still is ) needed to differentiate this widely diverse group.

Although living in Misenum, she was still very popular, powerful and influential.

Although many other chemists have repeated this advice, IUPAC and most chemistry texts still favour the usage of allotrope and allotropy for elements only.

Although Amalric still had a peace treaty with Shawar, Shawar was accused of attempting to ally with Nur ad-Din, and Amalric invaded.

Although still actively involved in running his many businesses, Carnegie had become a regular contributor to numerous magazines, most notably the Nineteenth Century, under the editorship of James Knowles, and the influential North American Review, led by editor Lloyd Bryce.

Although this produced a mode 7 that barely impacted upon CPU performance and gave the same visual quality as the BBC Micro, it remained compatible only with software that used the ROM routines for outputting text and graphics and still used 10 kB of memory for the display.

Although the Falcons selected many good players in those drafts, they still were not able to win right away.

The logo was redesigned with red and silver accents to depict a more powerful, aggressive falcon, which now more closely resembles the capital letter F. Although the Falcons still wore black helmets, the new uniforms featured jerseys and pants with red trim down the sides.

Although every Major League Baseball team cultivates fans from outside its immediate metropolitan area, and even though the greater Phoenix area has 2 / 3 of the statewide population, Colangelo still decided to call the team the " Arizona Diamondbacks " rather than the " Phoenix Diamondbacks ".

Although there has been considerable revision of this phylum ( the order Haemosporidia now has 17 genera rather than 9 ) it seems likely these numbers are still approximately correct.

Although modern analytical chemistry is dominated by sophisticated instrumentation, the roots of analytical chemistry and some of the principles used in modern instruments are from traditional techniques many of which are still used today.